Is BG EC?

Question

Picture_2.png Is BG > EC? (1) The area of triangle ABC is greater than the area of triangle DEF. (2) AD = CF Kudos for a correct solution .

romitsn · Accepted Answer

Statement 1 
If the area of triangle ABC > area of triangle DEF
 \frac{1}{2} *AC*BG >  \frac{1}{2} *DF*EC
or, AC*BG > DF*EC

Since we don't know the ratio of AC to DF we cannot comment on whether BG > EC.

Statement 2 
Given , AD = CF
Adding DC on both sides,
AD + DC = CF + DC
or, AC = DF
 Not sufficient.

Combining (1) and (2), we can say

AC*BG > DF*EC
or,  AC *BG >  AC *EC
or BG > EC

Hence C.

chetan2u · Answer

ans C..
1)statement 1 tells us that the area of triangle ABC is greater than the area of triangle DEF.. this means
 either altitude BG / base AC or both of triangle ABC are > than altitude CE / base DF or both of triangle DEF... insufficient.
2) statement two tells us that base are of equal length.. nothing about altitude ..insufficient
 
combined it tells us that the base are same so the triangle with more area area will have more altitude ... sufficient

pacifist85 · Answer

Also agree with C.

Area of ABC > Area of DEF
 \frac{AC*BG}{2} > \frac{DF*EC}{2}

We still need to know the value or relationship between AC and DF.

AC=DF. It doesn't say anything on its own.

As we can see AD is included in AC and CF in DF. Also, DC is common in both AC and DF. If we take this out, we see that AC = DF.

So,  ANS C

Bunuel · Answer

VERITAS PREP OFFICIAL SOLUTION:

The correct response is (C).

First notice that BG and EC represent the heights of triangles ABC and DEF respectively. To answer this question definitively yes or no, we need to know the values of the heights, or at least how they stack up against each other.

Statement (1) tells us that the area of ABC > the area of DEF. We can translate that into algebra as:

(1/2)(AC)(BG) > (1/2)(DF)(EC)

(AC)(BG) > (DF)(EC)

We still need more information about the bases before we can conclusively say BG > EC.

AC = AD + DC

DF = DC + CF

Statement (2) tells us that AD = CF. If this is true, then the bases are equal. The ONLY way for the area of ABC to be greater than the area of DEF is if BG > EC.

If you chose (A), that tells us that (AC)(BG) > (DF)(EC), but we don’t know “how much” of each base is made up of the overlapping DC. We cannot simply “eyeball” the figure. If you chose (B), this tells us that the bases of the triangles are equal, but without more information, we still can’t tell whether the heights are equal, or if one is larger than the other.

If you chose (D), we need BOTH pieces of information to answer the question definitively. Only by knowing that the area of one triangle is greater AND the bases are equal can we make a determination about the relationship between the heights.

If you chose (E), even though we cannot find VALUES for the heights, the information is sufficient because this is a Y/N question involving an inequality. Sometimes on Data Sufficiency question, you can achieve sufficiency even without knowing the concrete values!

bumpbot · Answer

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Is BG > EC?

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