Mathematics One-Liner PDF
Stage-01
Q1: In a library, 2/5 of the total books are Hadith books. Three fourths (3/4) of the remaining books are Mathematics books. The 642 books remaining are on other subjects. Find the total number of books in the library?
Solution:
Let total books = x
Hadith books = 2/5 × x → Remaining books = x – 2/5 x = 3/5 x
Mathematics books = 3/4 of remaining = 3/4 × 3/5 x = 9/20 x
Books of other subjects = Remaining – Mathematics = 3/5 x – 9/20 x = (12/20 x – 9/20 x) = 3/20 x
We are given 642 books are of other subjects → 3/20 x = 642 → x = 642 × 20 / 3 = 4280
Answer: 4280
Q2: The sum of all the exterior angles in a polygon is equal to ___?
Solution:
The sum of all exterior angles of any polygon is always 360°, independent of the number of sides.
Answer: 360°
Q3: If y = 3, then y³(y³ – y) = _____?
Solution:
y³ = 3³ = 27
y³ – y = 27 – 3 = 24
y³(y³ – y) = 27 × 24 = 648
Answer: 648
Q4: Hexagon has six sides and _____ angles.
Solution:
Number of sides of hexagon = 6 → Number of angles = 6
Answer: 6
Q5: If the sum of two angles is 180°, they are called?
Solution:
Two angles whose sum is 180° are called supplementary angles.
Answer: Supplementary angle
Q6: What is the prime factorization of 16?
Solution:
16 = 2 × 2 × 2 × 2
Answer: 2 × 2 × 2 × 2
Q7: Find x, if log₁₂(12³) = x?
Solution:
log₁₂(12³) = 3 × log₁₂12 = 3 × 1 = 3
Answer: 3
Q8: If an alloy contains copper and silver in the ratio 3:7, then the percentage quantity of silver to the alloy is?
Solution:
Total parts = 3 + 7 = 10
Percentage of silver = (7/10) × 100 = 70%
Answer: 70%
Q9: There were 600 students in a school. Each offered either English or Hindi or both. If 75% offered English and 45% Hindi, how many offered both?
Solution:
Students offered English = 75% of 600 = 0.75 × 600 = 450
Students offered Hindi = 45% of 600 = 0.45 × 600 = 270
Let x = students offered both → 450 + 270 – x = 600 → 720 – x = 600 → x = 120
Answer: 120
Q10: The sum of the two numbers is 28 and their difference is 4. Find the numbers.
Solution:
Let the numbers be a and b → a + b = 28, a – b = 4
Add both equations: 2a = 32 → a = 16
b = 28 – 16 = 12
Answer: 16, 12
Q11:1 Kg is equal to how many grams?
Solution:
1 kilogram = 1000 grams
Answer: 1000 grams
Q12: Mean value theorem is applied to _____ functions.
Solution:
The Mean Value Theorem is applied to functions that are continuous on a closed interval [a, b] and differentiable on the open interval (a, b).
Answer: Continuous and Differentiable
Q13: The average (arithmetic mean) of 5, 10, 15 and x is 20. What is the value of x?
Solution:
Average = (5 + 10 + 15 + x)/4 = 20
30 + x = 80 → x = 50
Answer: 50
Q14: Find the value of x in the proportion 2 : 7 :: 14 : x?
Solution:
2/7 = 14/x → x = 14 × 7 / 2 = 49
Answer: 49
Q15: Sum of the interior angles of a polygon = _____?
Solution:
Sum of interior angles = 180(n – 2), where n = number of sides of the polygon
Answer: 180(n – 2)
Q16: The area of a rectangle garden is 96 m². If its width is 3 m, find its length?
Solution:
Area = length × width → length = Area / width = 96 / 3 = 32 m
Answer: 32 m
Q17: Which one of the following is not a prime number?
Solution:
91 = 7 × 13 → not prime
Answer: 91
Q18: What is a formula of perimeter of rectangle?
Solution:
Perimeter = 2 × (length + width)
Answer: 2(length + width)
Q19: A bag contains 50 paisa, 1 rupee and 2 rupee coins in the ratio 2:5:8. If the total amount is Rs. 352, find the total number of coins in the bag?
Solution:
Let the number of parts = 2 + 5 + 8 = 15 parts
Value of one part = Total amount / total value units
Total coins = 2x + 5x + 8x = 15x → amount calculation gives total coins = 240
Answer: 240
Q20: 625 decreased by 12% is _____?
Solution:
Decrease = 12% of 625 = 0.12 × 625 = 75
New value = 625 – 75 = 550
Answer: 550
Q21: What is the sum of all angles in a triangle?
Solution:
Sum of angles of a triangle = 180°
Answer: 180°
Q22: If 3 men or 4 women can construct a wall in 43 days, then the number of days that 7 men and 5 women take to construct it is?
Solution:
4 women = 3 men → 1 woman = 3/4 men → 5 women = 15/4 men
Total workforce = 7 + 15/4 = 43/4 men
Work done by 3 men in 43 days = 3 × 43 = 129 man-days
Time taken by 43/4 men = 129 ÷ (43/4) = 129 × 4 / 43 = 12 days
Answer: 12 days
Q23: The mean proportional between 64 and 81 is?
Solution:
Mean proportional = √(64 × 81) = √5184 = 72
Answer: 72
Q24: The sum of the measures of all angles in a pie graph is _____?
Solution:
A pie graph represents a circle → sum of angles = 360°
Answer: 360°
Q25: The sum of ages of 5 children born at the intervals of 3 years each is 50 years. What is the age of the youngest child?
Solution:
Let youngest = x → Ages = x, x+3, x+6, x+9, x+12
Sum = x + x+3 + x+6 + x+9 + x+12 = 5x + 30 = 50 → 5x = 20 → x = 4
Answer: 4 years
Q26: A car travels at a speed of 65 miles per hour. How far will it travel in 5 hours?
Solution:
Distance = speed × time = 65 × 5 = 325 miles
Answer: 325 miles
Q27: Which of the following pair of prime numbers are twin prime?
Solution:
Twin primes are prime numbers with difference 2 → 3 and 5
Answer: 3, 5
Q28: Two taps X and Y can fill a tank in 10 hrs. and 15 hours respectively. If both taps are opened together, the tank will be full in?
Solution:
Work done by X in 1 hr = 1/10, Y in 1 hr = 1/15
Combined work = 1/10 + 1/15 = 1/6 → Time = 1 / (1/6) = 6 hours
Answer: 6 hours
Q29: What is the number of surfaces and their types in a square pyramid?
Solution:
Square pyramid → 1 square base + 4 triangular faces → Total = 5 surfaces
Answer: 5 surfaces: 1 square, 4 triangular
Q30: The angle of elevation of the sun, when the length of the shadow of a tree is equal to the height of the tree is?
Solution:
When shadow = height → tan θ = 1 → θ = 45°
Answer: 45 degree
Q31: The ratio of two numbers a and b is 3:5. If 2 is added to both the numbers, the ratio becomes 2:3. Find b?
Solution:
Let numbers be 3x and 5x → (3x + 2) / (5x + 2) = 2 / 3
Cross multiply: 3(3x + 2) = 2(5x + 2) → 9x + 6 = 10x + 4 → x = 2
b = 5x = 5 × 2 = 10
Answer: 10
Q32: If 10 workers can make 10 tables in 10 days, then how many days would it take for 5 workers to make 5 tables?
Solution:
Step 1: Find work done by 1 worker in 1 day
10 workers make 10 tables in 10 days → total work = 10 tables
Work done by 1 worker in 1 day = total work ÷ (number of workers × days)
= 10 ÷ (10 × 10) = 10 ÷ 100 = 0.1 table per day
Step 2: Work done by 5 workers in 1 day
5 workers × 0.1 table/day per worker = 0.5 table per day
Step 3: Time required for 5 workers to make 5 tables
Time = Total work ÷ Work done per day = 5 ÷ 0.5 = 10 days
Answer: 10 days
Q33: In a cuboid, number of vertices are _____?
Solution:
A cuboid has 8 corners → 8 vertices
Answer: 8
Q34: What is the average of first 150 natural numbers?
Solution:
Average = (Sum of first n numbers) / n = [n(n+1)/2] / n = (n+1)/2
n = 150 → Average = (150 + 1)/2 = 151/2 = 75.5
Answer: 75.5
Q35: 1.14 expressed as a percent of 1.9 is?
Solution:
Percent = (1.14 / 1.9) × 100 = 0.6 × 100 = 60%
Answer: 60%
Q36: Ten years ago, A was half of B’s age. If the ratio of their present ages is 3:4, what will be the total of their present ages?
Solution:
Let present ages = 3x and 4x
Ten years ago → 3x – 10 = 1/2 (4x – 10) → 3x – 10 = 2x – 5 → x = 5
Present ages → A = 3x = 15, B = 4x = 20 → Total = 15 + 20 = 35
Answer: 35 years
Q37: In a class of 40 students 20% are girls. How many boys are there in the class?
Solution:
20% of 40 = 8 girls → Boys = 40 – 8 = 32
Answer: 32
Q38: The number of diagonals of a 12 sided figure is _____?
Solution:
Number of diagonals = n(n–3)/2 → 12(12–3)/2 = 12 × 9 /2 = 54
Answer: 54
Q39: What is the average of 12, 15, 18?
Solution:
Average = (12 + 15 + 18)/3 = 45/3 = 15
Answer: 15
Q40: The binary equivalent of decimal 13 is ______?
Solution:
13 ÷ 2 = 6 remainder 1
6 ÷ 2 = 3 remainder 0
3 ÷ 2 = 1 remainder 1
1 ÷ 2 = 0 remainder 1 → Write remainders from bottom to top = 1101
Answer: 1101
Q41: The ratio of ages of two students is 3 : 2. One is older than the other by 5 years. What is the age of the younger student?
Solution:
Let ages = 3x and 2x → 3x – 2x = 5 → x = 5 → Younger = 2x = 10
Answer: 10
Q42: In ______ proportion, one quantity is increased by decreasing the other quantity.
Solution:
If one quantity increases as the other decreases → Inverse proportion
Answer: Inverse
Q43: An 82 cm long and 75 cm wide rectangle is enclosed by a strip outside it that is 4 cm wide. Find the area of the strip?
Solution:
Outer dimensions → Length = 82 + 2×4 = 90, Width = 75 + 2×4 = 83
Outer area = 90 × 83 = 7470
Original area = 82 × 75 = 6150
Strip area = 7470 – 6150 = 1320 cm²
Answer: 1320 cm²
Q44: 20 men can construct a building in 40 days. How long will it take 10 men to do this work?
Solution:
Work = 20 × 40 = 800 man-days
10 men → Time = 800 / 10 = 80 days
Answer: 80 days
Q45: Sum of 4 A.M between 18 and 3 is _____?
Solution:
4 A.M (Arithmetic Means) → Divide interval into 5 equal parts
Step = (3 – 18)/5 = –15/5 = –3
Numbers between 18 and 3 = 18 – 3 = 15 → 4 A.M = 18–3=15 → sequence: 15/5? Let’s calculate:
First term = 18, last = 3, n=6 numbers including 18 and 3
Step = (3–18)/5 = –3 → Numbers between: 15,12,9,6
Sum = 15 + 12 + 9 + 6 = 42
Answer: 42
Q46: There are 100 boys and 900 girls in a school. 50% boys and 40% girls are present. The total number of students present are?
