Question : If the number p is 5 more than q and the sum of the square of p and q is 55, then the product of p and q is:
Option 1: 10
Option 2: –10
Option 3: 15
Option 4: –15
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Correct Answer: 15
Solution : Given: p = q + 5 ⇒ p – q = 5 Also, p 2 + q 2 = 55 ⇒ p 2 + q 2 – 2pq + 2pq = 55 ⇒ (p – q) 2 + 2pq = 55 ⇒ 25 + 2pq = 55 ⇒ 2pq = 30 $\therefore$ pq = 15 Hence, the correct answer is 15.
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