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Quantitative Aptitude

ByAditya

Quantitative Aptitude

Arithmetic

  1. What is the value of 7+8×5−6÷27 + 8 \times 5 – 6 \div 27+8×5−6÷2?
    • A) 39
    • B) 38
    • C) 40
    • D) 42
    • Answer: C) 40
    • Explanation: According to the order of operations (PEMDAS/BODMAS), we first do multiplication and division from left to right, and then addition and subtraction: 7+(8×5)−(6÷2)=7+40−3=47−3=44 7 + (8 \times 5) – (6 \div 2) = 7 + 40 – 3 = 47 – 3 = 447+(8×5)−(6÷2)=7+40−3=47−3=44.
  2. What is the largest two-digit prime number?
    • A) 89
    • B) 97
    • C) 91
    • D) 93
    • Answer: B) 97
    • Explanation: A prime number is a number greater than 1 with no divisors other than 1 and itself. The prime numbers between 90 and 100 are 97.
  3. If a train travels at a speed of 60 km/h for 5 hours, how far does it travel?
    • A) 200 km
    • B) 300 km
    • C) 240 km
    • D) 150 km
    • Answer: B) 300 km
    • Explanation: Distance = Speed × Time. Therefore, Distance = 60 km/h × 5 h = 300 km.
  4. What is the square root of 144?
    • A) 10
    • B) 12
    • C) 14
    • D) 16
    • Answer: B) 12
    • Explanation: The square root of 144 is 12 because 12×12=14412 \times 12 = 14412×12=144.
  5. If 4x=204x = 204x=20, what is the value of xxx?
    • A) 2
    • B) 4
    • C) 5
    • D) 6
    • Answer: C) 5
    • Explanation: Solve for xxx by dividing both sides of the equation by 4: x=204=5x = \frac{20}{4} = 5x=420​=5.

Algebra

  1. What is the value of xxx in the equation 2x+3=112x + 3 = 112x+3=11?
    • A) 3
    • B) 4
    • C) 5
    • D) 6
    • Answer: B) 4
    • Explanation: Subtract 3 from both sides and then divide by 2: 2x+3=112x + 3 = 112x+3=11 2x=82x = 82x=8 x=4x = 4x=4.
  2. Solve for yyy in the equation 3y−4=113y – 4 = 113y−4=11:
    • A) 3
    • B) 4
    • C) 5
    • D) 6
    • Answer: C) 5
    • Explanation: Add 4 to both sides and then divide by 3: 3y−4=113y – 4 = 113y−4=11 3y=153y = 153y=15 y=5y = 5y=5.
  3. What is the value of 3a+4b3a + 4b3a+4b if a=2a = 2a=2 and b=3b = 3b=3?
    • A) 17
    • B) 18
    • C) 19
    • D) 20
    • Answer: B) 18
    • Explanation: Substitute the values of aaa and bbb: 3(2)+4(3)=6+12=183(2) + 4(3) = 6 + 12 = 183(2)+4(3)=6+12=18.
  4. If x−3=7x – 3 = 7x−3=7, what is xxx?
    • A) 8
    • B) 9
    • C) 10
    • D) 11
    • Answer: C) 10
    • Explanation: Add 3 to both sides: x−3=7x – 3 = 7x−3=7 x=10x = 10x=10.
  5. Solve for xxx: 5x+2=3x+105x + 2 = 3x + 105x+2=3x+10:
    • A) 4
    • B) 3
    • C) 2
    • D) 1
    • Answer: C) 2
    • Explanation: Subtract 3x3x3x from both sides and then subtract 2 from both sides: 5x+2=3x+105x + 2 = 3x + 105x+2=3x+10 2x+2=102x + 2 = 102x+2=10 2x=82x = 82x=8 x=4x = 4x=4.

