Quantitative Aptitude & Reasoning for Competitive Exams

Quantitative Aptitude & Reasoning

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

Q. What is the value of x in the equation x^2 - 2x - 8 = 0?

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

Solution

Factoring gives (x - 4)(x + 2) = 0, so x = 4 or x = -2.

Correct Answer: C — 4

Q. What is the value of √(16) + √(9)?

A. 5
B. 7
C. 9
D. 11

Solution

√(16) = 4 and √(9) = 3, so 4 + 3 = 7.

Correct Answer: B — 7

Q. What is the value of √(25) - √(16)?

A. 1
B. 3
C. 5
D. 7

Solution

√(25) = 5 and √(16) = 4, so 5 - 4 = 1.

Correct Answer: B — 3

Q. Which of the following is a factor of 30?

A. 5
B. 7
C. 11
D. 13

Solution

5 divides 30 evenly, so it is a factor.

Correct Answer: A — 5

Q. Which of the following is a factor of 36?

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

Solution

6 is a factor of 36 since 36 ÷ 6 = 6.

Correct Answer: B — 6

Q. Which of the following is a prime number?

A. 4
B. 6
C. 9
D. 11

Solution

11 has no divisors other than 1 and itself.

Correct Answer: D — 11

Q. Which of the following is a solution to the equation 2x + 3 = 11?

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

Solution

Solving for x gives 2x = 8, so x = 4.

Correct Answer: C — 4

Q. Which of the following is a solution to the equation x^2 - 4 = 0?

A. -2
B. 0
C. 2
D. Both -2 and 2

Solution

The equation factors to (x - 2)(x + 2) = 0, giving solutions x = -2 and x = 2.

Correct Answer: D — Both -2 and 2

Q. Which of the following is a solution to the equation x^2 - 5x + 6 = 0?

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

Solution

Factoring gives (x-2)(x-3)=0, so x=2 or x=3.

Correct Answer: B — 2

Q. Which of the following is a valid proof for the statement: If n is an even integer, then n^2 is even?

A. n = 2k for some integer k
B. n = 2k + 1
C. n = k^2
D. n = 2k - 1

Solution

If n = 2k, then n^2 = (2k)^2 = 4k^2, which is even.

Correct Answer: A — n = 2k for some integer k

Q. Which of the following is an even integer?

A. 3
B. 5
C. 8
D. 11

Solution

8 is an even integer as it is divisible by 2.

Correct Answer: C — 8

Q. Which of the following is equal to 5^(2/3)?

A. √(25)
B. 5√(5)
C. 25
D. √(125)

Solution

5^(2/3) = (5^(1/3))^2 = 5√(5).

Correct Answer: B — 5√(5)

Q. Which of the following is equivalent to (x^(1/2))^4?

A. x^(2)
B. x^(1)
C. x^(1/4)
D. x^(1/8)

Solution

Using the power of a power property, (x^(1/2))^4 = x^(1/2 * 4) = x^(2).

Correct Answer: A — x^(2)

Q. Which of the following is equivalent to 2^(3) * 2^(2)?

A. 2^(5)
B. 2^(6)
C. 2^(7)
D. 2^(8)

Solution

Using the property a^m * a^n = a^(m+n), we have 2^(3+2) = 2^(5).

Correct Answer: A — 2^(5)

Q. Which of the following is equivalent to 2^(3/2)?

A. √8
B. 4
C. 2√2
D. 8

Solution

2^(3/2) = √(2^3) = √8.

Correct Answer: A — √8

Q. Which of the following is equivalent to 3(2x + 4)?

A. 6x + 12
B. 6x + 4
C. 6x + 8
D. 2x + 12

Solution

Distributing gives 6x + 12.

Correct Answer: A — 6x + 12

Q. Which of the following is equivalent to log10(0.01)?

A. -1
B. -2
C. 1
D. 2

Solution

log10(0.01) = log10(10^-2) = -2.

Correct Answer: B — -2

Q. Which of the following is equivalent to log5(25)?

A. 1
B. 2
C. 0.5
D. 5

Solution

log5(25) = log5(5^2) = 2.

Correct Answer: B — 2

Q. Which of the following is true for the expression 3^(2x) = 27?

A. x = 1
B. x = 2
C. x = 3
D. x = 0

Solution

27 = 3^(3), so 2x = 3, thus x = 3/2.

Correct Answer: A — x = 1

Q. Which of the following is true for the expression 4^(x) = 16?

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

Solution

16 = 4^(2), thus x = 2.

Correct Answer: B — x = 2

Q. Which of the following is true for the expression 5^(x) = 25?

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

Solution

25 = 5^(2), thus x = 2.

Correct Answer: B — x = 2

Q. Which of the following is true for the polynomial x^2 - 5x + 6?

A. It has no real roots
B. It has one real root
C. It has two real roots
D. It is always positive

Solution

The roots are x = 2 and x = 3, so it has two real roots.

Correct Answer: C — It has two real roots

Q. Which of the following is true for √(x^2)?

A. x
B. -x
C.
D. x
.
. x^2

Solution

√(x^2) = |x|.

Correct Answer: C —

Q. Which of the following numbers is divisible by 3?

A. 14
B. 22
C. 27
D. 31

Solution

27 is divisible by 3 since 2 + 7 = 9, which is divisible by 3.

Correct Answer: C — 27

Q. Which of the following numbers is divisible by 6?

A. 14
B. 18
C. 25
D. 30

Solution

18 is divisible by both 2 and 3, hence by 6.

Correct Answer: B — 18

Q. Which of the following numbers is divisible by 9?

A. 123
B. 234
C. 345
D. 456

Solution

456 is divisible by 9 since 4+5+6 = 15, and 15 is divisible by 9.

Correct Answer: D — 456

Q. Which of the following numbers is prime?

A. 4
B. 9
C. 11
D. 15

Solution

11 is only divisible by 1 and itself, making it prime.

Correct Answer: C — 11

Q. Which of the following pairs of numbers has an HCF of 10?

A. 20 and 30
B. 25 and 35
C. 40 and 50
D. 15 and 25

Solution

The HCF of 40 and 50 is 10, as it is the largest number that divides both.

Correct Answer: C — 40 and 50

Q. Which polynomial has a degree of 3?

A. x^2 + 2
B. 2x^3 + x
C. x + 1
D. 3

Solution

The polynomial 2x^3 + x has the highest exponent of 3.

Correct Answer: B — 2x^3 + x

Q. Which polynomial has a root at x = 2?

A. x^2 - 4
B. x^2 + 4
C. x - 2
D. x + 2

Solution

x^2 - 4 = 0 has roots at x = 2 and x = -2.

Correct Answer: A — x^2 - 4

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