Quantitative Aptitude & Reasoning for Competitive Exams

Quantitative Aptitude & Reasoning

Algebra & Number Theory Arithmetic Aptitude Data Interpretation Geometry & Mensuration Logical Reasoning

Q. If 2^(x) = 32, what is the value of x?

A. 4
B. 5
C. 6
D. 7

Solution

32 = 2^(5), so x = 5.

Correct Answer: B — 5

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Q. If 3^(x) = 81, what is the value of x?

A. 2
B. 3
C. 4
D. 5

Solution

81 = 3^(4), so x = 4.

Correct Answer: C — 4

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Q. If 4x + 2 = 18, what is the value of x?

A. 3
B. 4
C. 5
D. 6

Solution

Subtract 2 from both sides: 4x = 16. Divide by 4: x = 4.

Correct Answer: A — 3

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Q. If 4x^2 - 16 = 0, what is the value of x?

A. x = 2
B. x = -2
C. x = 4
D. x = -4

Solution

Add 16 to both sides: 4x^2 = 16. Divide by 4: x^2 = 4. Thus, x = ±2.

Correct Answer: A — x = 2

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Q. If 5 kg of sugar costing $10 per kg is mixed with 3 kg of sugar costing $15 per kg, what is the average cost per kg of the mixture?

A. $12.50
B. $13.75
C. $14.00
D. $11.00

Solution

Total cost = (5*10 + 3*15) = 50 + 45 = $95. Average cost = 95 / (5 + 3) = 95 / 8 = $11.875.

Correct Answer: B — $13.75

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Q. If 5 workers can complete a job in 10 days, how many days will it take for 10 workers to complete the same job?

A. 5 days
B. 10 days
C. 15 days
D. 20 days

Solution

If 5 workers take 10 days, then 10 workers will take 10/2 = 5 days.

Correct Answer: A — 5 days

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Q. If 5x + 2 = 17, what is the value of x?

A. 2
B. 3
C. 4
D. 5

Solution

Subtract 2 from both sides to get 5x = 15, then divide by 5 to find x = 3.

Correct Answer: B — 3

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Q. If 5x + 3 = 18, what is the value of x?

A. 2
B. 3
C. 4
D. 5

Solution

5x = 18 - 3 = 15, so x = 15/5 = 3.

Correct Answer: B — 3

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Q. If 5x - 10 = 0, what is the value of x?

A. 0
B. 2
C. 5
D. 10

Solution

5x = 10, so x = 10/5 = 2.

Correct Answer: B — 2

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Q. If 5x - 2 = 3x + 6, what is the value of x?

A. x = 2
B. x = 3
C. x = 4
D. x = 5

Solution

Subtract 3x from both sides: 2x - 2 = 6. Add 2: 2x = 8. Divide by 2: x = 4.

Correct Answer: B — x = 3

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Q. If 5x - 3 = 12, what is the value of x?

A. 2
B. 3
C. 4
D. 5

Solution

Add 3 to both sides to get 5x = 15, then divide by 5 to find x = 3.

Correct Answer: B — 3

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Q. If 5x - 3 = 2x + 12, what is the value of x?

A. 3
B. 4
C. 5
D. 6

Solution

Rearranging gives 5x - 2x = 12 + 3, so 3x = 15, thus x = 5.

Correct Answer: B — 4

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Q. If 5x - 3 = 2x + 12, what is x?

A. 3
B. 4
C. 5
D. 6

Solution

5x - 2x = 12 + 3, so 3x = 15, thus x = 5.

Correct Answer: B — 4

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Q. If 5x - 3 = 2x + 6, what is the value of x?

A. 1
B. 2
C. 3
D. 4

Solution

5x - 2x = 6 + 3, so 3x = 9, thus x = 3.

Correct Answer: B — 2

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Q. If 5x - 3 = 2x + 6, what is x?

A. 1
B. 2
C. 3
D. 4

Solution

5x - 2x = 6 + 3, so 3x = 9, thus x = 3.

Correct Answer: B — 2

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Q. If 5x - 7 = 3x + 5, what is the value of x?

A. 1
B. 6
C. 8
D. 4

Solution

Subtract 3x from both sides: 2x - 7 = 5. Add 7 to both sides: 2x = 12. Divide by 2: x = 6.

