If a, b, c, d, and e are integers and cde=0 (GMATPrep Softwa

[nancydong2012]

Hi, just got this problem (Data Sufficiency on GMATPrep Exam) and can't seem to find any forum posts on this specific problem.


GMAT Prep 11/21 (purchased extra Exam prep pack)


If a, b, c, d, and e are integers and cde=0, is d=0?
(1) abc=30
(2) ace=0

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I initially put C, but the OA is E.

My rationale:

(1) abc=30. Here we know that if cde=0, then c is a non-zero integers. If they were zero, then abc=0, but abc=30. Back to the original question, we now know that c is NOT 0. But either d or e could still be 0 (or both d and e could be 0). INSUFFICIENT.

(2) ace=0. Here we know that one of the integers is 0. It is either a, c, or e. Or it is a combination of those 3 integers. We know nothing about d still.

(1) and (2). From (1) we know that either d or e is 0. From (2) we know that either a, c, or e is 0. Both (1) and (2) together we then know that e is 0, contributing to cde=0. D is NOT 0, which answers the question. Thus I answered C.

However, the OA of E suggests that neither provides sufficient enough evidence. My bigger question is - is this because d could ALSO be 0? I was under the impression that if GMAT presents different letters such as a, b, c, d, and e -- then that means they are DIFFERENT integers. Do I have the wrong assumption here?

[stucked]

Hi Nancy,

Lets look at the problem first,
a,b,c,d,e are integers and cde=0. This means any c,d or e or all three can be zero.
(1) Lets look at statement 1. abc=30. That means none of a,b,c is zero.
Now as stated in the question cde=0 and we know now that c is no zero. Therefore we have 3 possibilities:
d=0
e=0
both d and e is zero.

If e=0, to be cde=0 to be true, d may or may not be zero.We cannot tell precisely the nature of d as zero or non zero. So answer choices AD are eliminated

(2) Now lets see statement 2. ace=0
This is possible when:
a=0, c=0, e=0 or three of them(a,c,e) are zero.
if c or e is zero, d may or may not be zero. Answer choice B is elimated.

Now lets see both of the statements together. We know:
c is clearly not zero.
e could or could not be zero.
If e is zero cde=0, while d may or may not be zero.
If e is not zero, d has to be zero.

So taking both statements together is no help too to determine d if zero or not. So E is the correct answer.

Hope this helps

Ashahid

[RonPurewal]

However, the OA of E suggests that neither provides sufficient enough evidence. My bigger question is - is this because d could ALSO be 0? I was under the impression that if GMAT presents different letters such as a, b, c, d, and e -- then that means they are DIFFERENT integers. Do I have the wrong assumption here?

If they mean different integers, they'll say "different integers". Otherwise, no.

In general, you should assume a lack of restrictions, unless restrictions are actually stated. E.g., if the problem statement says that ABCD is a rectangle, that doesn't rule out the possibility that ABCD is actually a square.