Surface area

[grandh01]

The surface area of a square
tabletop was changed so that one of
the dimensions was reduced by 1
inch and the other dimension was
increased by 2 inches. What was the
surface area before these changes
were made?
(1) After the changes were made, the
surface area was 70 square
inches.
(2) There was a 25 percent increase
in one of the dimensions.

OA is D

[Anurag@Gurome]

The surface area of a square
tabletop was changed so that one of
the dimensions was reduced by 1
inch and the other dimension was
increased by 2 inches. What was the
surface area before these changes
were made?
(1) After the changes were made, the
surface area was 70 square
inches.
(2) There was a 25 percent increase
in one of the dimensions.

OA is D

Say, the length of each side of the square = x inches
We need to find the area of the square = x² sq. inches

After the change, the length of the sides of the rectangle are (x - 1) and (x + 2) inches.

Statement 1:
--> (x - 1)(x + 2) = 70
--> (x² + x - 72) = 0
--> (x - 8)(x + 9) = 0
--> x = 8 or x = -9

As length of a side of a square cannot be negative, x must be equal to 8.

Sufficient

Statement 2: We know only one dimension has been increased.
So, (x + 2) = (x + 25% of x) = (x + x/4) = 5x/4
--> (5/4 - 1)*x =2
--> x/4 = 2
--> x = 8

Sufficient

The correct answer is D.