Quantitative Aptitude & Reasoning for Competitive Exams

Quantitative Aptitude & Reasoning

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

Q. If a number is even, which of the following must also be even?

A. Its square
B. Its cube
C. The sum of it and 2
D. All of the above

Solution

All options result in even numbers when an even number is used.

Correct Answer: D — All of the above

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Q. If a number is even, which of the following must be true?

A. It is divisible by 2
B. It is divisible by 3
C. It is odd
D. It is prime

Solution

An even number is defined as being divisible by 2.

Correct Answer: A — It is divisible by 2

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Q. If a number n is odd, what can we say about n^2?

A. n^2 is even
B. n^2 is odd
C. n^2 is prime
D. n^2 is composite

Solution

The square of an odd number is always odd.

Correct Answer: B — n^2 is odd

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Q. If a person borrows $5000 at a rate of 8% per annum compounded annually, what will be the amount after 2 years?

A. $5832
B. $6000
C. $5200
D. $5400

Solution

Amount = Principal * (1 + Rate)^Time = 5000 * (1 + 0.08)^2 = 5000 * 1.1664 = $5832.

Correct Answer: A — $5832

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Q. If a person buys a watch for $120 and sells it for $150, what is the percentage profit?

A. 20%
B. 25%
C. 30%
D. 35%

Solution

Profit = Selling Price - Cost Price = 150 - 120 = $30. Percentage Profit = (Profit/Cost Price) × 100 = (30/120) × 100 = 25%.

Correct Answer: B — 25%

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Q. If a person earns $5000 and spends $3500, what percentage of his income does he save?

A. 20%
B. 30%
C. 40%
D. 50%

Solution

Savings = Income - Expenditure = 5000 - 3500 = 1500. Savings Percentage = (1500/5000) * 100 = 30%.

Correct Answer: C — 40%

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Q. If a person incurs a loss of 15% on selling a book for $85, what was the cost price?

A. $100
B. $90
C. $95
D. $80

Solution

Let Cost Price = x. Selling Price = x - 15% of x = 0.85x. 0.85x = 85. x = 85/0.85 = 100.

Correct Answer: A — $100

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Q. If a person invests $1000 at a compound interest rate of 8% per annum, what will be the amount after 1 year?

A. $1080
B. $1000
C. $1100
D. $1200

Solution

Amount = 1000 * (1 + 0.08)^1 = 1000 * 1.08 = $1080.

Correct Answer: A — $1080

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Q. If a person invests $1000 at a rate of 5% per annum for 3 years, what will be the total amount at the end of the period using simple interest?

A. $1150
B. $1200
C. $1100
D. $1250

Solution

Simple Interest = Principal * Rate * Time = 1000 * 0.05 * 3 = $150. Total Amount = Principal + Interest = 1000 + 150 = $1150.

Correct Answer: A — $1150

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Q. If a person invests $1000 at a simple interest rate of 5% per annum for 3 years, what will be the total amount at the end?

A. $1150
B. $1200
C. $1100
D. $1250

Solution

Simple Interest = Principal * Rate * Time = 1000 * 5/100 * 3 = 150. Total Amount = Principal + Interest = 1000 + 150 = 1150.

Correct Answer: A — $1150

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Q. If a person invests $1000 at an interest rate of 5% per annum, what will be the total amount after 3 years using simple interest?

A. $1150
B. $1200
C. $1100
D. $1050

Solution

Simple Interest = Principal * Rate * Time = 1000 * 0.05 * 3 = 150. Total Amount = Principal + Interest = 1000 + 150 = 1150.

Correct Answer: A — $1150

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Q. If a person invests $2000 at a simple interest rate of 5% per annum, how much interest will he earn in 3 years?

A. $300
B. $200
C. $150
D. $250

Solution

Simple Interest = PRT = 2000 * 5/100 * 3 = $300.

Correct Answer: A — $300

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Q. If a person invests $5000 at a compound interest rate of 4% per annum, how much will he have after 3 years?

A. $5624.64
B. $6000
C. $5800
D. $5500

Solution

Amount = P(1 + r)^t = 5000(1 + 0.04)^3 = 5000(1.124864) = $5624.64.

Correct Answer: A — $5624.64

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Q. If a person invests $5000 at a compound interest rate of 8% per annum, what will be the total amount after 3 years?

A. $5920
B. $6000
C. $5934
D. $5800

Solution

Amount = 5000 * (1 + 0.08)^3 = 5000 * 1.259712 = $6298.56.

