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# MATH QUESTION OF THE DAY

 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 > 5A. 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.
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
 Bx is +ve. Case I - consider the min x.. or x as 1A = 1 * 1 = 1Increase in length = 1 % of 1 = 0.01New length = 1.01New Area = 1.01 * 1.01 = 1.0201Increase in Area = 0.0201/1 = 2 %which is less than 10%Now consider x = 10A = 10 * 10 = 100Increase in length = 10 % of 10 = 1New length = 10 + 1 = 11New area = 11 * 11 = 121Increase in Area = (121-100)/100 = 21 % which is > 10 % so A alone is not sufficientB = Consider X = 5Area = 5 * 5 = 25Increase in length = 5 % of 5 = 0.25New length = 5 + 0.25 = 5.25New Area = 5.25 * 5.25 = 27.56Increase in Area = 27.56 - 25 = 2.56= 2.56/25 > 10 %So B alone is sufficient.