- If p and q are both positive integers, is q a multiple of 5?

(1) p^{3}.q^{3} = 225^{3}

(2) p is a single digit integer

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April 30, 2018

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- If p and q are both positive integers, is q a multiple of 5?

(1) p^{3}.q^{3} = 225^{3}

(2) p is a single digit integer

**Answer: C .**

**Explanation:**

**1 alone:**

p and q are positive integers, p.q = 225 = 3.3.5.5. Therefore p and q can have any values.

Suppose, p can be 9, and q can be 25 (YES) – q is multiple of 5.

p can be 25 and q can be 9 (NO) – q is not a multiple of 5.

Insufficient

**2 alone:**

p is a single digit integer and nothing about q.

Insufficient

**1 and 2 together:**

p.q = 225 and p is a single digit integer.

So p can be 1, 3, 5 or 9 and corresponding values of q are 225, 75, 45, and 25(YES) – in each case ‘q’ will be multiple of 5.

Sufficient

**Hence the correct answer C.**

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