Solution:
Boys present = 50% of 100 = 50
Girls present = 40% of 900 = 360
Total present = 50 + 360 = 410 → Percentage = 410/1000 ×100 = 41%
Answer: 41%
Q47: Ibrahim and Marwa are preparing first aid kits for the students. They have 30 perforated adhesive bandages, 60 triangular bandages and 75 rectangular bandages. They must distribute these equally in the kits, with nothing left over. What is the greatest number of kits they can make this quantity of bandages?
Solution:
Find HCF of 30, 60, 75
Factors: 30=2×3×5, 60=2²×3×5, 75=3×5² → HCF = 3×5=15
Greatest number of kits = 15
Answer: 15
Q48: A fruit seller had some apples. He sells 40% apples and still has 420 apples. Originally, he had _____?
Solution:
Remaining = 60% → 0.6 × Total = 420 → Total = 420 / 0.6 = 700
Answer: 700
Q49: During the school assembly, 96 students are standing in 6 equal rows. How many students are there in 1 row?
Solution:
Number per row = 96 / 6 = 16
Answer: 16
Q50: If the sum of the quantities is 1840 and their average is 115, then find the number of quantities?
Solution:
Average = Sum / Number → Number = Sum / Average = 1840 / 115 = 16
Answer: 16
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Stage-02
Q.51. Which number will complete the number series? 2, 5, 12, 23, 38, 57, _____?
Answer: 80
Solution:
Find the differences: 5–2=3, 12–5=7, 23–12=11, 38–23=15, 57–38=19 → Difference increases by 4 each time. Next difference = 19+4=23 → Next number = 57+23=80
Q.52. What is the ratio of the circumference of a circle to its radius?
Answer: 2π
Solution:
Circumference = 2πr → Circumference / radius = 2πr / r = 2π
Q.53. What number will come next in the series? 1, 2, 4, 8, 16, _____?
Answer: 32
Solution:
Series is multiplying by 2 each time: 1×2=2, 2×2=4, 4×2=8, 8×2=16, 16×2=32
Q.54. Find the odd one out: 10, 25, 45, 54, 60, 75, 80
Answer: 54
Solution:
All numbers except 54 are multiples of 5. 54 is not divisible by 5 → Odd one out
Q.55. What number comes next in the series 34, 24, 16, 10, 6 ?
Answer: 4
Solution:
Find differences: 34–24=10, 24–16=8, 16–10=6, 10–6=4 → Next difference = 2 → Next number = 6–2=4
Q.56. A is father of C, D is son of B, E is brother of A. If C is sister of D, how is B related to E?
Answer: Sister-in-law
Solution:
C is D’s sister → B must be C’s mother/father → E is brother of A → B is married to A → B is sister-in-law of E
Q.57. The angle of elevation of the top of a tower from a point 20 m away from its base is 60°. Find the height of the tower.
Answer: 20√3 m ≈ 34.64 m
Solution:
tan θ = height / distance → tan 60° = h / 20 → √3 = h / 20 → h = 20√3 ≈ 34.64 m
Q.58. My mother is the sister of your brother. What relation am I to you?
Answer: Nephew
Solution:
Your brother’s sister is your mother → You are the child of my aunt → Your relation to me = nephew
Q.59. If 4x + 12 = 36, find x + 3.
Answer: 9
Solution:
4x + 12 = 36 → 4x = 24 → x = 6 → x + 3 = 6 + 3 = 9
Q.60. Two lines that make an angle are called?
Answer: Vertex
Solution:
The point where two lines meet to form an angle is called the vertex
Q.61. 25 is 125% of what number?
Answer: 20
Solution:
125% of number = 25 → 1.25 × number = 25 → number = 25 / 1.25 = 20
Q.62. π (pi) = ?
Answer: 3.14
Solution:
π is the ratio of circumference to diameter → 3.14 approximately
Q.63. Zain is facing North-West. He turns 90° clockwise, then 180° anticlockwise, then 90° clockwise. Which direction is he facing?
Answer: South-East
Solution:
Start facing NW → 90° clockwise → NE → 180° anticlockwise → SW → 90° clockwise → SE (final direction)
Q.64. How many zeros are there in 1 billion?
Answer: 9
Solution:
1 billion = 1,000,000,000 → 9 zeros
Q.65. The perimeter of a square with side 6 cm is?
Answer: 24 cm
Solution:
Perimeter = 4 × side = 4 × 6 = 24 cm
Q.66. What number comes next in the series? 6, 11, 21, 36, 56, ?
Answer: 81
Solution:
Find differences: 11–6=5, 21–11=10, 36–21=15, 56–36=20 → Difference increases by 5 → Next difference =25 → Next number = 56+25=81
Q.67. What is the sum of all angles in a triangle?
Answer: 180°
Solution:
By definition, sum of interior angles of triangle = 180°
Q.68. If a>b, b>c, and d>a then?
Answer: b<d
Solution:
b is less than a, a is less than d → b < d
Q.69. 1 radian is equal to?
Answer: 57.3°
Solution:
1 rad ≈ 57.2958° → Approx 57.3°
Q.70. Formula of area of square?
Answer: side²
Solution:
Area = side × side = a²
Q.71. Right-angled triangle with legs 6 cm and 8 cm, find hypotenuse.
Answer: 10
Solution:
Pythagoras theorem: hypotenuse² = 6² + 8² = 36 + 64 = 100 → hypotenuse = √100 = 10
Q.72. If the sum of two angles is 180°, they are called?
Answer: Supplementary angles
Solution:
By definition, sum = 180° → Supplementary
Q.73. Sum of interior angles of a triangle?
Answer: 180°
Solution:
By formula, sum = 180°
Q.74. There are 12 pens on table, you took 3. How many do you have?
Answer: 3
Solution:
You took 3 → You have 3
Q.75. If the day before yesterday was Saturday, what will be the day after tomorrow?
Answer: Wednesday
Solution:
-
Day before yesterday → Saturday
-
Yesterday → Sunday
-
Today → Monday
-
Tomorrow → Tuesday
-
Day after tomorrow → Wednesday
Q.76. 10% of 20% of 30% equals?
Answer: 0.6%
Solution:
0.1 × 0.2 × 0.3 = 0.006 → 0.6%
Q.77. The average (arithmetic mean) of 5, 10, 15 and x is 20. Find x.
Answer: 50
Solution:
(5+10+15+x)/4 = 20 → 30 + x = 80 → x = 50
Q.78. Average of 13 numbers is 60. Average of first 7 = 57, last 7 = 61. Find 7th number.
Answer: 68
Solution:
Sum of all 13 = 13×60=780
Sum of first 7 = 7×57=399
Sum of last 7 = 7×61=427
7th number = 399 + 427 – 780 = 46 → Wait check: 399+427=826 → 826-780=46 → Yes, 46
Q.79. Value of eccentricity of a circle?
Answer: 0
Solution:
Eccentricity of circle = 0
Q.80. If ROAD is coded as “WTFI”, find code for BEAT.
Answer: GJFY
Solution:
Each letter is shifted forward by 5 in the alphabet.
B + 5 = G, E + 5 = J, A + 5 = F, T + 5 = Y
So, BEAT → GJFY
Q.81. A train 100 m long runs at 30 km/h. Time to pass an 80 m bridge?
Answer: 21.6 sec
Solution:
Speed = 30 km/h = 30×1000/3600 = 8.33 m/s
Distance = 100+80=180 m → Time = 180 / 8.33 ≈ 21.6 sec
Q.82. 72496 → 1315, 62134 → 97, 85316 → 167, find 28439 → ?
Answer:1412
Solution:
Step 1: Split the number into two parts – first three digits and last two digits.
Step 2: Add the digits in each part:
-
72496 → First part 7+2+4 = 13, Second part 9+6 = 15 → Combine → 1315
-
62134 → First part 6+2+1 = 9, Second part 3+4 = 7 → Combine → 97
-
85316 → First part 8+5+3 = 16, Second part 1+6 = 7 → Combine → 167
Step 3: Apply the same logic to 28439:
-
First part 2+8+4 = 14
-
Second part 3+9 = 12
-
Combine → 1412
Final Answer: 1412
Q.83. 20% of 250 = ?
Answer: 50
Solution:
0.2 × 250 = 50
Q.84. SAW : CARPENTER :: Pen : ?
Answer: Writer
Solution:
Saw is tool for carpenter → Pen is tool for writer
Q.85. Complete series: 2, 6, 12, 20, 30, 42, ?
Answer: 56
Solution:
Differences: 6–2=4, 12–6=6, 20–12=8, 30–20=10, 42–30=12 → Next difference = 14 → Next number = 42+14=56
Q.86. For anti-clockwise rotation, direction of angular velocity is?
Answer: Positive
Solution:
By convention, anti-clockwise = positive direction
Q.87. How many millimeters in 1 centimeter?
Answer: 10
Solution:
1 cm = 10 mm
Q.88. Analogy: Book : Reading :: Fork : ?
Answer: Eating
Solution:
Book is used for reading → Fork is used for eating
Q.89. 15% of 400 = ?
Answer: 60
Solution:
0.15 × 400 = 60
Q.90. Next term in 2,4,8,16,?
Answer: 32
Solution:
Multiply by 2 → 16×2=32
Q.91. Sorrow : Death :: Happiness : ?
Answer: Birth
Solution:
Opposite emotions analogy → Sorrow:Death → Happiness:Birth
Q.92. If 1st day of month is Monday, date of 3rd Friday?
Answer: 15
Solution:
1st Friday = 5th, 2nd = 10th, 3rd = 15th → Correct 15
Q.93. If x³=27, find x
Answer: 3
Solution:
x³=27 → x = ∛27 =3
Q.94. If PQ = P+Q+P/Q, then 82 = ?
Answer: 14
Solution:
8*2 = 8+2 + 8/2 = 10+4=14
Q.95. Value of lim 2/x as x→∞
Answer: 0
Solution:
2/x → 0 as x→∞
Q.96. 1 kilometer = ? meters
Answer: 1000
Solution:
By definition, 1 km = 1000 m
Q.97. 1 kilometer = ?
Answer: 1000 meters
Solution:
1 km = 1000 meters
Q.98. Complete series: 2,5,9,?,20,27,35
Answer: 14
Solution:
Differences: 5–2=3, 9–5=4, next difference =5 → Next number = 9+5=14
Q.99. Which is different? Karachi, Kabul, Delhi, Dhaka
Answer: Karachi
Solution:
Karachi is in Pakistan, others are capitals of other countries → Different
Q.100. Find missing letter: A,D,H,M,S, ?
Answer: Z
Solution:
The sequence increases the gap between letters by 1 each time:
A → D (gap +3), D → H (gap +4), H → M (gap +5), M → S (gap +6)
Next gap = +7 → S + 7 = Z
Final Answer: Z
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Stage-03
Q.101. How much 60% of 50 is greater than 40% of 30?
Solution:
60% of 50 = 0.6 × 50 = 30
40% of 30 = 0.4 × 30 = 12
Difference = 30 – 12 = 18
Answer: 18
Q.102. What is the name of a triangle with two sides of equal length?
Solution:
A triangle with two equal sides is called Isosceles.
Answer: Isosceles
Q.103. What equal amount of coins of Rs 5, Rs 2, Rs 1 makes a total of 1152?
Solution:
Let number of each coin = x
Total = 5x + 2x + 1x = 8x = 1152 → x = 1152 ÷ 8 = 144
Answer: 144
Q.104. How many times in a day are the hands of clock in straight line but opposite in direction?
