amitmj wrote: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
Statement 1: After the changes were made, the surface area was 2,500 square feet.
Test one case that also satisfies statement 2.
Case 1: After the changes, L=50 and W=50, so that LW = 50*50 = 2500
Since one dimension was reduced by 10 feet (
from 60 to 50), while the other dimension was increased by 20 feet (
from 30 to 50), the original surface area =
60*30 = 1800.
Test one case that DOESN'T also satisfy statement 2.
Case 1: After the changes, L=25 and W=100, so that LW = 25*100 = 2500
If the length was reduced by 10 feet (
from 35 to 25), while the width was increased by 20 feet (
from 80 to 100), the original surface area =
35*80 = 2800.
Since the original surface area can be different values, INSUFFICIENT.
Statement 2: The length and width of the field were equal after the changes were made
Case 1 also satisfies statement 2.
In this case, the original surface area = 1800.
Case 3: After the changes, L=40 and W=40
Since one dimension was reduced by 10 feet (
from 50 to 40), while the other dimension was increased by 20 feet (
from 20 to 40), the original surface area =
50*20 = 1000.
Since the original surface area can be different values, INSUFFICIENT.
Statements combined:
Both statements are satisfied only by Case 1, implying that the original surface area = 1800.
SUFFICIENT.
The correct answer is
C.
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