Hi Radhika11,

This question can be solved with a mix of TESTing VALUES and arithmetic.

We're told that 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. We're asked for the surface area BEFORE the changes were made.

Fact 1: After the changes were made, the surface area was 2,500 square feet.

Using 2,500 square feet as the ENDING area, we can 'work backwards' and consider possibilities for the original dimensions...

IF....

the end dimensions were...50 x 50

the original dimensions were....60 x 30

and the answer to the question is (60)(30) = 1800 square feet

IF....

the end dimensions were...25 x 100

the original dimensions were....35 x 80

and the answer to the question is (35)(80) = 2800 square feet

Fact 1 is INSUFFICIENT

Fact 2: The length and width of the field were EQUAL after the changes were made.

IF....

the end dimensions were...50 x 50

the original dimensions were....60 x 30

and the answer to the question is (60)(30) = 1800 square feet

IF....

the end dimensions were...40 x 40

the original dimensions were....50 x 20

and the answer to the question is (50)(20) = 1000 square feet

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.

The ONLY example that fits BOTH Facts is 50 x 50 (with a final answer of 1800 square feet).

Combined, SUFFICIENT

Final Answer:

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