Solution:
Hands are opposite (180°) twice every hour except the 12th hour overlaps → 12 × 2 – 2 = 22 times
Answer: 22
Q.105. If an increase of 30% charged the price of shirt to Rs. 520, then the original price of shirt is _______?
Solution:
Let original price = x
x + 30% of x = 520 → x(1 + 0.3) = 520 → x × 1.3 = 520 → x = 520 ÷ 1.3 = 400
Answer: 400
Q.106. Two automobiles are 75 kilometers apart and travelling towards each other. One at 60 km/h, the other at 40 km/h. In how many minutes will they meet?
Solution:
Relative speed = 60 + 40 = 100 km/h
Time = distance ÷ speed = 75 ÷ 100 = 0.75 hours = 0.75 × 60 = 45 minutes
Answer: 45 minutes
Q.107. What is the length of each side of a square whose area is 576 cm²?
Solution:
Side = √Area = √576 = 24 cm
Answer: 24 cm
Q.108. The sum of the two numbers is 28 and their difference is 4?
Solution:
Let numbers be x and y
x + y = 28, x – y = 4 → Solving: x = 16, y = 12 → Numbers: 16, 12 (smaller first: 12,16)
Answer: 12,16
Q.109. The sum of four consecutive even numbers is 292. What is the smallest number?
Solution:
Let numbers be x, x+2, x+4, x+6
Sum = 4x + 12 = 292 → 4x = 280 → x = 70
Answer: 70
Q.110. In a certain class the ratio of men to women is 3:5. If the class has 24 people in it, how many are women?
Solution:
Total parts = 3+5=8
Each part = 24 ÷ 8 = 3 → Women = 5 × 3 = 15
Answer: 15
Q.111. Insert the missing number: 14, 9, 5, 21, 8, 13, 28, 9, _____?
Solution:
Pattern alternates subtraction and addition: 14–5=9, 9–4=5, 5+16=21, 21–13=8, 8+5=13, 13+15=28, 28–19=9 → Next = 9+9 = 18
Answer: 18
Q.112. The angle of elevation of a ladder leaning against a wall is 60° and the foot of the ladder is 4.6 m away from the wall. Find the length of the ladder.
Solution:
Ladder = hypotenuse, base = 4.6 m, angle = 60°
cos 60° = base / hypotenuse → 0.5 = 4.6 / L → L = 4.6 ÷ 0.5 = 9.2 m
Answer: 9.2 m
Q.113. Find the missing term in the given pattern: H38, K33, N28, ____?, T18.
Solution:
Letters H→K→N→Q→T (skip 2 each time), Numbers: 38→33→28→23→18
Answer: Q23
Q.114. If 6 men can make 10 sofas in 2 days, then 8 men can make 8 sofas in ______?
Solution
Step 1: Calculate total man-days for the initial work:
6 men × 2 days = 12 man-days to make 10 sofas
Step 2: Man-days required per sofa:
12 ÷ 10 = 1.2 man-days per sofa
Step 3: Total man-days for 8 sofas:
8 × 1.2 = 9.6 man-days
Step 4: Time required for 8 men:
9.6 ÷ 8 = 1.2 days
Answer: 1.2 days
Q.115. If √n/3 is an even integer, which of the following could be the value of n?
Solution:
Let √n / 3 = 2 → √n = 6 → n = 36 (even integer)
Check options: 144 → √144/3 = 12/3=4 → even integer → correct
Answer: 144
Q.116. Complete the series: 4, 8, 9, 13, 14, 18, _____?
Solution:
Pattern: +4, +1, +4, +1, +4 → Last term: 18+1=19
Answer: 19
Q.117. Which one of the following options is suitable to fill the blank? SCD, TEF, UGH, _____, WKL.
Solution:
Answer: VIJ
Solution:
First letters go S → T → U → V → W.
The next two letters form pairs: CD → EF → GH → IJ → KL.
Combine V + IJ → VIJ.
Q.118. Which one of the following is least like the other three? Football, Baseball, Golf, Billiard
Solution:
All are outdoor sports except Billiard
Answer: Billiard
Q.119. If the sum of two numbers is 16 and their product is 63. Then the smaller number is ______?
Solution:
Let numbers x and y → x + y = 16, xy = 63
x² – 16x + 63=0 → x=7, y=9 → Smaller =7
Answer: 7
Q.120. Some months have 31 days, how many have 30?
Solution:
4 months have 30 days: April, June, September, November
Answer: 4
Q.121. What is the probability of getting one Head and one Tail when a coin is tossed twice?
Solution:
Sample space = {HH, HT, TH, TT} → favorable outcomes = {HT, TH} → Probability = 2/4 = 1/2
Answer: 1/2
Q.122. The sum of first 10 natural numbers is equal to ____?
Solution:
Sum = n(n+1)/2 = 10×11/2 = 55
Answer: 55
Q.123. The average of first 10 even numbers is _______?
Solution:
First 10 even numbers = 2,4,6,…,20 → Sum = 2+4+…+20 = 110 → Average = 110 ÷ 10 = 11
Answer: 11
Q.124. If GOAL is coded as LTFQ, then what is the code for BEAT?
Solution:
Each letter shifted +7 positions: B+7=G, E+7= L → Follow same → BEAT = GJFY
Answer: GJFY
Q.125. What is the Arithmetic Mean of the following data 3, 6, 9, 12, 15?
Solution:
Sum = 3+6+9+12+15=45 → Number of terms=5 → Mean = 45/5 = 9
Answer: 9
Q.126. 60% of a number is added to 120, the result is the same number. Find the number?
Solution:
Let number = x → x = 0.6x + 120 → x – 0.6x = 120 → 0.4x = 120 → x = 120/0.4 = 300
Answer: 300
Q.127. If you arrange the letters “BARBIT”, you would have the name of a(n) ______?
Solution:
Rearranging letters → Animal = Rabbit
Answer: Anima
Q.128. Find the number of triangles which can be formed by joining the angular points of a polygon of 8 sides.
Solution:
Formula = nC3 = 8C3 = 8×7×6/6=56
Answer: 56
Q.129. Complete the number series: 1, 6, 13, 22, 33, ______?
Solution:
Differences: 5,7,9,11 → Next difference =13 → 33+13=46
Answer: 46
Q.130.Arrange the words in a meaningful sentence: 1. Key 2. Door 3. Lock 4. Room 5. Switch on
Answer: 1, 3, 2, 4, 5
Solution:
Step 1: Key – you need the key to start.
Step 2: Lock – insert the key into the lock.
Step 3: Door – open the door after unlocking.
Step 4: Room – enter the room.
Step 5: Switch on – finally, switch on the light.
Q.131. If A={1,2,3,4,5} and B={1,2,5,9}, which is true?
Solution:
Common elements = 1,2,5 → Sets are overlapping
Answer: A and B are overlapping
Q.132. If 28 men can finish a work in 15 days, 21 men can finish the same work in ______?
Solution:
Work = 28×15 = 420 man-days → 21 men → Days = 420/21 = 20 days
Answer: 20 days
Q.133. After decreasing 24% the price of an article costs Rs. 912. Find the actual cost of the article.
Solution:
Let original price = x → x – 24% of x = 912 → 0.76x = 912 → x = 912/0.76 = 1200
Answer: 1200
Q.134. Today is Maryam’s birthday. After one year, she will become two times as she was ten years ago. What is the current age of Maryam?
Solution:
Let age = x → x +1 = 2(x – 10) → x +1 = 2x –20 → 2x – x = 21 → x = 21
Answer: 21
Q.135. The sum of ages of 5 children born at the intervals of 3 years each is 50 years. What is the age of the youngest child?
Solution:
Let youngest = x → x + x+3 + x+6 + x+9 + x+12 = 50 → 5x+30=50 → 5x=20 → x=4
Answer: 4 years
Q.136. Find the missing letter: Group 1 = B, E, H Group 2 = M, O, Q Group 3 = R, _____, T.
Solution:
Middle letter = S (pattern moves forward 3,2,2 etc)
Answer: S
Q.137. The total sum of all sides of a closed surface is called?
Solution:
The perimeter of a closed figure is the sum of its sides.
Answer: Perimeter
Q.138. If a/2 + 4 = 7/2, then a = ______?
Solution:
a/2 +4 = 7/2 → a/2 = 7/2 – 8/2 = –1/2 → a = –1
Answer: –1
Q.139. Visitors were charged Rs. 15 each on the first day, Rs. 7.50 on the second day and Rs. 2.50 on the third day. Total attendance ratio = 2:5:13. Find average charge per person.
Solution:
Let number of visitors = 2x,5x,13x → Total visitors = 20x
Total charge = 2x15 +5x7.5 +13x*2.5 = 30x+37.5x+32.5x=100x → Average = 100x/20x=5
Answer: Rs. 5.00
Q.140. If 10 workers can make 10 tables in 10 days, then how many days would it take for 5 workers to make 5 tables?
Solution:
Work = 10×10=100 worker-days → 5 workers → 100/5=20 days for 10 tables → For 5 tables = 10 days
Answer: 10
Q.141. There are 12 pens on the table, you took 3. How many do you have?
Solution:
You took 3 pens → You have 3
Answer: 3
Q.142. 25% of 30% of 45% is equal to _____?
Solution:
0.25 × 0.30 × 0.45 = 0.03375
Answer: 0.03375
Q.143. If A and B are in the ratio 3:4 and B and C are in the ratio 12:13, then A and C will be in the ratio ______?
Solution:
A:B = 3:4, B:C=12:13 → Scale B: multiply A:B by 3 → A:C=9:13
Answer: 9:13
Q.144. Co-ordinates of origin are _______?
Solution:
Origin = (0,0)
Answer: (0,0)
Q.145. What is 45% of 300?
Solution:
45% of 300 = 0.45×300=135
Answer: 135
Q.146. The ratio of the length of a rod and its shadow is 1:√3. The angle of elevation of the sun is _____?
Solution:
tan θ = height/length of shadow = 1/√3 → θ = 30°
Answer: 30°
Q.147. 1 acre is equal to ______ square foot.
Solution:
1 acre = 43560 sq. ft
Answer: 43560 sq. ft
Q.148. 85% of a number is added to 24, the result is the same number. Find the number?
Solution:
Let number = x → 0.85x + 24 = x → 0.15x = 24 → x = 24/0.15 = 160
Answer: 160
Q.149. An angle measuring less than 90 degree is called?
Solution:
Angle < 90° = Acute angle
Answer: Acute angle
Q.150. In how many ways 2 students can be chosen from the class of 20 students?
Solution:
20C2 = 20×19/2=190
Answer: 190
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Q.151. A man has 42 blue socks, 15 red socks, 24 black socks in one box. It is totally dark and he cannot recognize the colors. How many socks does he have to take out of the box to be sure to have at least two black socks?
Answer: 59
Solution:
Worst case, he picks all blue and red socks first: 42 + 15 = 59.
To get at least 2 black socks, he needs 42 + 15 + 2 = 59 socks.
Q.152. At a conference, 10 members shook hands with each other before the meeting. How many handshakes occurred?
Answer: 45
Solution:
Number of handshakes = n(n-1)/2 = 10×9/2 = 45.
Q.153. If x/4 = y/2, then?
Answer: x = 2y
Solution: Multiply both sides by 4: x = 2y.
Q.154. 50 miles is equal to how many kilometers?
Answer: 80 km
Solution: 1 mile ≈ 1.6 km → 50×1.6 = 80 km.
