Arithmetic Aptitude for Competitive Exam Success

Arithmetic Aptitude

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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 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 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 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 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

Q. Which polynomial is a factor of x^2 - 5x + 6?

A. x - 2
B. x - 3
C. x + 2
D. x + 3

Solution

x^2 - 5x + 6 factors to (x - 2)(x - 3).

Correct Answer: A — x - 2

Q. Which polynomial is equivalent to 2x + 3x - 4?

A. 5x - 4
B. 5x + 4
C. x - 4
D. x + 4

Solution

Combine like terms: 2x + 3x = 5x, so the polynomial is 5x - 4.

Correct Answer: A — 5x - 4

Q. Which polynomial is equivalent to 2x^2 + 3x - 5 + 4x^2 - x?

A. 6x^2 + 2x - 5
B. 2x^2 + 4x - 5
C. 6x^2 + 4x - 5
D. 4x^2 + 2x - 5

Solution

Combine like terms: (2x^2 + 4x^2) + (3x - x) - 5 = 6x^2 + 2x - 5.

Correct Answer: A — 6x^2 + 2x - 5

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