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If, in the figure above, ABCD is a rectangular region

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If, in the figure above, ABCD is a rectangular region

by AbeNeedsAnswers » Sun May 05, 2019 9:27 pm

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If, in the figure above, ABCD is a rectangular region, what is the value of the ratio of (area of triangle EDA)/(area of triangle EBC)?

(1) AD = 4
(2) AE = 2 and EB = 4

B

Source: Official Guide 2020
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by [email protected] » Sun May 12, 2019 12:23 pm

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Hi All,

We're told that in the figure above, ABCD is a rectangular region. We're asked for the value of the ratio of (area of triangle EDA)/(area of triangle EBC)? This question is based on a couple of Geometry rules. It's worth noting that all 3 triangles (EDA, EBC and EDC) all have the SAME height (so the height of the triangles is actually IRRELEVENT to the question that is asked - as that number will 'cancel out' in the numerator and denominator of the fraction). Thus we ultimately need to know how the two 'bases' of EDA and EBC relate to one another to answer this question.

(1) AD = 4

Fact 1 gives us the height of the triangles, but that does not impact the question at all. The calculation would be:
(1/2)(Base of EDA)(4) / (1/2)(Based of EBC)(4) = ?
(Base of EDA) / (Base of EBC) = ?
Fact 1 is INSUFFICIENT

(2) AE = 2 and EB = 4

Fact 2 gives us the exact lengths of the two 'bases' - and that's all we need to answer the question. The answer would be 2/4 = 1/2
Fact 2 is SUFFICIENT

Final Answer: B

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Re: If, in the figure above, ABCD is a rectangular region

by Scott@TargetTestPrep » Wed May 12, 2021 7:31 am

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AbeNeedsAnswers wrote: ↑
Sun May 05, 2019 9:27 pm
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If, in the figure above, ABCD is a rectangular region, what is the value of the ratio of (area of triangle EDA)/(area of triangle EBC)?

(1) AD = 4
(2) AE = 2 and EB = 4

B

Source: Official Guide 2020
Solution:

Question Stem Analysis:

We need to determine the ratio of the area of triangle EDA to that of triangle EBC. Notice the two triangles have the same height. Therefore, we are really determining the ratio of AE to BE.

Statement One Alone:

Knowing AD (the height of triangle EDA) does not allow us to determine the desired ratio. Statement one alone is not sufficient.

Statement Two Alone:

Recall that in the stem analysis, the ratio of area of triangle EDA to that of triangle EBC is equal to the ratio of AE to BE. Therefore, knowing AE and BE is sufficient to determine the desired ratio. In fact, (area of triangle EDA)/(area of triangle EBC) = AE/BE = 2/4 = 1/2. Statement two alone is sufficient.

Answer: B

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