The surface area of a rectangular field was changed so that the length

It appears you interpreted the question to mean that one dimension was decreased by 10%, and the other was increased by 20%. If the question had said that, your work (and answer) would be correct. But instead the question says one dimension was decreased by 10 feet, and the other increased by 20 feet. So if x is the original dimension, in feet, that was then decreased, it becomes x-10, and not 0.9x.

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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St 1 not suf to derive the length of each prior to the change.
st 2 not suf as it does not reveal any thing about the present area.

1+2 is suff

X^2=2500
X=50

therefore
one side was 50+10=60
the other 50-20= 30
Area was 60*30

[1] insufficient, for the reasons outlined above, meaning that you cannot solve the equation.
[2] insufficient. it means that the field is actually shapped as a square. So, we would get (x-10)=(y+20) and from that (x-10)^2 = 2500, x=60.
So, we used [1,2] together, ANS C.
Right..?

Statement 1. After the changes were made, the surface area was 2,500 square feet.
Statement 1 gives (l – 10)(b + 20) = 2500. Hence, Insufficient.
Statement 2. The length and width of the field were equal after the changes were made.
Statement 2 gives l – 10 = b + 20
l = b + 30. Hence, Insufficient.
Statement 1 & 2 together. ( l -10)(b + 20) = 2500 & l = b + 30.
(b + 30 – 10)(b + 20) = 2500 = (b + 20)2 .
So, b+ 20 = 50 i.e. b = 30 and l = 60. Hence, sufficient.
Hence, c is the answer.

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