Scott Woodbury-Stewart

GMAT OFFICIAL GUIDE PS – The product of two negative numbers is 160. If the lesser of the two numbers…

The product of two negative numbers is 160. If the lesser of the two numbers…

Solution:

We are given that the product of two negative numbers is 160 and that the lesser of the two numbers is 4 less than twice the greater.

We can let x = the larger number and y = the smaller number, and we can create the following equations:

(x)(y) = 160

AND

y = 2x – 4

Substituting (2x – 4) for y in the first equation yields:

x(2x – 4) = 160

2x^2 + 4x = 160

x^2 – 2x – 80 = 0

(x – 10)(x + 8) = 0

x = 10 or x = -8

Since x is negative, x = -8 and y = 2(-8) -4 = -20.

Thus, the greater number is -8.

Answer: D

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