Given that the length of the side of a square is and that the length of the side is increased by x%. State whether the area of the square is increased by more than 10%.
(1) x < 10 (2) x > 5
A. Statement (1) ALONE is sufficient but Statement (2) ALONE is not sufficient. B. Statement (2) ALONE is sufficient but Statement (1) ALONE is not sufficient. C. BOTH Statements TOGETHER are sufficient, but NEITHER Statement alone is sufficient. D. Each Statement ALONE is sufficient. E. Statements (1) and (2) TOGETHER are NOT sufficient.
Submitted Answers
Student: 2/12/2010 4:22:36 AM
E
Student: 2/21/2010 4:35:40 AM
e
Student: 4/24/2011 10:06:19 PM
B
x is +ve. Case I - consider the min x.. or x as 1 A = 1 * 1 = 1 Increase in length = 1 % of 1 = 0.01 New length = 1.01 New Area = 1.01 * 1.01 = 1.0201
Increase in Area = 0.0201/1 = 2 % which is less than 10%
Now consider x = 10 A = 10 * 10 = 100 Increase in length = 10 % of 10 = 1 New length = 10 + 1 = 11 New area = 11 * 11 = 121 Increase in Area = (121-100)/100 = 21 % which is > 10 % so A alone is not sufficient
B = Consider X = 5 Area = 5 * 5 = 25 Increase in length = 5 % of 5 = 0.25 New length = 5 + 0.25 = 5.25 New Area = 5.25 * 5.25 = 27.56 Increase in Area = 27.56 - 25 = 2.56 = 2.56/25 > 10 %
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Answer