If cube X has an edge of length e and cube Y has an edge of length e + 1, how much greater is the total surface area of

[BTGmoderatorDC]

If cube X has an edge of length e and cube Y has an edge of length e + 1, how much greater is the total surface area of cube Y than that of cube X ?

A. 12e + 6
B. 6(e + 1)2
C. e + 1
D. e
E. 1


OA A

Source: GMAT Prep

[Jay@ManhattanReview]

If cube X has an edge of length e and cube Y has an edge of length e + 1, how much greater is the total surface area of cube Y than that of cube X ?

A. 12e + 6
B. 6(e + 1)2
C. e + 1
D. e
E. 1

OA A

Source: GMAT Prep

Note that the total surface area of a cube = 6*side^2

Total surface area of a cube X = 6e^2;
Total surface area of a cube Y = 6(e +1)^2

Total surface area of cube Y is greater than that of cube X by 6(e +1)^2 – 6e^2 = 12e + 6

The correct answer: A

Hope this helps!

-Jay
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[Scott@TargetTestPrep]

If cube X has an edge of length e and cube Y has an edge of length e + 1, how much greater is the total surface area of cube Y than that of cube X ?

A. 12e + 6
B. 6(e + 1)2
C. e + 1
D. e
E. 1


OA A

Solution:

The total surface area of cube Y is 6(e + 1)^2 = 6(e^2 + 2e + 1) = 6e^2 + 12e + 6.

The total surface area of cube X is 6e^2.

Therefore, the total surface area of cube Y exceeds that of cube X by 12e + 6.

Answer: A