Tricky aptitude Question with Solution

1)If a positive integer n is divided by 5, the remainder is 3. Which of the numbers below yields a remainder of 0 when it is divided by 5?

A) n + 3 B) n + 2 C) n - 1 D) n - 2 E) n + 1

Solution

n divided by 5 yields a remainder equal to 3 is written as follows

n = 5 k + 3 , where k is an integer.

add 2 to both sides of the above equation to obtain

n + 2 = 5 k + 5 = 5(k + 1)

The above suggests that n + 2 divided by 5 yields a remainder equal to zero. The answer is B.

2) If an integer n is divisible by 3, 5 and 12, what is the next larger integer divisible by all these numbers?

A) n + 3 B) n + 5 C) n + 12 D) n + 60 E) n + 15

Solution

If n is divisible by 3, 5 and 12 it must a multiple of the lcm of 3, 5 and 12 which is 60.

n = 60 k

n + 60 is also divisible by 60 since

n + 60 = 60 k + 60 = 60(k + 1)

The answer is D.

3) What is the smallest integer that is multiple of 5, 7 and 20?

A) 70 B) 35 C) 200 D) 280 E) 140

Solution

It is the lcm of 5, 7 and 20 which is 140.

The answer is E.

4) When the integer n is divided by 8, the remainder is 3. What is the remainder if 6n is divided by 8?

A) 0 B) 1 C) 2 D) 3 E) 4

Solution

When n is divided by 8, the remainder is 3 may be written as

n = 8 k + 3

multiply all terms by 6

6 n = 6(8 k + 3) = 8(6k) + 18

Write 18 as 16 + 2 since 16 = 8 * 2.

= 8(6k) + 16 + 2

Factor 8 out.

= 8(6k + 2) + 2

The above indicates that if 6n is divided by 8, the remainder is 2. The answer is C