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ABCD and AFGE are rectangles and the area of rectangle ABCD

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ABCD and AFGE are rectangles and the area of rectangle ABCD

by Max@Math Revolution » Mon Jul 22, 2019 5:35 pm

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[GMAT math practice question]

ABCD and AFGE are rectangles and the area of rectangle ABCD is 120. What is the area of rectangle AFGE?



1) the area of triangle GBC is 24
2) the area of triangle EGD is 9

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Source: — Data Sufficiency |
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by Max@Math Revolution » Tue Jul 23, 2019 11:54 pm

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=>

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question. We should simplify conditions if necessary.

Since finding the area of a rectangle requires 2 variables, C is most likely to be the answer. So, we should consider conditions 1) & 2) together first. After comparing the number of variables and the number of equations, we can save time by considering conditions 1) & 2) together first.

Conditions 1) & 2)

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Let H be the point of intersection of the extension of FG with side CD. Since the area of rectangle BCHF is twice the area of triangle GBC, condition 1) tells us that the area of rectangle BCHF is 48. Since the area of rectangle EDGH is twice the area of triangle EGD, condition 2) tells us that the area of rectangle EDGF is 18.
Now, the area of rectangle AFGE is the area of rectangle ABCD minus the sum of the areas of rectangles BCHF and EDGH. It is 120 - ( 48 + 18 ) = 120 - 66 = 54.

Therefore, C is the answer.
Answer: C
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