Geometry

  1. What is the area of a rectangle with length 10 units and width 5 units?
    • A) 50 square units
    • B) 40 square units
    • C) 30 square units
    • D) 20 square units
    • Answer: A) 50 square units
    • Explanation: Area of a rectangle = Length × Width = 10 × 5 = 50 square units.
  2. What is the perimeter of a square with side length 7 units?
    • A) 14 units
    • B) 28 units
    • C) 21 units
    • D) 35 units
    • Answer: B) 28 units
    • Explanation: Perimeter of a square = 4 × Side length = 4 × 7 = 28 units.
  3. What is the circumference of a circle with radius 4 units? (Use π=3.14\pi = 3.14π=3.14)
    • A) 25.12 units
    • B) 26.12 units
    • C) 27.12 units
    • D) 28.12 units
    • Answer: A) 25.12 units
    • Explanation: Circumference of a circle = 2πr = 2 × 3.14 × 4 = 25.12 units.
  4. If the area of a triangle is 20 square units and the base is 10 units, what is the height?
    • A) 2 units
    • B) 4 units
    • C) 6 units
    • D) 8 units
    • Answer: B) 4 units
    • Explanation: Area of a triangle = 12×base×height\frac{1}{2} \times \text{base} \times \text{height}21​×base×height. Solve for height: 20=12×10×height20 = \frac{1}{2} \times 10 \times \text{height}20=21​×10×height. 20=5×height20 = 5 \times \text{height}20=5×height. Height = 4 units.
  5. What is the volume of a cube with side length 3 units?
    • A) 9 cubic units
    • B) 18 cubic units
    • C) 27 cubic units
    • D) 36 cubic units
    • Answer: C) 27 cubic units
    • Explanation: Volume of a cube = Side length³ = 3³ = 27 cubic units.

Percentages

  1. What is 20% of 200?
    • A) 20
    • B) 30
    • C) 40
    • D) 50
    • Answer: C) 40
    • Explanation: 20% of 200 = 20100×200=40\frac{20}{100} \times 200 = 4010020​×200=40.
  2. If a product’s price increases from $50 to $60, what is the percentage increase?
    • A) 15%
    • B) 20%
    • C) 25%
    • D) 30%
    • Answer: B) 20%
    • Explanation: Percentage increase = IncreaseOriginal price×100\frac{\text{Increase}}{\text{Original price}} \times 100Original priceIncrease​×100 =60−5050×100=20= \frac{60 – 50}{50} \times 100 = 20%=5060−50​×100=20.
  3. What is 150% of 80?
    • A) 100
    • B) 120
    • C) 130
    • D) 140
    • Answer: B) 120
    • Explanation: 150% of 80 = 150100×80=120\frac{150}{100} \times 80 = 120100150​×80=120.
  4. If a number is increased by 25%, it becomes 100. What is the original number?
    • A) 60
    • B) 70
    • C) 80
    • D) 90
    • Answer: C) 80
    • Explanation: Let the original number be xxx. x+0.25x=100x + 0.25x = 100x+0.25x=100 1.25x=1001.25x = 1001.25x=100 x=1001.25=80x = \frac{100}{1.25} = 80x=1.25100​=80.
  5. If a product’s price decreases from $80 to $64, what is the percentage decrease?
    • A) 10%
    • B) 15%
    • C) 20%
    • D) 25%
    • Answer: C) 20%
    • Explanation: Percentage decrease = DecreaseOriginal price×100\frac{\text{Decrease}}{\text{Original price}} \times 100Original priceDecrease​×100 =80−6480×100=20= \frac{80 – 64}{80} \times 100 = 20%=8080−64​×100=20.

Ratios and Proportions

  1. What is the ratio of 50 to 200?
    • A) 1:2
    • B) 1:3
    • C) 1:4
    • D) 1:5
    • Answer: C) 1:4
    • Explanation: Simplify the ratio 50200=14=1:4\frac{50}{200} = \frac{1}{4} = 1:420050​=41​=1:4.
  2. If 3a=2b3a = 2b3a=2b, what is the ratio of aaa to bbb?
    • A) 2:3
    • B) 3:2
    • C) 3:4
    • D) 4:3
    • Answer: B) 3:2
    • Explanation: 3a=2b⇒ab=23=3:23a = 2b \Rightarrow \frac{a}{b} = \frac{2}{3} = 3:23a=2b⇒ba​=32​=3:2.
  3. If x:y=4:5x:y = 4:5x:y=4:5 and y:z=6:7y:z = 6:7y:z=6:7, what is x:zx:zx:z?
    • A) 24:35
    • B) 25:35
    • C) 30:35
    • D) 35:24
    • Answer: A) 24:35
    • Explanation: Combine the ratios x:y=4:5x:y = 4:5x:y=4:5 and y:z=6:7y:z = 6:7y:z=6:7: x:y=4:5⇒4:5×6:7=24:35x:y = 4:5 \Rightarrow 4:5 \times 6:7 = 24:35x:y=4:5⇒4:5×6:7=24:35.
  4. If the ratio of apples to oranges is 3:4 and there are 12 apples, how many oranges are there?
    • A) 16
    • B) 15
    • C) 18
    • D) 20
    • Answer: A) 16
    • Explanation: Let the number of oranges be xxx. Then, 34=12x⇒3x=48⇒x=16\frac{3}{4} = \frac{12}{x} \Rightarrow 3x = 48 \Rightarrow x = 1643​=x12​⇒3x=48⇒x=16.
  5. If a car travels 60 km in 1 hour, how far will it travel in 4 hours at the same speed?
    • A) 180 km
    • B) 200 km
    • C) 240 km
    • D) 300 km
    • Answer: C) 240 km
    • Explanation: Distance = Speed × Time. Therefore, Distance = 60 km/h × 4 h = 240 km.

