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Math Expert V
Joined: 02 Sep 2009
Posts: 57298
M05-01  [#permalink]

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1 00:00

Difficulty:   5% (low)

Question Stats: 94% (00:35) correct 6% (00:43) wrong based on 225 sessions

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If $$a$$, $$b$$, and $$c$$ are 3 different integers and $$a * b * c = 55$$, what is the value of c?

(1) a = 5

(2) b = 11

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Math Expert V
Joined: 02 Sep 2009
Posts: 57298
Re M05-01  [#permalink]

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1
Official Solution:

Statement (1) by itself is insufficient. We don't know the value of $$b$$.

Statement (2) by itself is insufficient. We don't know the value of $$a$$.

Statements (1) and (2) combined are sufficient. Taking both statements together, $$a = 5$$ and $$b = 11$$, therefore $$c = 1$$.

Answer: C
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Intern  B
Joined: 23 Dec 2015
Posts: 3
Re: M05-01  [#permalink]

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Hi Bunuel,

shoudnt the answer be E? since in either case, C can take up a value of 1, -1. Am i missing anything? A,b,c are distinct integers not that they are positive only.
Math Expert V
Joined: 02 Sep 2009
Posts: 57298
Re: M05-01  [#permalink]

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san01sin wrote:
Hi Bunuel,

shoudnt the answer be E? since in either case, C can take up a value of 1, -1. Am i missing anything? A,b,c are distinct integers not that they are positive only.

If a = 5 and b = 11, then c can only be 1 for abc to be equal to 55. If c = -1, then abc = -55.
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Intern  S
Joined: 16 May 2019
Posts: 42
Re: M05-01  [#permalink]

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Bunuel wrote:
If $$a$$, $$b$$, and $$c$$ are 3 different integers and $$a * b * c = 55$$, what is the value of c?

(1) a = 5

(2) b = 11

For this problem, I found it useful to start by creating a factor tree. 55 breaks down into 5 x 11, both prime numbers, so the only integer left has to be 1. The rest of the question deals with how negatives and positives interact, since it would not be safe to assume that integers means only positive ones.

Statement (1), as the official solution points out, tells us nothing about "b," so we cannot speculate on which of the other integers "c" may be. Out go (A) and (D).

Statement (2) also reveals nothing about one of the other two unknowns, this time "a," so we are in the same boat as before. (B) is out.

Taken together, we know a * b * c = 55 and, by substitution, that (5) * (11) * c = 55. We could solve this one algebraically, but there is no need, once we understand that a positive times a positive times some unknown to yield a positive product must mean that the unknown is positive itself. Thus, "c" can only be 1, and (C) is the answer. Re: M05-01   [#permalink] 06 Aug 2019, 08:37
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