Question

Mark the correct alternative in each of the following:

If x = (−1) × (−1) × (−1) × (−1) × ... 25 times, y = (−3) × (−3) × (−3), then xy

(a) −27 (b) 27 (c) 26 (d) −26

Answer 1

x = (−1) × (−1) × (−1) × (−1) × ... 25 times

The number of integers in the given product is odd.

∴ x = (−1) × (−1) × (−1) × (−1) × ... 25 times

= −(1 × 1 × 1 × ... 25 times)

= −1

y = (−3) × (−3) × (−3)

The number of integers in the given product is odd.

∴ y = (−3) × (−3) × (−3)

= −(3 × 3 × 3)

= −27

So,

xy = (−1) × (−27) = 27 (Product of two negative integers is always positive)

Hence, the correct answer is option (b).