Q.155. A drink contains 20% mango juice and the rest is apple juice. What is the ratio of mango juice to apple juice?
Answer: 1:4
Solution: Mango juice = 20%, Apple juice = 80% → Ratio = 20:80 = 1:4.
Q.156. How many zeros are there in 1 billion?
Answer: 9
Solution: 1 billion = 1,000,000,000 → 9 zeros.
Q.157. The day after the day after tomorrow is four days before Monday. What day is it today?
Answer: Tuesday
Solution:” Four days before Monday” is Thursday. That day is the day after the day after tomorrow. So, if the day after the day after tomorrow is Thursday, today must be Tuesday.
Q.158. What is the smallest number of ducks that could swim in this formation: two ducks in front of a duck, two ducks behind a duck, and a duck between two ducks?
Answer: 3
Solution: Place 3 ducks: middle duck has 2 in front and 2 behind in the formation → minimum 3 ducks.
Q.159. Aslam has 1.5 times as many as Akram, and Akram has 1.5 times as many as Abdul. Altogether they have 76. How many does each have?
Answer: Aslam 36, Akram 24, Abdul 16
Solution: Let Abdul = x → Akram = 1.5x, Aslam = 1.5×1.5x = 2.25x → x + 1.5x + 2.25x = 76 → 4.75x = 76 → x = 16 → Akram = 24, Aslam = 36.
Q.160. Which of the following can be arranged into a 5-letter English word: H R G S T, R I L S A, T O O M B D, W Q R G S?
Answer: R I L S A → ARILS
Solution: Letters R I L S A can form the word ARILS.
Q.161. PEACH is to HCAEP. The number 26541 should be?
Answer: 14562
Solution: Number order follows reverse of letters. PEACH → HCAEP → 2→1 becomes 1→4→5→6→2 = 14562.
Q.162. If 3z/2 + 4z/2 + 5z/2 = 36, what is the value of z?
Answer: 6
Solution: Sum = (3+4+5)z/2 = 12z/2 = 6z → 6z = 36 → z = 6.
Q.163. Find the missing letter: A, D, H, M, S, ____?
Answer: Z
Solution: Differences in alphabet positions: A→D (+3), D→H (+4), H→M (+5), M→S (+6), next = S +7 → Z.
Q.164. If the length of a square-shaped crop field is 31 meters, what will be its perimeter?
Answer: 124 meters
Solution: Perimeter = 4×side = 4×31 = 124 meters.
Q.165. A person washes 8 cars in 18 minutes. At this rate, how many cars can he wash in 3 hours?
Answer: 80
Solution: 3 hours = 180 minutes. Rate = 8/18 cars per min → Cars in 180 min = 8/18×180 = 80 cars.
Q.166. There are 100 boys and 900 girls in a school. 50% of boys and 40% of girls are present. Total number of students present?
Answer: 410
Solution: Boys present = 50% of 100 = 50, Girls present = 40% of 900 = 360 → Total = 50+360 = 410.
Q.167. My mother is the sister of your brother. What relation am I to you?
Answer: Nephew
Solution: Mother is sister of your brother → You are her nephew.
Q.168. 25 is 125% of what number?
Answer: 20
Solution: 125% of x = 25 → x = 25×100/125 = 20.
Q.169. What is the total cost if a Rs. 40 item is taxed at 5%?
Answer: 42
Solution: Tax = 5% of 40 = 2 → Total cost = 40+2=42.
Q.170. The average of first 10 odd numbers is?
Answer: 10
Solution: First 10 odd numbers: 1,3,5,…,19 → Sum = 100 → Average = 100/10 = 10.
Q.171. CAACCAC is to 3113313 as CACAACAC is to?
Answer: 31311313
Solution: C=3, A=1, map each letter accordingly.
Q.172. If a right-angled triangle has legs of length 6 cm and 8 cm, the hypotenuse?
Answer: 10 cm
Solution: Hypotenuse² = 6²+8² = 36+64=100 → Hypotenuse = √100=10.
Q.173. Milk is to glass as letter is to?
Answer: Envelope
Solution: Letter is contained in envelope like milk in glass.
Q.174. X and Y are children of Z. Z is father of X, but Y is not son of Z. What is Y to Z?
Answer: Daughter
Solution: Z is father of X. Y is not son → Y is daughter.
Q.175. Which of the following is closest to 29.8 × 9.8?
Answer: 300
Solution: Approximate 29.8≈30, 9.8≈10 → 30×10=300.
Q.176. In-order traversal of tree E A C K F H D B G, preorder traversal?
Answer: FAEKCDHGB
Solution: Apply preorder traversal rules on the tree.
Q.177. How many distinct arrangements can be made from the letters of “BOOK”?
Answer: 12
Solution: BOOK → 4 letters, O repeats twice → 4!/2! = 12 arrangements.
Q.178. Three students X, Y, Z in a 100m race. X faster than Y, Z faster than X → Who wins?
Answer: Z wins
Solution: Z > X > Y → Z wins.
Q.179. Insert the missing letter: D, K, G, N, ____ Q, M, T.
Answer: J
Solution: Pattern alternates between letters → J fits the missing position.
Q.180. If a doctor gives 3 pills to take one every half hour, how long until all are taken?
Answer: 1 hour
Solution: Take first pill at 0 min, second at 30 min, third at 60 min → Total 1 hour.
Q.181. Average of 4 consecutive odd numbers is 24. Largest number?
Answer: 27
Solution: Let numbers = n, n+2, n+4, n+6 → Average = (4n+12)/4= n+3=24 → n=21 → Numbers = 21,23,25,27 → Largest = 27.
Q.182. A box has 6 black, 4 red, 2 white, 3 blue shirts. Probability of picking at least 1 red in 4 shirts?
Solution: Total shirts = 15. Non-red shirts = 11.
Ways to pick 4 non-red shirts = 11C4 = 330
Total ways to pick 4 shirts = 15C4 = 1365
Probability of at least 1 red = 1 – (330 / 1365) = 1035 / 1365 = 69/91
Answer: 69/91
Q.183. Shahid taller than Usman, Ali shorter than Shahid. Which statement is accurate?
Answer: It is impossible to tell whether Ali or Usman is taller.
Solution: No info about Usman vs Ali.
Q.184. Complete the series: 4, 9, 16, 25, _____?
Answer: 36
Solution: Series of squares: 2²,3²,4²,5²,6² → Next = 6² =36.
Q.185. Two apples and three mangoes cost Rs. 86. Four apples and one mango cost Rs. 112. Cost of one apple?
Solution: Let the cost of one apple = A, one mango = M
From the problem:
2A + 3M = 86
4A + 1M = 112
From the second equation: M = 112 – 4A
Substitute M into the first equation:
2A + 3(112 – 4A) = 86
2A + 336 – 12A = 86
-10A + 336 = 86
-10A = 86 – 336
-10A = -250
A = 25
Answer: 25
Q.186. √22 + √6 + √9 = ?
Answer: 10.14
Solution: √22 ≈4.69, √6 ≈2.45, √9=3 → Sum≈4.69+2.45+3=10.14.
Q.187. A train 100 m long running at 30 km/h. Time to pass 80 m bridge?
Answer: 21.6 sec
Solution: Speed =30 km/h=8.33 m/s → Distance =100+80=180 m → Time=180/8.33≈21.6 sec.
Q.188. A boy is “son of the daughter of the father of my uncle.” How is he related?
Solution:
-
Father of my uncle → Girl’s grandfather
-
Daughter of grandfather → Girl’s mother or aunt
-
Son of that daughter → Girl’s brother or cousin
Answer: Brother (or sometimes cousin) of a girl.
Q.189. Zain facing NW, turns 90° CW, 180° ACW, 90° CW. Final direction?
Answer: South-East
Solution: NW→90°CW→NE, 180°ACW→SW, 90°CW→SE.
Q.190. 72496 →1315, 62134 →97, 85316 →167. Then 28439 → ?
Answer: 1412
Solution: Split digits: sum first 3, sum last 2 → 28439 → 2+8+4=14, 3+9=12 → 1412.
Q.191. If a and b are integers, which is NOT necessarily integer?
Solution:
-
a ÷ b is not always an integer.
-
Example: a = 1, b = 2 → a/b = 1/2, which is not an integer.
Answer: a ÷ b
Q.192. Next number in series: 1,2,2,4,4,6,8,8,16, ?
Answer: 16
Solution: Pattern: repeated number then next even → Next=16.
Q.193. Average of 13 numbers is 60. First 7 average 57, last 7 average 61. Find 7th number?
Solution:
-
Total sum of 13 numbers = 13 × 60 = 780
-
Sum of first 7 numbers = 7 × 57 = 399
-
Sum of last 7 numbers = 7 × 61 = 427
-
7th number is counted in both sums, so:
7th number = 399 + 427 − 780 = 46
Answer: 46
Q.194. Months have 30 or 31 days, how many have at least 28 days?
Answer: 12
Solution: Every month has ≥28 days.
Q.195. Aslam moves 3 km east, then 6 km north, then 5 km east. Distance from start?
Answer: 10 km
Solution: Displacement = √((3+5)²+6²)=√(64+36)=√100=10 km.
Q.196. Employee wages Rs.30/hr upto 40 hrs. Overtime 2×wage. Paid Rs.1680. How many overtime hours?
Answer: 8 hrs
Solution: Regular pay=30×40=1200 → Overtime=1680−1200=480 → Overtime hours=480/(2×30)=8.
Q.197. Expression true for −2 < x < 7?
Answer: {x | −2 < x < 7}
Solution: Interval notation for numbers between −2 and 7.
Q.198. A is B’s sister, C is B’s mother, D is C’s father, E is D’s mother. How is A related to D?
Answer: Granddaughter
Solution: D→C→B→A → A is granddaughter of D.
Q.199. Express 15 as percentage of 60?
Answer: 25%
Solution: 15/60×100 =25%.
Q.200 Ali is very hungry, his stomach is completely empty. He has many cookies and eats one by one. How many cookies can Ali eat in his completely empty stomach?
Solution:
-
When the stomach is completely empty, he can eat only one cookie.
-
After eating one, his stomach is no longer empty, so the condition is met only for the first cookie.
Answer: 1
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Q.201. If Aqsa is older than Noor, and Noor is older than Rabia, who is the youngest?
Answer: Rabia
Solution: Aqsa > Noor > Rabia, so Rabia is the youngest.
Q.202. If an alloy contains copper and silver in the ratio 3:7, then the percentage quantity of silver to the alloy is?
Answer: 70%
Solution: Total parts = 3 + 7 = 10 → Silver = 7/10 × 100 = 70%.
Q.203. 20 men can construct a building in 40 days. How long will it take 10 men to do this work?
Answer: 80 days
Solution: Work × Men = constant → 20 × 40 = 10 × x → x = 80.
Q.204. What is the number of surfaces and their types in a square pyramid?
Answer: 5 surfaces: 1 square, 4 triangular
Solution: 1 base + 4 triangular sides = 5 surfaces.
Q.205. Pie graph is divided into _____?
Answer: Sectors
Solution: Each part of pie graph is a sector.
Q.206. Hexagon has six sides and _____ angles.
Answer: 6
Solution: Number of angles = number of sides = 6.
Q.207. The mean proportional between 64 and 81 is?
Answer: 72
Solution: √(64 × 81) = √5184 = 72.
Q.208. Which one of the following is not a prime number?
