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The surface area of a rectangular field was changed so that

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The surface area of a rectangular field was changed so that

by BTGmoderatorLU » Tue Aug 07, 2018 2:14 pm
Source: Veritas Prep

The surface area of a rectangular field was changed so that the length of one of the dimensions was reduced by 10 feet and the length of the other dimension was increased by 20 feet. What was the surface area before these changes were made?

(1) After the changes were made, the surface area was 2,500 square feet.
(2) The length and width of the field were equal after the changes were made.

The OA is C.
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Source: — Data Sufficiency |

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by [email protected] » Tue Aug 07, 2018 6:08 pm
Hi All,

We're told that the surface area of a rectangular field was changed so that one of its dimensions was REDUCED by 10 feet and the other dimension was INCREASED by 20 feet. We're asked for the area of the field BEFORE these changes were made. This question can be solved by TESTing VALUES.

1) AFTER the changes were made, the surface area was 2,500 square feet.
IF....
the dimensions AFTER the change were 50 and 50, then the dimensions BEFORE the change were 60 and 30, so the original area was (60)(30) = 1800 ft^2.
the dimensions AFTER the change were 25 and 100, then the dimensions BEFORE the change could have been 35 and 80, so the original area was (35)(80) = 2800 ft^2.
Fact 1 is INSUFFICIENT

2) The length and width of the field were EQUAL AFTER the changes were made.
IF....
the dimensions AFTER the change were 50 and 50, then the dimensions BEFORE the change were 60 and 30, so the original area was (60)(30) = 1800 ft^2.
the dimensions AFTER the change were 40 and 40, then the dimensions BEFORE the change could have been 50 and 20, so the original area was (50)(20) = 1000 ft^2.
Fact 2 is INSUFFICIENT

Combined, we know...
-After the changes were made, the surface area was 2,500 square feet.
-The length and width of the field were EQUAL after the changes were made.

Since the area AFTER the changes was 2500 square feet, and the two dimensions were EQUAL after the changes were made, the "new" dimensions had to be 50x50. Thus, the dimensions before the change had to be 60x30 and the original area must have been 1800 ft^2.

Combined, SUFFICIENT

Final Answer: C

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Rich
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