If cube X has an edge of length e and cube Y has an edge of length e +

Aera of cube x = 6 e²

Aera of cube Y = 6 (e+1)² = 6e²+12e +6

Difference of two aera = 6+12e

Answer A

Surface Area of a cube is \(6a^2\)

So, Difference in the total surface area of cube Y than that of cube X is -

\(= 6 { ( e + 1 )^2 - e^2 }\)

\(= 6 { ( e + 1 - e ) ( e + 1 + e ) }\)

\(= 6 { (1 ) ( 2e + 1) }\)

\(= 12e + 6\), Answer must be (A)
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Option A.
TSA Cube X = 6 e^2
TSA Cube Y = 6 ( e + 1 )^2 = 6e^2 + 12e + 6.
Difference = 6e^2 + 12e + 6 - 6e^2
12e + 6

These kinds of questions (Variables in the Answer Choices - VIACs) can be answered algebraically or using the INPUT-OUTPUT approach.
The posters above have solved the question algebraically, so let's use the INPUT-OUTPUT approach.

Let's say e = 3

Cube X
Each edge has length 3
Since each face of the cube is a SQUARE, the area of ONE face = 3² = 9
So, the area of all SIX faces = (6)(9) = 54

Cube Y
Each edge has length 3 + 1. So, each edge has length 4
Since each face of the cube is a SQUARE, the area of ONE face = 4² = 16
So, the area of all SIX faces = (6)(16) = 96

How much greater is the total surface area of cube Y than that of cube X?
Difference = 96 - 54 = 42

So, when we INPUT e = 3, the answer to the question (i.e., the OUTPUT) is 42

Now we'll examine each answer choice, to see which one yields and output of 42 when we replace e with 3

We get:
A. 12(3) + 6 = 42 Great! Keep.
B. 6(3 + 1)² = 24. We want an output of 42. ELIMINATE B
C. 3 + 1 = 4. We want an output of 42. ELIMINATE C
D. 3 = 3. We want an output of 42. ELIMINATE D
E. 1 = 1. We want an output of 42. ELIMINATE E

Answer: A

Cheers,
Brent
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SA for cube = 6 * (side)^2
SA for X = 6e^2
SQ for Y = 6(e+1)^2

SA for Y - SA for X = 6(e+1)^2 - 6e^2 = 6(e^2 + 2e + 1) -6e^2 = 12e + 6

Hence A
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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

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could you please explain the difference between "how much greater" and "how many greater"?