Correct Answer: C — $5934

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Q. If a person mixes two types of tea costing $20 and $30 per kg in the ratio 2:3, what is the cost price per kg of the mixture?

A. $24
B. $26
C. $28
D. $22

Solution

Cost = (2*20 + 3*30) / (2 + 3) = (40 + 90) / 5 = 130 / 5 = $26.

Correct Answer: B — $26

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Q. If a person sells an article for $1200 at a profit of 20%, what was the cost price?

A. $1000
B. $1100
C. $900
D. $1200

Solution

Cost Price = Selling Price / (1 + Profit%) = 1200 / 1.2 = $1000

Correct Answer: A — $1000

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Q. If a person spends 30% of his salary on rent and 20% on food, what percentage of his salary is left?

A. 50%
B. 40%
C. 30%
D. 60%

Solution

Total expenditure = 30% + 20% = 50%. Salary left = 100% - 50% = 50%.

Correct Answer: A — 50%

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Q. If a person walks 5 km in 1 hour, how far will he walk in 3 hours at the same speed?

A. 10 km
B. 12 km
C. 15 km
D. 18 km

Solution

Distance = Speed x Time = 5 km/h x 3 h = 15 km.

Correct Answer: C — 15 km

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Q. If a person walks 5 km in 1 hour, how long will it take to walk 20 km?

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

Solution

Time = Distance / Speed = 20 km / (5 km/h) = 4 hours

Correct Answer: C — 5 hours

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Q. If a person walks at a speed of 4 km/h, how far can he walk in 3 hours?

A. 10 km
B. 12 km
C. 14 km
D. 15 km

Solution

Distance = Speed × Time = 4 km/h × 3 h = 12 km.

Correct Answer: B — 12 km

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Q. If a person walks at a speed of 5 km/h, how long will it take to walk 15 km?

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

Solution

Time = Distance / Speed = 15 km / 5 km/h = 3 hours.

Correct Answer: B — 3 hours

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Q. If a person works 8 hours a day and completes a task in 5 days, what is the total work done in hours?

A. 30 hours
B. 35 hours
C. 40 hours
D. 45 hours

Solution

Total Work = Hours per Day * Days = 8 * 5 = 40 hours

Correct Answer: C — 40 hours

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Q. If a polynomial f(x) = x^2 - 4, what are its roots?

A. -2, 2
B. 0, 4
C. 1, -1
D. 2, 2

Solution

Setting f(x) = 0 gives x^2 - 4 = 0, so x = ±2.

Correct Answer: A — -2, 2

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Q. If a polynomial f(x) = x^2 - 4x + 4, what is f(2)?

A. 0
B. 1
C. 2
D. 4

Solution

f(2) = 2^2 - 4*2 + 4 = 0.

Correct Answer: A — 0

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Q. If a polynomial f(x) = x^2 - 5x + 6, what are its roots?

A. 1 and 6
B. 2 and 3
C. 3 and 2
D. 5 and 1

Solution

Factoring gives (x-2)(x-3) = 0, so roots are 2 and 3.

Correct Answer: B — 2 and 3

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Q. If a product is bought for $80 and sold for $100, what is the profit?

A. $20
B. $15
C. $25
D. $30

Solution

Profit = Selling Price - Cost Price = 100 - 80 = $20.

Correct Answer: A — $20

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Q. If a product is marked at $150 and sold at a discount of 20%, what is the selling price?

A. $120
B. $130
C. $140
D. $110

Solution

Discount = 20% of 150 = 0.20 * 150 = $30. Selling Price = Marked Price - Discount = 150 - 30 = $120.

Correct Answer: A — $120

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Q. If a product is marked at $250 and sold at a discount of 20%, what is the selling price?

A. $200
B. $210
C. $220
D. $230

Solution

Selling Price = Marked Price - Discount = 250 - (20/100 * 250) = 250 - 50 = $200.

Correct Answer: A — $200

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Q. If a product is marked at $500 and sold at a discount of 10%, what is the selling price?

A. $450
B. $400
C. $475
D. $425

Solution

Selling Price = Marked Price - Discount = 500 - (10% of 500) = 500 - 50 = $450.

Correct Answer: C — $475

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Q. If a product is sold for $120 after a profit of 20%, what was the cost price of the product?

A. $80
B. $90
C. $100
D. $110

Solution

Let Cost Price = x. Then, 120 = x + 0.2x => 120 = 1.2x => x = 120/1.2 = $100.

Correct Answer: A — $80

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Quantitative Aptitude & Reasoning

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