Answer: 91
Solution: 91 = 7 × 13, not prime.
Q.209. In a class of 40 students 20% are girls. How many boys are there in the class?
Answer: 32
Solution: 20% of 40 = 8 girls → 40 – 8 = 32 boys.
Q.210. Sum of the interior angles of a polygon = _____?
Answer: 180(n – 2)
Solution: Formula for sum of interior angles of n-sided polygon.
Q.211. The ratio of two numbers a and b is 3:5. If 2 is added to both numbers, the ratio becomes 2:3. Find b.
Answer: 10
Solution:
Let the numbers be a=3xa = 3x and b=5xb = 5x.
According to the new ratio:
a+2b+2=23\frac{a + 2}{b + 2} = \frac{2}{3}
Substitute a=3xa = 3x and b=5xb = 5x:
3x+25x+2=23\frac{3x + 2}{5x + 2} = \frac{2}{3}
Cross multiply:
3(3x+2)=2(5x+2)3(3x + 2) = 2(5x + 2) 9x+6=10x+49x + 6 = 10x + 4 x=2x = 2
Find b:
b=5x=5×2=10b = 5x = 5 \times 2 = 10
Q.212. In ______ proportion, one quantity increases by decreasing the other quantity.
Answer: Inverse
Solution: In inverse proportion, as one increases, the other decreases.
Q.213. The ratio of ages of two students is 3:2. One is older than the other by 5 years. Age of younger?
Answer: 10 years
Solution:
Let the ages be 3x3x and 2x2x.
Difference between ages:
3x−2x=53x – 2x = 5 x=5x = 5
Age of younger student:
2x=2×5=102x = 2 \times 5 = 10
Q.214. What is the prime factorization of 16?
Answer: 2 × 2 × 2 × 2
Solution: 16 = 2⁴.
Q.215. Angle of elevation of sun when shadow = height of tree?
Answer: 45 degree
Solution: Height = shadow → tan θ = 1 → θ = 45°.
Q.216. If x + 8 = 4, then x + 4 = ___?
Answer: 0
Solution: x = 4 – 8 = –4 → x + 4 = 0.
Q.217. If all roses are flowers and some flowers are red. Which is true?
Answer: Some roses are red
Solution: Only some flowers are red, some roses may be red.
Q.218. If 3 men or 4 women can construct a wall in 43 days, then the number of days that 7 men and 5 women take to construct it is?
Answer: 12 days
Solution: Work rates → 7M + 5W finish wall in 12 days.
Q.219. Which pair of prime numbers are twin primes?
Answer: 3, 5
Solution: Twin primes differ by 2 → 3 and 5.
Q.220. In a library, 2/5 of the total books are Hadith books. Three fourths (3/4) of the remaining books are Mathematics books. The 642 books remaining are on other subjects. Find the total number of books in the library?
Answer: 4280
Solution: Let total books = T. Hadith books = 2/5 T → remaining books = 3/5 T. Mathematics books = 3/4 of remaining = 3/4 × 3/5 T = 9/20 T. Other books = remaining – math = 3/20 T.
We know other books = 642 → 3/20 T = 642 → T = 642 × 20 ÷ 3 = 4280.
So, the total number of books in the library is 4280.
Q.221. A fruit seller had some apples. He sells 40% apples and still has 420 apples. Originally, he had _____?
Answer: 700
Solution: Remaining 60% = 420 → total apples = 420 ÷ 0.6 = 700.
Q.222. The sum of all the exterior angles in a polygon is equal to ___?
Answer: 360°
Solution: Sum of exterior angles of any polygon = 360°.
Q.223. The number of diagnosis of a 12 sided figure is _____?
Answer: 54
Solution: Number of diagonals = n(n–3)/2 → 12×9/2 = 54.
Q.224. The sum of 4th multiple of 3 and 6th multiple of 2 is?
Answer: All of these (2nd multiple of 12, 6th multiple of 4, 3rd multiple of 8)
Solution:
4×3 + 6×2 = 12 + 12 = 24 → matches all given options.
Q.225. Mean value theorem is applied to _____ functions.
Answer: Both A and B (continuous and differentiable)
Solution: MVT requires function to be continuous and differentiable.
Q.226. In a cuboid, number of vertices are _____?
Answer: 8
Solution: Cuboid has 8 corners.
Q.227. What is the average of first 150 natural numbers?
Answer: 75.5
Solution: Average = (1 + 150)/2 = 75.5.
Q.228. In a code language, if BEAT is coded as 5642 and SWEET is coded as 66912, how would you code TEASE?
Answer:96625
Solution:
Based on the letter-to-number code from BEAT = 5642 and SWEET = 66912, the letters correspond to numbers as follows: T → 2, E → 6, A → 4, S → 9. Using this mapping, the word TEASE is coded as 96625.
Q.229. What is the average of 12, 15, 18?
Answer: 15
Solution: (12+15+18)/3 = 45/3 = 15.
Q.230. 1 Kg is equal to how many grams?
Answer: 1000 grams
Q.231. What is 30% of 0.333?
Answer: 0.0999
Solution: 0.333 × 0.3 = 0.0999.
Q.232. If y = 3, then y³(y³ – y) = _____?
Answer: 648
Solution: 3³(3³ – 3) = 27×24 = 648.
Q.233. Sum of 4 A.M between 18 and 3 is _____?
Answer: 42
Solution: 18 + 3 + 4 + 17 = 42.
Q.234. During the school assembly, 96 students are standing in 6 equal rows. How many students are there in 1 row?
Answer: 16
Solution: 96 ÷ 6 = 16.
Q.235. Ibrahim and Marwa are preparing first aid kits for the students. They have 30 perforated adhesive bandages, 60 triangular bandages and 75 rectangular bandages. They must distribute these equally in the kits, with nothing left over. What is the greatest number of kits they can make this quantity of bandages?
Answer: 15
Solution:
To make equal kits without any bandage left, we find the GCD (HCF) of 30, 60 and 75.
GCD of 30, 60 and 75 = 15
So, the maximum number of kits that can be made is 15.
Q.236. Find the value of x in the proportion 2 : 7 :: 14 : x?
Answer: 49
Solution: 2/7 = 14/x → 2x = 98 → x = 49.
Q.237. 1.14 expressed as a percent of 1.9 is?
Answer: 60%
Solution: (1.14 ÷ 1.9) × 100 ≈ 60%.
Q.238. What is a formula of perimeter of rectangle?
Answer: 2(length + width)
Q.239. The binary equivalent of decimal 13 is ______?
Answer: 1101
Q.240. Two taps X and Y can fill a tank in 10 hrs. and 15 hours respectively. If the both taps are opened together, the tank will be full in?
Answer: 6 hours
Solution: 1/10 + 1/15 = 1/x → x = 6 hours.
Q.241. 625 decreased by 12% is _____?
Answer: 550
Solution: 625 × 0.88 = 550.
Q.242. A car travels at a speed of 65 miles per hour. How far will it travel in 5 hours?
Answer: 325
Solution: Distance = speed × time = 65 × 5 = 325.
Q.243. If the sum of the quantities 1840 and their average is 115, then find the number of quantities?
Answer: 16
Solution: 1840 ÷ 115 = 16.
Q.244. What is the ratio of 3½ kg to 50 g?
Answer: 70:1
Solution: 3.5 kg = 3500 g → 3500 ÷ 50 = 70 → ratio = 70:1.
Q.245. Ten years ago. A was half of B’s in age. If the ratio of their present ages is 3:4, what will be the total of their present ages?
Answer: 35 years
Solution:
Let the present ages of A and B be in the ratio 3:4 → A = 3x, B = 4x.
Ten years ago, A was half of B → (3x – 10) = ½ (4x – 10)
Solve: 3x – 10 = 2x – 5 → 3x – 2x = –5 + 10 → x = 5
Now, A’s age = 3x = 3 × 5 = 15 years, B’s age = 4x = 4 × 5 = 20 years
Sum of their present ages = 15 + 20 = 35 years
Q.246. The area of a rectangle garden is 96m². If it’s width is 3m, find its length?
Answer: 32m
Solution: Length = 96 ÷ 3 = 32.
Q.247. A bag contains 50 paisa, 1 rupee and 2 rupee coins in the ratio 2:5:8. If the total amount is Rs. 352, find the total number of coins in the bag?
Answer: 240
Solution:
Let the number of 50 paisa, 1 rupee, and 2 rupee coins be 2x, 5x, and 8x.
Value in rupees: 50p → 1x, 1₹ → 5x, 2₹ → 16x.
Total amount = 352 → 1x + 5x + 16x = 22x = 352 → x = 16.
Total coins = 2x + 5x + 8x = 15x = 15 × 16 = 240.
Answer: 240 coins.
Q.248. Find the odd letter: R, O, L, H.
Answer: O
Solution: O is the only vowel in the group, and it has a curved shape, while R, L, and H are consonants made of straight lines.
Q.249. There were 600 students in a school. Each offered either English or Hindi or both. If 75% offered English and 45% Hindi, How many offered both?
Answer: 120
Solution: English + Hindi – both = total → 450 + 270 – both = 600 → both = 120.
Q.250. The sum of the measures of all angles in a pie graph is _____?
Answer: 360°
Solution: Pie graph is complete circle → sum of angles = 360°.
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Q.251. In an examination, 80% of candidates passed English and 85% of candidates passed in Mathematics. If 73% candidates passed in both these subjects, then what percent of candidates failed in both the subjects?
Answer: 8%
Solution:
Use the formula for union of two sets:
Percent passed at least one subject = %English + %Math – %both = 80 + 85 – 73 = 92%.
Percent failed in both subjects = 100 – 92 = 8%.
So the correct answer is 8%.
Q.252. If 8 people work for 60 days, how many days will it take for 6 people to complete the same work?
Answer: 80 days
Solution: Work × Days × People = Constant.
8 × 60 = 6 × x → x = (8×60)/6 = 480/6 = 80 days.
Q.253. The product of 513 with itself is?
Answer: 263169
Solution: 513 × 513 = 263169.
Q.254. Half of 1 percent written as a decimal is?
Answer: 0.005
Solution: 1% = 0.01 → half of 0.01 = 0.005.
Q.255. 15 men can do a work in 12 days. How long it will take 9 men to do the same work?
Answer: 20 days
Solution: Work × Men × Days = Constant
15 × 12 = 9 × x → x = 180/9 = 20 days.
Q.256. Angle of measure of 72° can be drawn by?
Answer: Protector only
Solution: A protractor (protector) is used to measure specific angles directly. Compass alone cannot draw an exact 72° angle, so only a protractor is sufficient.
Q.257. The smallest 4-digit number using 0, 3, 5, and 8, is?
Answer: 3058
Solution: Smallest 4-digit number cannot start with 0. Arrange digits in ascending order: 3,0,5,8 → 3058.
Q.258. The bridge is completed in 20 days by 80 men. How long will it take 70 men to complete the work?
Answer: 22.86 days ≈ 23 days
Solution: 80 × 20 = 1600 man-days. 1600 ÷ 70 ≈ 22.86 days.
Q.259. Which of the following is a factor of 36?
Answer: All of these ( 4,6,12)
Solution: Factors of 36: 1,2,3,4,6,9,12,18,36 → 4,6,12 are all factors.
Q.260. What is the measure of each interior angle of a regular hexagon?
Answer: 120°
Solution: Interior angle = (n–2)×180/n = (6–2)×180/6 = 720/6 = 120°.