Number Series

  1. What is the next number in the series: 2, 4, 6, 8, __?
    • A) 9
    • B) 10
    • C) 11
    • D) 12
    • Answer: B) 10
    • Explanation: The series increases by 2 each time. Next number = 8 + 2 = 10.
  2. What is the next number in the series: 1, 3, 7, 15, __?
    • A) 25
    • B) 27
    • C) 29
    • D) 31
    • Answer: D) 31
    • Explanation: The pattern is to double the previous number and subtract 1. Next number = 15 × 2 – 1 = 31.
  3. What is the next number in the series: 5, 10, 20, 40, __?
    • A) 60
    • B) 70
    • C) 80
    • D) 90
    • Answer: C) 80
    • Explanation: The series is doubling each time. Next number = 40 × 2 = 80.
  4. What is the next number in the series: 11, 13, 17, 19, __?
    • A) 21
    • B) 23
    • C) 25
    • D) 27
    • Answer: B) 23
    • Explanation: The series alternates between adding 2 and 4. Next number = 19 + 4 = 23.
  5. What is the next number in the series: 2, 5, 10, 17, __?
    • A) 25
    • B) 26
    • C) 28
    • D) 30
    • Answer: C) 26
    • Explanation: The pattern is to add consecutive odd numbers (3, 5, 7, 9). Next number = 17 + 9 = 26.

Simple Interest

  1. What is the simple interest on $1000 at 5% per annum for 3 years?
    • A) $100
    • B) $150
    • C) $200
    • D) $250
    • Answer: B) $150
    • Explanation: Simple Interest = P×R×T100\frac{P \times R \times T}{100}100P×R×T​ =1000×5×3100=150= \frac{1000 \times 5 \times 3}{100} = 150=1001000×5×3​=150.
  2. If $500 is invested at 4% per annum simple interest, what will be the amount after 2 years?
    • A) $520
    • B) $540
    • C) $560
    • D) $580
    • Answer: C) $540
    • Explanation: Simple Interest = P×R×T100\frac{P \times R \times T}{100}100P×R×T​ =500×4×2100=40= \frac{500 \times 4 \times 2}{100} = 40=100500×4×2​=40. Amount = Principal + Interest = 500 + 40 = 540.
  3. How long will it take for $800 to earn $160 as simple interest at a rate of 5% per annum?
    • A) 3 years
    • B) 4 years
    • C) 5 years
    • D) 6 years
    • Answer: B) 4 years
    • Explanation: Simple Interest = P×R×T100\frac{P \times R \times T}{100}100P×R×T​ 160=800×5×T100160 = \frac{800 \times 5 \times T}{100}160=100800×5×T​ 160=40T⇒T=16040=4160 = 40T \Rightarrow T = \frac{160}{40} = 4160=40T⇒T=40160​=4.
  4. If the simple interest on $400 for 2 years is $32, what is the rate of interest?
    • A) 2%
    • B) 3%
    • C) 4%
    • D) 5%
    • Answer: D) 4%
    • Explanation: Simple Interest = P×R×T100\frac{P \times R \times T}{100}100P×R×T​ 32=400×R×210032 = \frac{400 \times R \times 2}{100}32=100400×R×2​ 32=8R⇒R=328=432 = 8R \Rightarrow R = \frac{32}{8} = 432=8R⇒R=832​=4.
  5. Find the simple interest on $1000 at 4% per annum for 3 years.
    • A) $100
    • B) $120
    • C) $140
    • D) $160
    • Answer: B) $120
    • Explanation: Simple Interest = P×R×T100\frac{P \times R \times T}{100}100P×R×T​ =1000×4×3100=120= \frac{1000 \times 4 \times 3}{100} = 120=1001000×4×3​=120.

