Arithmetic Aptitude for Competitive Exam Success

Arithmetic Aptitude

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Q. If 2x + 3 = 11, what is the value of x?

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

Solution

2x = 11 - 3 = 8, so x = 8/2 = 4.

Correct Answer: B — 3

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

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

Solution

Adding 3 to both sides gives 2x = 8, so x = 4.

Correct Answer: B — 2

Q. If 2x - 3 = 7, what is the value of x?

A. 2
B. 3
C. 5
D. 7

Solution

2x = 10, so x = 5.

Correct Answer: C — 5

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

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

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

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

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

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

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

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

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

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

Q. If a number is divisible by both 2 and 3, what is it also divisible by?

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

Solution

A number divisible by both 2 and 3 is also divisible by their least common multiple, which is 6.

Correct Answer: C — 6

Q. If a number is divisible by both 2 and 3, what is the smallest number it could be?

A. 6
B. 12
C. 3
D. 9

Solution

The least common multiple of 2 and 3 is 6.

Correct Answer: A — 6

Q. If a number is divisible by both 2 and 3, what is the smallest possible value?

A. 2
B. 3
C. 6
D. 12

Solution

The least common multiple of 2 and 3 is 6.

Correct Answer: C — 6

Q. If a number is divisible by both 4 and 6, what is the smallest positive integer that is also divisible by 12?

A. 12
B. 24
C. 36
D. 48

Solution

The least common multiple of 4 and 6 is 12.

Correct Answer: A — 12

Q. If a number is divisible by both 4 and 6, what is the smallest positive integer it can be?

A. 12
B. 24
C. 6
D. 8

Solution

The least common multiple of 4 and 6 is 12.

Correct Answer: A — 12

Q. If a number is divisible by both 4 and 6, what is the smallest possible value?

A. 12
B. 24
C. 36
D. 48

Solution

The least common multiple of 4 and 6 is 12.

Correct Answer: A — 12

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

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

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

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

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

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

Q. If a sequence is defined as a_n = 2n + 1, what is a_5?

A. 9
B. 10
C. 11
D. 12

Solution

a_5 = 2(5) + 1 = 10 + 1 = 11.

Correct Answer: A — 9

Q. If a sequence is defined as a_n = 3n + 1, what is a_4?

A. 10
B. 11
C. 12
D. 13

Solution

a_4 = 3(4) + 1 = 12 + 1 = 13.

Correct Answer: B — 11

Q. If a sequence is defined as a_n = 3n + 2, what is a_4?

A. 10
B. 14
C. 12
D. 8

Solution

a_4 = 3(4) + 2 = 12 + 2 = 14.

Correct Answer: B — 14

Q. If a sequence is defined by a_n = 2n + 1, what is a_4?

A. 7
B. 8
C. 9
D. 10

Solution

a_4 = 2(4) + 1 = 8 + 1 = 9.

Correct Answer: A — 7

Q. If a sequence is defined by a_n = 3n + 1, what is a_4?

A. 10
B. 11
C. 12
D. 13

Solution

Substituting n = 4 gives a_4 = 3(4) + 1 = 12 + 1 = 13.

Correct Answer: B — 11

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