Q.261. The set of integers is a subset of?
Answer: Rational Numbers
Solution: Every integer can be written as a fraction (like 5 = 5/1), so integers are part of rational numbers.
Q.262. A rectangular front-wall of a hospital has a perimeter of 294 meters. If its length is 85 meters, find its area.
Answer: 5270 m²
Solution:
Perimeter of rectangle = 2(length + width) → 294 = 2(85 + width)
Divide both sides by 2 → 147 = 85 + width
Subtract 85 → width = 147 – 85 = 62
Area = length × width = 85 × 62 = 5270 m²
Q.263. The difference of two positive integers is 3 and the sum of their squares is 89. The integers are?
Answer: 5 and 8
Solution: Let the numbers be x and y → y – x = 3 → y = x + 3
x² + y² = 89 → x² + (x + 3)² = 89 → 2x² + 6x + 9 = 89 → 2x² + 6x – 80 = 0 → x² + 3x – 40 = 0
Factor: (x + 8)(x – 5) = 0 → x = 5 → y = 8
Q.264. 60 men can do a work in 40 days. How long will it take 40 men to complete the same work?
Answer: 60 days
Solution: Work = men × days = constant → 60 × 40 = 2400 man-days
For 40 men: 2400 ÷ 40 = 60 days
Q.265. Digital number 9 can be represented in binary number as?
Answer: 1001
Solution: Convert 9 to binary: 9 ÷ 2 = 4 remainder 1, 4 ÷ 2 = 2 remainder 0, 2 ÷ 2 = 1 remainder 0, 1 ÷ 2 = 0 remainder 1 → 1001
Q.266. While watching television from 7 PM to 8 PM you count 20 commercials each 30 seconds long. What nearest percent of the hour is taken by the commercials?
Answer: 17%
Solution: Total commercial time = 20 × 30 sec = 600 sec = 10 min
Percent of hour = 10 ÷ 60 × 100 = 16.67% ≈ 17%
Q.267. What number is 25% of 150?
Answer: 37.5
Solution: 25% of 150 = 150 × 0.25 = 37.5
Q.268. If 15 men can manufacture 27 baskets in an hour, how many baskets would 45 men manufacture in 40 minutes?
Answer: 54
Solution: Baskets per man per hour = 27 ÷ 15 = 1.8
For 45 men in 1 hour: 45 × 1.8 = 81 baskets
In 40 minutes (2/3 hour): 81 × 2/3 = 54 baskets
Q.269. A number whose 7 percent is 42 is?
Answer: 600
Solution: 7% of number = 42 → number × 0.07 = 42 → number = 42 ÷ 0.07 = 600
Q.270. a³ – b³ , a² – b² , a² + ab + b² and x are in a proportion. The value of x is?
Answer: a + b
Solution: Proportion: (a³ – b³)/(a² – b²) = (a² + ab + b²)/x → simplify → x = a + b
Q.271. Distance between points (2,3) and (7,3) is?
Answer: 5
Solution: Distance = √((x₂ – x₁)² + (y₂ – y₁)²) = √((7–2)² + (3–3)²) = √25 = 5
Q.272. Find x, if log₁₂(12³) = x?
Answer: 3
Solution: logₐ(aᵏ) = k → log₁₂(12³) = 3
Q.273. 7/4 ÷ [77/8 ÷ 30/5] = ?
Answer: 12/11
Solution: First, 77/8 ÷ 30/5 = 77/8 × 5/30 = 385/240 = 77/48
Then 7/4 ÷ 77/48 = 7/4 × 48/77 = 336/308 = 12/11
Q.274. A bag contains 6 black and 8 white balls. 1 ball is drawn at random. Probability it is white?
Answer: 4/7
Solution: Total balls = 6 + 8 = 14 → Probability white = 8 ÷ 14 = 4/7
Q.275. If 70 men can work in 35 days, 40 men complete this work in how many days?
Answer: 61.25 days
Solution: Total work = 70 × 35 = 2450 man-days → 40 men: 2450 ÷ 40 = 61.25 days
Q.276. If A’s salary is 25% higher than B’s, B’s salary is what percent lower than A’s?
Answer: 20%
Solution: Let B = 100 → A = 125 → Difference = 25 → 25 ÷ 125 × 100 = 20%
Q.277. 40 cows eat 40 bags of husk in 40 days. In how many days will 1 cow eat 1 bag?
Answer: 40 days
Solution: Husk per cow per day = 40 ÷ (40 × 40) = 1/40 → 1 bag → 40 days
Q.278. Perimeter of a rhombus with side 6 cm?
Answer: 24 cm
Solution: Perimeter = 4 × side = 4 × 6 = 24 cm
Q.279. In a quadratic equation, the highest power of variable?
Answer: 2
Solution: Standard quadratic: ax² + bx + c → highest power = 2
Q.280. Product of two numbers is 2500. LCM is 125. HCF is?
Answer: 20
Solution: Product = LCM × HCF → HCF = 2500 ÷ 125 = 20
Q.281. 80 men dug 4 holes in 12 months. How many men needed for 6 holes?
Answer: 360
Solution:
Step 1: Total man-months for 80 men digging 4 holes = 80 × 12 = 960
Step 2: Man-months needed per house = 960 ÷ 4 = 240
Step 3: Total man-months for 6 houses = 240 × 6 = 1440
Step 4: Number of men needed in 4 months = 1440 ÷ 4 = 360
Answer: 360 men.
Q.282. How many two-digit numbers are divisible by 6?
Answer: 15
Solution: Two-digit numbers divisible by 6: 12, 18, …, 96 → (96–12)/6 + 1 = 15 numbers
Q.283. A fort had food for 150 men for 45 days. After 10 days, 25 men left. Remaining food will last?
Answer: 42 days
Solution: Initial food = 150 × 45 = 6750 man-days
After 10 days: 150 × 10 = 1500 man-days used → remaining = 5250
Remaining men = 150 – 25 = 125 → 5250 ÷ 125 = 42 days
Q.284. A fraction where numerator degree > denominator degree is called?
Answer: Improper fraction
Solution: Numerator degree > denominator degree → Improper fraction
Q.285. 6 men can work in 10 hrs, 4 men can do this work in?
Answer: 15 hrs
Solution: Work = men × hours → 6 × 10 = 60 man-hours → 4 men: 60 ÷ 4 = 15 hrs
Q.286. How many acres are there in 1 hectare?
Answer: 2.47
Solution: 1 hectare = 2.471 acres ≈ 2.47 acres
Q.287. What percent of 720 is 36?
Answer: 5%
Solution: (36 ÷ 720) × 100 = 5%
Q.288. A flagstaff 17.5 m high casts a shadow of 40.25 m. A building casts shadow of 28.75 m. Height of building?
Answer: 12.5 m
Solution: Height/shadow ratio constant → 17.5/40.25 = h/28.75 → h = 17.5 × 28.75 ÷ 40.25 ≈ 12.5 m
Q.289. A triangle with no equal sides and no equal angles is?
Answer: Scalene triangle
Solution: Scalene → all sides and angles are unequal
Q.290. 20 men can do a work in 8 days. How many men in 10 days?
Answer: 16
Solution: Work = men × days = constant → 20 × 8 = 160 → 160 ÷ 10 = 16 men
Q.291. 250 men can finish work in 20 days working 5 hours/day. To finish in 10 days working 8 hours/day, men required?
Answer: 313 men
Solution: Total man-hours = 250 × 20 × 5 = 25,000
New work hours/day = 10 × 8 = 80 → men = 25,000 ÷ 80 = 312.5 → 313
Q.292. 7 spiders make 7 webs in 7 days. 1 spider makes 1 web in how many days?
Answer: 7 days
Solution: Each spider makes 1 web in 7 days
Q.293. 3/8 + 4/2 = ?
Answer: 19/8
Solution: 4/2 = 16/8 → 3/8 + 16/8 = 19/8
Q.294. In a cage, there are pigeons and rabbits. 20 heads, 48 feet. Rabbits?
Answer: 4
We have pigeons and rabbits.
Let pigeons = P and rabbits = R.
Total heads = 20
So, P + R = 20
Total feet = 48
Pigeons have 2 feet and rabbits have 4 feet, so:
2P + 4R = 48
From the first equation:
P = 20 − R
Put this value in the second equation:
2(20 − R) + 4R = 48
40 − 2R + 4R = 48
40 + 2R = 48
2R = 8
R = 4
Answer: There are 4 rabbits in the cage.
Q.295. What number is 20% of 80?
Answer: 16
Solution: 20% of 80 = 0.2 × 80 =16
Q.296. If 40 men build 4 buildings in 12 months, how many men needed to build 6 houses in 4 months?
Answer: 180 men
Solution: Work = men × months × buildings → 40 × 12 × 4 = 1920 man-months per building
6 buildings in 4 months → men = 1920 ÷ 4 ÷ 6 = 180
Q.297. A man climbs a hill: ascends 20 yards, slips 5 yards each minute. Time to climb 80 yards?
Answer: 5 minutes
Solution: Net climb per minute = 20 – 5 = 15
Before last step, climb 80 – 20 = 60 → 60 ÷ 15 = 4 minutes
Last 20 yards = 1 minute → total = 5 minutes
Each minute: climbs 20, slips 5 → net 15
Total height 80 → last step doesn’t slip → 80 – 20 = 60 → 60 ÷ 15 = 4 → total minutes = 4 +1 = 5 minutes
Q.298. Greatest number which exactly divides 1050 and 750?
Answer: 150
Solution: HCF of 1050 and 750 → 1050=2×3×5²×7, 750=2×3×5³ → HCF=2×3×5²=150
Q.299. Rectangle 82 cm × 75 cm, enclosed by 4 cm wide strip outside. Area of strip?
Answer:1320 cm²
Solution: Outer rectangle: (82+8) × (75+8)=90×83=7470
Original area = 82×75=6150
Area of strip = 7470 – 6150 = 1320 Answer
check 82+8=90, 75+8=83 → 90×83=7470 → 7470–6150=1320
1320 cm²
Q.300. How many years in a decade?
Answer: 10 years
Solution: By definition, 1 decade = 10 years
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Q301. A man sold his motorcycle for Rs. 24,000 and earned 20% profit. What was the original price?
Answer: 20,000
Step/Explain: Agar 20% profit ho, to selling price = 120% of cost price → Cost price = 24,000 ÷ 1.2 = 20,000
Q302. Find the surface area of a sphere whose radius is 7 cm?
Answer: 616 cm²
Step/Explain: Surface area of sphere = 4πr² → 4×3.14×7×7 ≈ 616 cm²
Q303. In a group of 26 students, 21 like football and 14 like cricket. What is the number of students who like both football and cricket?
Answer: 9
Step/Explain: Students liking both = (21 + 14) − 26 = 35 − 26 = 9
Q304. Which number is divisible by both 4 and 9?
Answer: 5256
Step/Explain: Last two digits 56 → divisible by 4, sum of digits 5+2+5+6=18 → divisible by 9 → 5256 divisible by both
Q305. If x ∝ 1/y and y ∝ 1/z, then _____?
Answer: x ∝ z
Step/Explain: x inversely proportional to y, y inversely proportional to z → x directly proportional to z
Q306. What comes next in the series: 64, 48, 40, 36, 34, ______?
Answer: 33
Step/Explain: Differences: 64−48=16, 48−40=8, 40−36=4, 36−34=2, next difference 1 → 34−1=33
Q307. The binary number (101011) change into decimal?
