BTGmoderatorDC wrote:The top 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 D
Source: Official Guide
Say the squared top measures a*a = a^2 squared inches.
After the change:
Area = (a - 1)*(a + 2)
We have to get the value of a^2.
Let's take each statement one by one.
(1) After the changes were made, the surface area was 70 square inches.
=> (a - 1)*(a + 2) = 70 => a^2 + a - 2 = 70 => a^2 + a - 72 = 0 => a^2 +9a -8a - 71 = 0 => a(a + 9) -8(a + 9) = 0 => a = 8 or -9. Since a is a positive number, a cannot be - 9. Thus, a = 8. And a^2 = 64. Sufficient.
(2) There was a 25 percent increase in one of the dimensions.
There is a decrease in one dimension and an increase in the other. The increased dimension is (a + 2) from a. There is an increase of 2 inches.
=> (2/a)*100% = 25%
=> a = 8. Thus, a^2 = 64. Sufficient.
The correct answer:
D
Hope this helps!
-Jay
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