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

The Logical approach to this question will start off with the understanding that since both triangles are regular triangles which share one equal leg (the width of the rectangle), all we need in order to find the ratio between their areas is to find the ratio between their other legs. Statement (1) doesn't relate to AE and EB, but statement (2) does - so the correct answer is (B).

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Let \(w\) be the width of the rectangle. The original question: \(\frac{\frac{AE\cdot w}{2}}{\frac{EB\cdot w}{2}}=\frac{AE}{EB}=?\)

1) We know that \(w=4\), but no information is given about \(AE\) or \(EB\). Thus, we can't get a unique value to answer the original question. \(\implies\) Insufficient

2) We know that \(AE=2\) and \(EB=4\), so \(\frac{AE}{EB}=\frac{2}{4}=\frac{1}{2}\). Thus, the answer to the original question is a unique value. \(\implies\) Sufficient

Answer: B

\(area \ of \ EDA=\frac{1}{2}*AD*AE\)
\(area \ of \ EBC=\frac{1}{2}*BC*BE\)

RATIO =\(\frac{1}{2}*AD*AE/\frac{1}{2}*BC*BE.\) BUT \(AD=BC\), SO RATIO IS \(\frac{AE}{BE}\).
WHICH STATEMENT 2 PROVIDES. imo, OPTION b.

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:

GMAT assassins aren't born, they're made,
Rich

We are finding the area, so we just need 1/2 BH.
They both share the same H so we just need to figure out the Base.
In 1) We are given the H, no thank you GMAT (this won't help us)
2) They give us 2 bases, well if the triangles share the same height then we can just compare the bases. Suff (B)

Wanted: AE/EB?
Height doesn't matter since it cancelled out as it's the same for both

1) Not sufficient

2) Sufficient

Why EDA and EBC triangles are not right triangles here? as both of them are on Rectangular region hences they should be 30 60 90 degree triangle. and only the value of AD then will be sufficient to find out the area.

i have a question on this.

If the questions says "rectangular region" do we automatically assume that opoosite sides are of equal length?
I thought that a rectangle can have 4 sides of different length.

Rectangular region means that we have a rectangle, a quadrilateral with four right angles. So, its opposite sides are parallel and congruent. Check more here: Math: Polygons
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Hi johannaj,

A "quadrilateral" is any 4-sided shape (regardless of the length of the 4 sides). However, there are specific types of quadrilaterals that are based on how the sides (and the angles) relate to one another - including squares, rectangles, parallelograms, etc. - and knowing those math rules is essential to dealing with those shapes when they appear in questions.

GMAT assassins aren't born, they're made,
Rich

which is the common leg that is shared? it seems like 2 independent triangles. Could you please elaborate?

Hi Jaya6,

We're told that in the figure above, ABCD is a RECTANGULAR region. All 3 triangles (EDA, EBC and EDC) all have the SAME height (re: the height of the rectangle), meaning that 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.

GMAT assassins aren't born, they're made,
Rich

Answer: Option B

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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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EMPOWERgmatRichC

Why do the heights cancel out in statement 2? In the drawing, the heights look to be the same, but what if segment EC did not exactly hit the point C (so the height of BC was a bit shorter than AD)?

=1/2bh for ae would be (1/2)(2)(h)/(1/2)(4)h

Hi woohoo921,

We're told that the overall shape is a RECTANGULAR region; this means that in ABCD, there are four 90-degree angles and the two pairs of opposite sides are EQUAL in length. This means that regardless of what the actual height of the rectangle is, the three triangles would all have the SAME height (re: AD = BC = an altitude drawn from E to the side DC, creating a 90-degree angle).

GMAT assassins aren't born, they're made,
Rich

Contact Rich at: Rich.C@empowergmat.com

can the answer not be C?

with st1 we can get AD=BC=4 (since abcd is a rectangle) which are heights of the 2 right-angled triangles resp and from st2 we have AE & BE which are bases of 2 right-angled triangles resp.

then we can find the 2 areas using formula (base*ht)/2

As explained above, to answer the question, you don't need the first statement at all; the second statement alone is enough. This means that the answer is B: Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.

Below are the options for DS questions, and what they mean:

The data sufficiency problem consists of a question and two statements, labeled (1) and (2), in which certain data are given. You have to decide whether the data given in the statements are sufficient for answering the question. Using the data given in the statements, plus your knowledge of mathematics and everyday facts (such as the number of days in July or the meaning of the word counterclockwise), you must indicate whether—

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
C. BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
D. EACH statement ALONE is sufficient to answer the question asked.
E. Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.
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