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## If a^2*b^2*c^3 = 4500. Is b+c = 7 ?

tagged by: VJesus12

This topic has 1 expert reply and 0 member replies

### Top Member

VJesus12 Master | Next Rank: 500 Posts
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Posted:
211 messages

#### If a^2*b^2*c^3 = 4500. Is b+c = 7 ?

Wed Nov 08, 2017 7:40 am
If a^2*b^2*c^3 = 4500. Is b+c = 7 ?

(1) a, b and c are positive integers
(2) a > b

The OA is E.

Experts, can you clarify this DS question to me? I don't have it clear. Some friends told me the answer should be C. Is this correct?

### GMAT/MBA Expert

Rich.C@EMPOWERgmat.com Elite Legendary Member
Joined
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Posted:
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Wed Nov 08, 2017 6:52 pm
Hi VJesus12,

We're told that (A^2)(B^2)(C^3) = 4500. We're asked if B+C = 7. This is a YES/NO question. This question really tests the 'thoroughness' of your thinking - and it's likely that many Test Takers would get this question wrong because they wouldn't consider all of the possible options.

To start, it would help to 'break down' 4500 into pieces...
4500 = (9)(500) =
(3^2)(5)(100) =
(3^2)(5)(2^2)(5^2) =
(2^2)(3^2)(5^3)

Based on the starting equation, we know that C MUST be +5. However, there are more than just these two possible values for A and B. Since we're SQUARING terms, A and B could be (2 or -2) and (3 or -3). In addition, this question is NOT forcing us to deal with Prime Numbers, so there is another option besides "2 and 3" to consider.... "1 and 6" is another possible pairing of values for A and B....
(1^2)(6^2)(5^3)
...meaning that we would have to also consider that the values could be (1 or -1) and (6 or -6):

(1) A, B and C are POSITIVE integers

IF....
A=2, B=3, C=5 then the answer to the question is NO
A=3, B=2, C=5 then the answer to the question is YES
Fact 1 is INSUFFICIENT

2) A > B
A=3, B=2, C=5 then the answer to the question is YES
A=6, B=1, C=5 then the answer to the question is NO
Fact 2 is INSUFFICIENT

Combined, we already have two groups of values that fit both Facts and produce different answers to the given question:
A=3, B=2, C=5 then the answer to the question is YES
A=6, B=1, C=5 then the answer to the question is NO
Combined, INSUFFICIENT

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

_________________
Contact Rich at Rich.C@empowergmat.com

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