Correct Answer: A — 1

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Q. If 5x - 7 = 3x + 9, what is the value of x?

A. 8
B. 7
C. 6
D. 5

Solution

Subtract 3x from both sides: 2x - 7 = 9. Add 7: 2x = 16. Divide by 2: x = 8.

Correct Answer: A — 8

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Q. If 5x = 20, what is the value of x?

A. 2
B. 4
C. 5
D. 10

Solution

Dividing both sides by 5 gives x = 4.

Correct Answer: B — 4

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Q. If 5x^2 - 20 = 0, what is the value of x?

A. -2
B. 2
C. 4
D. 0

Solution

Add 20 to both sides: 5x^2 = 20. Divide by 5: x^2 = 4. Thus, x = ±2.

Correct Answer: B — 2

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Q. If 7x + 3 = 24, what is the value of x?

A. 2
B. 3
C. 4
D. 5

Solution

7x = 24 - 3 = 21, so x = 21/7 = 3.

Correct Answer: B — 3

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Q. If a 3x3 matrix is filled with consecutive integers starting from 1, what is the value at the position (2, 2)?

A. 4
B. 5
C. 6
D. 7

Solution

The matrix would be [[1, 2, 3], [4, 5, 6], [7, 8, 9]], so the value at (2, 2) is 5.

Correct Answer: B — 5

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Q. If A = 1, B = 2, C = 3, what is the code for 'CAB'?

A. 123
B. 321
C. 213
D. 132

Solution

C=3, A=1, B=2, so 'CAB' = 312.

Correct Answer: B — 321

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Q. If a = 2^(3) and b = 2^(2), what is the value of a/b?

A. 2^(1)
B. 2^(2)
C. 2^(3)
D. 2^(5)

Solution

a/b = 2^(3)/2^(2) = 2^(3-2) = 2^(1).

Correct Answer: A — 2^(1)

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Q. If a = 3 and b = 2, what is the value of a^(b+1)?

A. 6
B. 9
C. 27
D. 81

Solution

a^(b+1) = 3^(2+1) = 3^3 = 27.

Correct Answer: C — 27

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Q. If a = 3^(1/2), what is a^4?

A. 9
B. 27
C. 81
D. 3

Solution

a^4 = (3^(1/2))^4 = 3^2 = 9.

Correct Answer: C — 81

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Q. If a bank offers a simple interest rate of 5% per annum, how much interest will be earned on a principal of $2,000 after 4 years?

A. $200
B. $300
C. $400
D. $500

Solution

Simple Interest = Principal * Rate * Time = 2000 * 0.05 * 4 = $400

Correct Answer: C — $400

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Q. If a bank offers compound interest at a rate of 10% per annum, how much will $1000 grow in 2 years?

A. $1100
B. $1210
C. $1300
D. $1500

Solution

Amount = Principal × (1 + Rate)^Time = 1000 × (1 + 0.10)^2 = 1000 × 1.21 = $1210.

Correct Answer: B — $1210

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Q. If a boat takes 3 hours to go 36 km upstream, what is the speed of the boat in still water if the speed of the current is 2 km/h?

A. 10 km/h
B. 12 km/h
C. 14 km/h
D. 16 km/h

Solution

Speed upstream = Distance / Time = 36 km / 3 hours = 12 km/h. Speed of boat in still water = Speed upstream + Speed of current = 12 km/h + 2 km/h = 14 km/h.

Correct Answer: B — 12 km/h

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Q. If a bus travels at a speed of 45 km/h, how far can it travel in 3.5 hours?

A. 150 km
B. 160 km
C. 170 km
D. 180 km

Solution

Distance = Speed * Time = 45 km/h * 3.5 h = 157.5 km.

Correct Answer: C — 170 km

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Q. If A can complete a work in 10 days and B can complete the same work in 15 days, how long will they take to complete the work together?

A. 5 days
B. 6 days
C. 7 days
D. 8 days

Solution

A's work rate = 1/10, B's work rate = 1/15. Together, they work at (1/10 + 1/15) = 1/6. Therefore, they will complete the work in 6 days.

Correct Answer: B — 6 days

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Quantitative Aptitude & Reasoning

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