Answer: 43
Step/Explain: 1×32 + 0×16 + 1×8 + 0×4 + 1×2 + 1×1 = 32 + 8 + 2 + 1 = 43
Q308. If A = {1, 2} and B = {a, b, c, d} then the number of elements in B × A?
Answer: 8
Step/Explain: Cartesian product → number of elements = 4×2 = 8
Q309. 2 × 25 ÷ 5 + 10 – 2 = _____?
Answer: 18
Step/Explain: 25 ÷ 5 = 5 → 2×5=10 → 10+10−2=18
Q310. Pointing to a photograph, a man said, “I have no brother, and that girl’s father is my father’s son.” Whose photograph was it?
Answer: His daughter
Step/Explain: “My father’s son” = himself (no brother) → the girl’s father = him → girl = his daughter
Q311. What is 60 percent of 100?
Answer: 60
Step/Explain: 100×60/100 = 60
Q312. The decreased population of a city from 25,000 to 24,500. Find the percentage?
Answer: 2%
Step/Explain: Decrease = 25,000−24,500=500 → % decrease = (500/25,000)×100 = 2%
Q313. If a/b = c/d then alternendo property is?
Answer: a/c = b/d
Step/Explain: Alternendo → diagonals swap → a/c = b/d
Q314. The straight angle is ____?
Answer: 180°
Step/Explain: Straight line angle = 180°
Q315. A light shop sells lights, they sold 25 percent of the lights and still had 1500 lights left. How many lights were there in the beginning?
Answer: 2000
Step/Explain: Remaining = 75% → 1500 ÷ 0.75 = 2000
Q316. 25 is what percent of 75?
Answer: 33%
Step/Explain: (25/75)×100 ≈ 33%
Q317. The solution of equation 3/2 x − 5/2 = 1/2?
Answer: 2
Step/Explain: 3/2 x − 5/2 = 1/2 → 3/2 x = 6/2 → x = 2
Q318. 0.05 is equal to which of the following fractions?
Answer: 1/20
Step/Explain: 0.05 = 5/100 = 1/20
Q319. 4 mat-weavers can weave 4 mats in 4 days. At the same rate, how many mats would be woven by 8 mat-weavers in 4 days?
Answer: 8
Step/Explain: Workers double → mats double → 8 mats
Q320. Akbar sold his old gun Rs. 900, which he bought for Rs. 2500. What is his % loss?
Answer: 64%
Step/Explain: Loss = 2500−900=1600 → % loss = (1600/2500)×100 = 64%
Q321. The number whose 3% is 60, is _____?
Answer: 2000
Step/Explain: 3% of number = 60 → number = 60×100/3 = 2000
Q322. Complete the series 1, 8, 27, 64, 125 _____?
Answer: 216
Step/Explain: Series = cubes: 1³,2³,3³,4³,5³ → next 6³=216
Q323. 120 men are used to build huge building for 30 days. How long will it take 80 men to do the same work?
Answer: 45 days
Step/Explain: Work = men×days → 120×30 = 80×Days → Days = 3600/80 = 45
Q324. 3.29 × 1000 is equal to ____?
Answer: 3290
Step/Explain: Decimal point moves 3 places → 3.29 ×1000=3290
Q325. If 15 toys cost Rs. 234, what will 35 toys cost?
Answer: Rs. 546
Step/Explain: 1 toy = 234/15 = 15.6 → 35 toys = 15.6×35 = 546
Q326. 45 is 72% of what number?
Answer: 62.5
Step/Explain: Percent formula: part = % × whole → Whole = Part ÷ (%/100) → 45 ÷ 0.72 = 62.5
Q327. Two vertical angles measure 80° and 4x. Find x.
Answer: 20°
Step/Explain: Vertical angles = barabar → 4x = 80 → x = 80 ÷ 4 = 20
Q328. The total age of A and B is 12 years more than the total age of B and C. C is how many years younger than A?
Answer: 12
Step/Explain: (A + B) = (B + C) + 12 → A = C + 12 → C is 12 years younger than A
Q329. Which fraction is less than 7/8 and greater than 1/3?
Answer: 17/24
Step/Explain: 1/3 ≈ 0.33, 7/8 ≈ 0.875 → 17/24 ≈ 0.708, jo dono ke darmiyan hai
Q330. Zaid is six times as old as his daughter Zoya. How old was Zaid when Zoya was born if the sum of their ages will be 49 in 7 years?
Answer: 25
Step/Explain: 7 saal baad sum = 49 → ab sum = 49−14 = 35
Let Zoya = x → Zaid = 6x → x + 6x = 35 → 7x=35 → x=5
Zoya born → Zaid = 30−5=25
Q331. The area of a square whose side is 8 m?
Answer: 64 m²
Step/Explain: Area = Side × Side = 8 × 8 = 64
Q332. In a group of 550 students, 42% go on a tour. How many students go on tour?
Answer: 231
Step/Explain: 42% of 550 → (42/100)×550 = 231
Q333. Ahmed’s age after 15 years will be 5 times his age 5 years back. Find present age.
Answer: 10
Step/Explain: Let Ahmed’s age now = x → x + 15 = 5(x − 5) → x + 15 = 5x − 25 → 40 = 4x → x = 10
Q334. A solid body bounded by six ______ faces is called a cuboid.
Answer: Rectangular
Step/Explain: Cuboid has 6 rectangular faces
Q335. Complete the series: 2, 6, 18, 54, _____?
Answer: 162
Step/Explain: Each number ×3 → 54×3 = 162
Q336. If a train runs 180 km/hr, how much distance will it travel in 8 hours?
Answer: 1440 km
Step/Explain: Distance = Speed × Time = 180×8 = 1440 km
Q337. If the central angle in a pie-chart is 90°, what is the proportion of that part?
Answer: 25%
Step/Explain: Proportion = 90/360 = 1/4 = 25%
Q338. Zero divided by any non-zero number is ______?
Answer: 0
Step/Explain: 0 ÷ any number = 0
Q339. A father is now three times as old as his son. Five years back, he was four times as old. Find the son’s age.
Answer: 15
Step/Explain: Let son = x → Father = 3x → 5 years back: 3x−5 = 4(x−5) → 3x−5=4x−20 → x=15
Q340. 148 is divisible by _____?
Answer: 37
Step/Explain: 37×4 = 148
Q341. Surface area of a sphere?
Answer: 4πr²
Step/Explain: Standard formula for sphere’s surface area
Q342. Given sequence: 4, 11, 7, 14, 10, 17, ______, 20.
Answer: 13
Step/Explain: Two interleaving series: 4,7,10,13 and 11,14,17,20
Q343. Which one among the following is not a prime number?
Answer: 1
Step/Explain: 1 is neither prime nor composite. Primes start from 2
Q344. Find the cube root of 64?
Answer: 4
Step/Explain: 4×4×4 = 64
Q345. A polygon which consists of 8 sides is called?
Answer: Octagon
Step/Explain: Polygon with 8 sides = Octagon
Q346. In octal system 18 is written as ______?
Answer: (22)₈
Step/Explain: 18 ÷ 8 = 2 remainder 2 → 22₈
Q347. Complete the series: 1, 9, 25, 49, ______, 121.
Answer: 81
Step/Explain: Series = squares of odd numbers → 1²,3²,5²,7²,9² → missing 9²=81
Q348. The H.C.F of 48, 64 and 120 is _____?
Answer: 8
Step/Explain: 8 is the largest number that divides all three numbers
Q349. A geometric figure, the measure of the shortest distance between the base and its opposite vertex is called?
Answer: Altitude
Step/Explain: Shortest perpendicular distance from base to opposite vertex = Altitude
Q350. The internal angle at each vertex of a regular octagon is?
Answer: 135°
Step/Explain: Formula: [(n−2)×180]/n = [(8−2)×180]/8 = 135°
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Q351. Look at this series: V, VIII, XI, XIV, _____ XX. What number should fill the blank?
Answer: XVII
Steps: V=5, VIII=8, XI=11, XIV=14. Series increases by 3 each time. 14+3=17 → XVII.
Q352. An Urdu class has 12 boys and 18 girls. Boys are what fraction of the class?
Answer: 2/5
Steps: Total students = 12+18=30. Fraction of boys = 12/30=2/5.
Q353. A figure whose all four sides are equal is called ____?
Answer: Square
Steps: All four sides equal → the shape is a square.
Q354. The Zoo had some lions and some parrots. The supervisor counted 15 heads and 50 legs. How many lions are there?
Answer: 10
Steps: If all were parrots, legs = 15×2=30. Actual legs=50 → extra legs = 50−30=20. Each lion contributes 2 extra legs → 20/2=10 lions.
Q355. The age of Ashraf is 15 years, 10 months and the age of Akmal is 17 years, 5 months. Find the ratio between their ages?
Answer: 10:11
Steps: Ashraf = 15×12+10=190 months, Akmal =17×12+5=209 months. Ratio=190:209=10:11.
Q356. 3/4 + 5/8 – 1/2 =?
Answer: 0.875
Steps: Convert to same denominator 8: 3/4=6/8, 5/8=5/8, 1/2=4/8 → 6+5−4=7/8=0.875.
Q357. 12 men can do a piece of work in 10 days. How many men would be required to do the same work in 8 days?
Answer: 15
Steps: 12×10 = M×8 → M=120/8=15 men.
Q358. Convert 2/5 into percentage?
Answer: 40%
Steps: 2/5 ×100=40%.
Q359. Complete the series: 0, 1, 3, 6, 10, ______?
Answer: 15
Steps: Add +1,+2,+3,+4,+5 → next=10+5=15.
Q360. Complete the series: 0, 1, 3, 6, 10, ______?
Answer: 15
Steps: Same as Q359.
Q361. A, B and C together earn Rs. 150 per day while A and C together earn Rs. 94 and B and C together earn Rs. 76. They daily earning of C is _____?
Answer: Rs. 20
Steps: (A+C)+(B+C)=94+76=170 → C=170−150=20.
Q362. 1 square foot is equal to ______?
Answer: 144 square inches
Steps: 1 foot =12 inches → area =12×12=144 sq in.
Q363. Which number should come next in the pattern: 37, 34, 31, 28, _____?
Answer: 25
Steps: Series subtracts 3 each time → 28−3=25.
Q364. Which of the following is divisible by 12?
Answer: 4404
Steps: 4404 ÷12=367 → divisible.
Q365. If 100 Kg of meat is divided into packages of 4/7 kg each, the total number of packages will be ____?
Answer: 175
Steps: 100 ÷(4/7)=100×7/4=175.
Q366. There are 56 boys in a class of 140 students. What is the percentage of boys?
Answer: 40%
Steps: 56 ÷140 ×100=40%.
Q367. 9 is 1/3% of what number?
Answer: 2700
Steps: 1/3% × X=9 → X=9×3×100=2700.
Q368. A is thrice as good as B in work. A is able to finish a job in 60 days less than B. They can finish the work in ______ days if they work together.
Answer: 22.5 days
Steps: B=90 days, A=30 days → Together = (30×90)/(30+90)=2700/120=22.5 days.
Q369. What is 25% of 200?
Answer: 50
Steps: 25/100 ×200=50.
Q370. Complete the series: 2, 4, 6, 8, ______?
Answer: 10
Steps: Series +2 → 8+2=10.
Q371. Complete the series: 1, 4, 9, 16, _____?
Answer: 25
Steps: Series of squares: 1²,2²,3²,4²,5²=25.
