The sum of two integers is \(x.\) If the larger integer is greater than the smaller integer by \(8,\) what is the produc

[Gmat_mission]

The sum of two integers is \(x.\) If the larger integer is greater than the smaller integer by \(8,\) what is the product of \(x\) and the smaller integer, in terms of \(x?\)

A. \(x^2 + 12x\)

B. \(2x^2 - 8\)

C. \(\dfrac{x^2}2 - 4x\)

D. \(x^2 - 8x\)

E. \(\dfrac{x^2}2 + 4x - 8\)

Answer: C

Source: Princeton Review

[Scott@TargetTestPrep]

The sum of two integers is \(x.\) If the larger integer is greater than the smaller integer by \(8,\) what is the product of \(x\) and the smaller integer, in terms of \(x?\)

A. \(x^2 + 12x\)

B. \(2x^2 - 8\)

C. \(\dfrac{x^2}2 - 4x\)

D. \(x^2 - 8x\)

E. \(\dfrac{x^2}2 + 4x - 8\)

Answer: C

Solution:

We can let s be the smaller integer, and thus the larger integer is s + 8. We can create the equation:

s + (s + 8) = x

2s + 8 = x

2s = x - 8

s = (x - 8)/2 = x/2 - 4

Therefore, the product of x and the smaller integer is:

x(x/2 - 4) =(x^2)/2 - 4x

Answer: C