Compound Interest

  1. What is the compound interest on $1000 at 5% per annum for 2 years?
    • A) $102.50
    • B) $110.25
    • C) $112.50
    • D) $115.00
    • Answer: B) $110.25
    • Explanation: Compound Interest = P(1+R100)T−PP \left(1 + \frac{R}{100}\right)^T – PP(1+100R​)T−P =1000(1+5100)2−1000= 1000 \left(1 + \frac{5}{100}\right)^2 – 1000=1000(1+1005​)2−1000 =1000(1.05)2−1000=1102.50−1000=110.25= 1000 \left(1.05\right)^2 – 1000 = 1102.50 – 1000 = 110.25=1000(1.05)2−1000=1102.50−1000=110.25.
  2. What is the compound interest on $800 at 4% per annum for 3 years?
    • A) $98.56
    • B) $100.00
    • C) $104.48
    • D) $110.24
    • Answer: C) $104.48
    • Explanation: Compound Interest = P(1+R100)T−PP \left(1 + \frac{R}{100}\right)^T – PP(1+100R​)T−P =800(1+4100)3−800= 800 \left(1 + \frac{4}{100}\right)^3 – 800=800(1+1004​)3−800 =800(1.04)3−800≈904.48−800=104.48= 800 \left(1.04\right)^3 – 800 \approx 904.48 – 800 = 104.48=800(1.04)3−800≈904.48−800=104.48.
  3. Find the compound interest on $500 at 6% per annum for 2 years.
    • A) $61.80
    • B) $63.00
    • C) $64.80
    • D) $66.00
    • Answer: C) $64.80
    • Explanation: Compound Interest = P(1+R100)T−PP \left(1 + \frac{R}{100}\right)^T – PP(1+100R​)T−P =500(1+6100)2−500= 500 \left(1 + \frac{6}{100}\right)^2 – 500=500(1+1006​)2−500 =500(1.06)2−500≈564.80−500=64.80= 500 \left(1.06\right)^2 – 500 \approx 564.80 – 500 = 64.80=500(1.06)2−500≈564.80−500=64.80.
  4. If the compound interest on $1000 for 2 years is $104.04, what is the rate of interest?
    • A) 4%
    • B) 5%
    • C) 6%
    • D) 7%
    • Answer: B) 5%
    • Explanation: Compound Interest = P(1+R100)T−PP \left(1 + \frac{R}{100}\right)^T – PP(1+100R​)T−P 104.04=1000(1+R100)2−1000104.04 = 1000 \left(1 + \frac{R}{100}\right)^2 – 1000104.04=1000(1+100R​)2−1000 Solving, (1+R100)2=1.10404⇒R=5\left(1 + \frac{R}{100}\right)^2 = 1.10404 \Rightarrow R = 5%(1+100R​)2=1.10404⇒R=5.
  5. What is the compound interest on $1500 at 3% per annum for 2 years?
    • A) $91.35
    • B) $92.70
    • C) $93.50
    • D) $94.00
    • Answer: A) $91.35
    • Explanation: Compound Interest = P(1+R100)T−PP \left(1 + \frac{R}{100}\right)^T – PP(1+100R​)T−P =1500(1+3100)2−1500= 1500 \left(1 + \frac{3}{100}\right)^2 – 1500=1500(1+1003​)2−1500 =1500(1.03)2−1500≈1591.35−1500=91.35= 1500 \left(1.03\right)^2 – 1500 \approx 1591.35 – 1500 = 91.35=1500(1.03)2−1500≈1591.35−1500=91.35.

Time and Work

  1. If A can do a piece of work in 10 days and B can do it in 15 days, how long will it take for both A and B to do the work together?
    • A) 5 days
    • B) 6 days
    • C) 7 days
    • D) 8 days
    • Answer: B) 6 days
    • Explanation: Work done by A in 1 day = 110\frac{1}{10}101​, Work done by B in 1 day = 115\frac{1}{15}151​. Combined work in 1 day = 110+115=16\frac{1}{10} + \frac{1}{15} = \frac{1}{6}101​+151​=61​. Time taken to complete the work = 6 days.
  2. If A can do a piece of work in 8 days and B can do it in 12 days, how long will it take for both A and B to do the work together?
    • A) 4.8 days
    • B) 5 days
    • C) 4 days
    • D) 6 days
    • Answer: C) 4 days
    • Explanation: Work done by A in 1 day = 18\frac{1}{8}81​, Work done by B in 1 day = 112\frac{1}{12}121​. Combined work in 1 day = 18+112=14\frac{1}{8} + \frac{1}{12} = \frac{1}{4}81​+121​=41​. Time taken to complete the work = 4 days.
  3. If 3 workers can complete a job in 15 days, how long will it take for 5 workers to complete the same job?
    • A) 9 days
    • B) 8 days
    • C) 7 days
    • D) 6 days
    • Answer: D) 9 days
    • Explanation: Total work = 3 workers × 15 days = 45 worker-days. Time taken by 5 workers = 455=9\frac{45}{5} = 9545​=9 days.
  4. If A can complete a task in 6 days and B can complete it in 9 days, how long will it take for A and B to complete the task together?
    • A) 3.6 days
    • B) 4 days
    • C) 4.5 days
    • D) 5 days
    • Answer: A) 3.6 days
    • Explanation: Work done by A in 1 day = 16\frac{1}{6}61​, Work done by B in 1 day = 19\frac{1}{9}91​. Combined work in 1 day = 16+19=13.6\frac{1}{6} + \frac{1}{9} = \frac{1}{3.6}61​+91​=3.61​. Time taken to complete the work = 3.6 days.
  5. If 6 workers can complete a job in 8 days, how many workers are needed to complete the job in 4 days?
    • A) 12 workers
    • B) 10 workers
    • C) 9 workers
    • D) 8 workers
    • Answer: A) 12 workers
    • Explanation: Total work = 6 workers × 8 days = 48 worker-days. Workers needed = 484=12\frac{48}{4} = 12448​=12 workers.

