Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 10129
Given Kudos: 4
GPA: 3.82
Re: The top surface area of a square tabletop was changed so that one of
[#permalink]
21 Dec 2015, 22:41
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.
The surface area of a square tabletop was changed so that one of the dimensions was reduced by 1 inch and the other dimension was increased by 2 inches. What was the surface area before these changes were made?
(1) After the changes were made, the surface area was 70 square inches.
(2) There was a 25 percent increase in one of the dimensions.
In the original condition, suppose one side is x. There is 1 variable(x), which should match with the number of equations. So you need 1 more equation. For 1) 1 equation, for 2) 1 equation, which is likely to make D the answer.
In 1), from (x-1)(x+2)=70, x^2+x-72=0, (x-8)(x+9)=0, x is 8, which is unique and sufficient.
In 2), from 2=0.25x, x is 8, which is unique and sufficient. Therefore, the answer is D.
-> For cases where we need 1 more equation, such as original conditions with “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 59 % chance that D is the answer, while A or B has 38% chance and C or E has 3% chance. Since D is most likely to be the answer using 1) and 2) separately according to DS definition. Obviously there may be cases where the answer is A, B, C or E.