Q372. 18 is 75 percent of what number?
Answer: 24
Steps: 18 ÷0.75=24.
Q373. 30 % of 100 is equal to 3% of ____?
Answer: 1000
Steps: 30 ÷0.03=1000.
Q374. If 2^x =32, What is x^2 ?
Answer: 25
Steps: 2^5=32 → x=5 → x²=25.
Q375. 120 men can do a work in 90 days, how many more men required to complete the same work in 40 days?
Answer: 150 more men
Steps: 120×90 = M×40 → M=270 → extra=270−120=150.
Q376. The population of a town increased from 1,75,000 to 2,62,500 in a decade. The average percent increase of population per year is _____?
Answer: 5%
Steps: Increase=2,62,500−1,75,000=87,500 → % increase=87,500/1,75,000×100=50% in 10 years → 50/10=5% per year.
Q377. Saeed receives a commission of Rs. 25 for every Rs. 250 worth of merchandise he sells; therefore, the percentage (%) of his commission is?
Answer: 10%
Steps: 25 ÷250 ×100=10%.
Q378. Ali ran around a 1/4 kilometer jogging track 17 times. How many kilometers did he run?
Answer: 4.25 km
Steps: 17×1/4=17/4=4.25 km.
Q379. One mile is equal to ______?
Answer: 1.6 km
Steps: 1 mile ≈1.6 km.
Q380. 3/1000 written as a decimal is?
Answer: 0.003
Steps: 3 ÷1000=0.003.
Q381. Complete the series: 21, 20, 18, 15, 11, ______?
Answer: 6
Steps: Differences: −1,−2,−3,−4 → next −5 →11−5=6.
Q382. Who was the founder of the basic laws of Geometry?
Answer: Pythagoras
Steps: Pythagoras gave the basic rules of geometry.
Q383. Which is the most common measure of central tendency?
Answer: Mean
Steps: Mean (average) is used most often.
Q384. What percent of 120 are 90?
Answer: 75%
Steps: 90 ÷120 ×100=75%.
Q385. 5448 rounded off to the nearest 1000 is _______?
Answer: 5000
Steps: 448<500 → round to 5000.
Q386. Izza gave 20% of her candies to Urooj and 15% to Mehwish. If she still had 520 candies, how many did she have originally?
Answer: 800
Steps: 100%−35%=65% left → 520 ÷0.65=800.
Q387. Which number can replace both the questions marks in 2/? = ?/50
Answer: 10
Steps: x² = 2×50=100 → x=10.
Q388. Complete the series: 3, 4, 6, 9, 13, ______?
Answer: 18
Steps: Differences +1,+2,+3,+4,+5 → 13+5=18.
Q389. Ramees buys goods worth Rs. 6650. He gets a rebate of 6% on it. After getting the rebate, he pays sales tax @ 10%. Find the amount he will have to pay for the goods.
Answer: Rs. 6876.10
Steps: 6650−6%=6251 → 6251+10%=6251+625.1=6876.1
Q390. If 15 men can do a piece of work in 20 days. In how many days can 25 men finish the same work?
Answer: 12
Steps: 15×20 = 25×D → D=300/25=12 days.
Q391. If 25 students took the exam and 4 of them fails. What percent of them passed?
Answer: 84%
Steps: Passed=25−4=21 → 21/25×100=84%.
Q392. What is the average of all prime numbers between 30 to 50?
Answer: 39.8
Steps: Primes=31,37,41,43,47 → sum=199 → average=199/5=39.8
Q393. A sum of money is to be distributed among A, B, C, D in the proportion of 5 : 2 : 4 : 3. If C gets Rs. 1000 more than D. What is B’s share?
Answer: 2000
Steps: C−D=1 share=1000 → B=2 shares → 2×1000=2000
Q394. What is the value of the product? 5/5 x 5/10 x 5/15 x 5/20 x 5/25 = ?
Answer: 1/120
Steps: Multiply fractions: 1×1/2×1/3×1/4×1/5=1/120
Q395. If a square is rotated by 90 degrees, what shape does it become?
Answer: Square
Steps: Square stays square even after rotation.
Q396. The square of 35 is ____?
Answer: 1225
Steps: 35×35=1225
Q397. Which letter is midway between the 8th letter from A and 7th letter from Z?
Answer: N
Steps: 8th from A=H, 7th from Z=T → midway=(H+T)/2=N
Q398. 40 is subtracted from 60% of a number, the result is 50. Find the number?
Answer: 150
Steps: 0.6x−40=50 → 0.6x=90 → x=150
Q399. The mean proportional of 4 and 16 is ______?
Answer: 8
Steps: √(4×16)=√64=8
Q400. A cyclist covers a distance of 750 meters in 2 minutes and 30 seconds. What is his speed in km/hr?
Answer: 18 km/hr
Steps: Time=2.5min=150s → speed=750/150=5 m/s → 5×18/5=18 km/hr
Q401. Find the average of 5/6, 4/3, 3/4?
Answer: 35/36
Steps: Sum=5/6+4/3+3/4=35/12 → Average=35/12÷3=35/36
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Stage-09
Q401. What is the value of 1 divided by 0.02 (1 ÷ 0.02)?
Answer: 50
Explanation:
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To remove the decimal from the denominator, multiply both numerator and denominator by 100:
1 ÷ 0.02 = 100 ÷ 2 = 50
Q402. In the analogy “Always : Never”, which pair follows the same logic?
Answer: Often : Rarely
Explanation:
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Always (Hamesha) is the opposite of Never (Kabhi nahi).
-
Similarly, Often (Aksar) is the opposite of Rarely (Kabhi kabaar).
Q403. A coach leaves at 22:55 and arrives at 06:05 the next day. How long is the journey?
Answer: 7 hours 10 minutes
Explanation:
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From 22:55 to 23:00 = 5 minutes
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From 23:00 to 06:00 = 7 hours
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From 06:00 to 06:05 = 5 minutes
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Total = 7 hours 10 minutes
Q404. A man walked for 1/3 hour and rode an automobile for 1/2 hour. What part of the total time was spent on the ride?
Answer: 0.6
Explanation:
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Total time = 1/3 + 1/2 = 2/6 + 3/6 = 5/6 hours
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Fraction of ride = (1/2) ÷ (5/6) = (1/2) × (6/5) = 3/5 = 0.6
Q405. The average age of 3 friends is 23. Even after adding a 4th friend, the average remains 23. What is the 4th friend’s age?
Answer: 23 years
Explanation:
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If adding a person does not change the average, that person’s age must equal the current average.
Q406. Complete the series: 6, 3, 12, 6, 24, ______?
Answer: 12
Explanation:
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There are two alternating patterns:
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6 → 12 → 24 (multiply by 2 each time)
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3 → 6 → ? (multiply by 2)
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Next number in second pattern = 6 × 2 = 12
Q407. What is the square root of √169?
Answer: None of these
Explanation:
-
√169 = 13
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Then √(13) = 3.605… which is not in the options
Q408. Complete the series: 6, 9, 18, 45, 126, ______?
Answer: 369
Explanation:
-
Differences between consecutive terms:
9 − 6 = 3 (3¹)
18 − 9 = 9 (3²)
45 − 18 = 27 (3³)
126 − 45 = 81 (3⁴) -
Next difference = 3⁵ = 243
-
Next term = 126 + 243 = 369
Q409. What is 0.26 ÷ 100?
Answer: 0.0026
Explanation:
-
Dividing by 100 moves the decimal two places left → 0.26 → 0.0026
Q410. Which number is farthest from -1 on the number line?
Answer: 10
Explanation:
-
Distance from -1 to 10 = |10 − (-1)| = 11
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Compare other options → 10 is farthest
Q411. What is 892 squared (892²)?
Answer: 795,664
Explanation:
-
Multiply: 892 × 892 = 795,664
Q412. Average weight of 10 people increases by 1.5 kg when a 45 kg person is replaced. Find the weight of the new person.
Answer: 60 kg
Explanation:
-
Total increase = 10 × 1.5 = 15 kg
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New person’s weight = 45 + 15 = 60 kg
Q413. What is 0.005 × 0.2?
Answer: 0.001
Explanation:
-
Multiply ignoring decimal: 5 × 2 = 10
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Total decimal places = 4 → 0.0010
Q414. Sum = 30, Difference = 8. Find the product.
Answer: 209
Explanation:
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First number = (30 + 8)/2 = 19
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Second number = (30 − 8)/2 = 11
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Product = 19 × 11 = 209
Q415. Series: 8, 27, 64, 100, 125, 216, 343. Which number is odd one out?
Answer: 100
Explanation:
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All numbers except 100 are perfect cubes (2³,3³,4³,…). 100 = 10² (a square) → odd one out
Q416. Series: 112, 100, 88, _____?
Answer: 76
Explanation:
-
Subtract 12 each step → 88 − 12 = 76
Q417. A salesman sells 42 red cars and 14 green cars. Find the ratio of red to green cars.
Answer: 3:1
Explanation:
-
42 ÷ 14 = 3 → Ratio = 3:1
Q418. Solve: 5/6 × 2/5 = ?
Answer: 1/3
Explanation:
-
Multiply numerators and denominators: (5 × 2)/(6 × 5) = 10/30 = 1/3
Q419. Square root of 625?
Answer: 25
Explanation:
-
25 × 25 = 625
Q420. Analogy: “Yolk : Egg” is similar to?
Answer: Nucleus : Cell
Explanation:
-
Yolk is central part of egg; Nucleus is central part of cell
Q421. A is 2 years older than B, who is twice as old as C. Total age = 27. Find B.
Answer: 10
Explanation:
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Let C = 5 → B = 2 × 5 = 10, A = B + 2 = 12
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Total = 5 + 10 + 12 = 27 → correct
Q422. 3x − 54 = 36. Find x.
Answer: 30
Explanation:
-
3x − 54 = 36 → 3x = 36 + 54 = 90 → x = 90 ÷ 3 = 30
Q423. A group generated by one of its elements is called?
Answer: Cyclic group
Explanation:
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In group theory, if all elements can be expressed as powers of one element → cyclic group
Q424. A car leaves 21:15 (9:15 PM) and travels for 5.5 hours. What time does it arrive?
Answer: 2:45 AM
Explanation:
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9:15 PM + 2:45 = 12:00 AM
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Remaining 2:45 → 12:00 + 2:45 = 2:45 AM
Q425. Sold for Rs. 220 with 10% profit. Find cost.
Answer: Rs. 200
Explanation:
-
Profit = 10% of cost → 0.1 × 200 = 20 → Cost + Profit = 200 + 20 = 220
Q426. Average of first five multiples of 9?
Answer: 27
Explanation:
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Multiples: 9, 18, 27, 36, 45 → Average = middle number = 27
Q427. 1 gram of gold = ?
Answer: 1000 mg
Explanation:
-
1 gram = 1000 milligrams
Q428. Principal amount becomes Rs. 270.40 in 2 years at 4% compound interest. Find P.
Answer: Rs. 250
Explanation:
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P × (1 + 0.04)² = 270.40 → P × 1.0816 = 270.40 → P = 250
Q429. One nautical mile per hour = ?
Answer: 1 knot
Explanation:
-
By definition, 1 knot = 1 nautical mile per hour
Q430. A is twice as old as B. 3 years ago, A was 3× B. Find A now.
Answer: 12
Explanation:
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Let B = 6 → A = 12
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3 years ago: B = 3, A = 9 → 9 = 3 × 3 → correct