Time and Distance

  1. If a car travels 60 km in 1 hour, how far will it travel in 3 hours?
    • A) 120 km
    • B) 150 km
    • C) 180 km
    • D) 200 km
    • Answer: C) 180 km
    • Explanation: Distance = Speed × Time. Therefore, Distance = 60 km/h × 3 h = 180 km.
  2. A train travels at a speed of 80 km/h. How long will it take to travel 320 km?
    • A) 3 hours
    • B) 4 hours
    • C) 5 hours
    • D) 6 hours
    • Answer: B) 4 hours
    • Explanation: Time = Distance ÷ Speed. Therefore, Time = 320 km ÷ 80 km/h = 4 hours.
  3. If a car travels at 90 km/h for 3.5 hours, how far does it travel?
    • A) 300 km
    • B) 315 km
    • C) 320 km
    • D) 330 km
    • Answer: B) 315 km
    • Explanation: Distance = Speed × Time. Therefore, Distance = 90 km/h × 3.5 h = 315 km.
  4. A person walks at a speed of 5 km/h. How long will it take to walk 20 km?
    • A) 3 hours
    • B) 4 hours
    • C) 5 hours
    • D) 6 hours
    • Answer: C) 5 hours
    • Explanation: Time = Distance ÷ Speed. Therefore, Time = 20 km ÷ 5 km/h = 5 hours.
  5. A cyclist travels at a speed of 15 km/h. How far will the cyclist travel in 2 hours 30 minutes?
    • A) 35 km
    • B) 37.5 km
    • C) 40 km
    • D) 42.5 km
    • Answer: B) 37.5 km
    • Explanation: Convert time to hours: 2 hours 30 minutes = 2.5 hours. Distance = Speed × Time. Therefore, Distance = 15 km/h × 2.5 h = 37.5 km.

Averages

  1. What is the average of the numbers 2, 4, 6, 8, and 10?
    • A) 5
    • B) 6
    • C) 7
    • D) 8
    • Answer: B) 6
    • Explanation: Average = Sum of numbersNumber of items\frac{\text{Sum of numbers}}{\text{Number of items}}Number of itemsSum of numbers​ =2+4+6+8+105=305=6= \frac{2 + 4 + 6 + 8 + 10}{5} = \frac{30}{5} = 6=52+4+6+8+10​=530​=6.
  2. The average of five numbers is 20. What is the sum of the numbers?
    • A) 80
    • B) 90
    • C) 100
    • D) 110
    • Answer: C) 100
    • Explanation: Sum = Average × Number of items =20×5=100= 20 \times 5 = 100=20×5=100.
  3. The average of three numbers is 15. If two of the numbers are 12 and 18, what is the third number?
    • A) 14
    • B) 15
    • C) 16
    • D) 17
    • Answer: C) 16
    • Explanation: Sum = Average × Number of items =15×3=45= 15 \times 3 = 45=15×3=45. Sum of first two numbers = 12 + 18 = 30. Third number = 45 – 30 = 15.
  4. The average of four numbers is 8. If three of the numbers are 7, 9, and 10, what is the fourth number?
    • A) 5
    • B) 6
    • C) 7
    • D) 8
    • Answer: B) 6
    • Explanation: Sum = Average × Number of items =8×4=32= 8 \times 4 = 32=8×4=32. Sum of first three numbers = 7 + 9 + 10 = 26. Fourth number = 32 – 26 = 6.
  5. If the average of five numbers is 18 and the sum of four of these numbers is 72, what is the fifth number?
    • A) 15
    • B) 16
    • C) 18
    • D) 20
    • Answer: D) 18
    • Explanation: Sum = Average × Number of items =18×5=90= 18 \times 5 = 90=18×5=90. Fifth number = 90 – 72 = 18.

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