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# M05-01

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Math Expert
Joined: 02 Sep 2009
Posts: 64242

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15 Sep 2014, 23:24
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5% (low)

Question Stats:

93% (00:36) correct 7% (00:40) wrong based on 369 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
Joined: 02 Sep 2009
Posts: 64242

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15 Sep 2014, 23:24
2
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 $$c = 1$$.

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Joined: 23 Dec 2015
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31 Jul 2019, 18:52
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.
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31 Jul 2019, 22:11
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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06 Aug 2019, 07:37
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.
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Joined: 17 Apr 2020
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09 May 2020, 07:26
We have
a*b*c = 55

And we need to find out the value of c

Simplifying the equation:
c=55/a*b

Statement 1: a=5
Putting this in the equation:
c=55/5*b
c=11/b

From this equation we can understand that for c to be an integer, b can take only 2 values - 1,11.

But we don't know the value of b so statement 1 is not enough. We can rule out options A & D

Statement 2:b=11
Putting this in the equation :

c=55/a*11
c=5/a

Now for c to be an integer a can take only 2 values i.e 1 & 5.
But we don't know a unique value for a. So that takes out option B.

Now using the 2 statements together :
a=5, b=11

We get
c=55/11*5
c=1

Therefore option C is the correct answer.

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Joined: 30 Oct 2019
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09 May 2020, 07:40
(1) a= 5,
So c can be either 1 or 11
Not Sufficient

(2) b=11
So c can be either 1 or 5
Not Sufficient

(1) + (2)
a=5,b=11
c has to be 1
Sufficient

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Joined: 18 Dec 2017
Posts: 1377
Location: United States (KS)
GMAT 1: 600 Q46 V27

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09 May 2020, 08:32
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

a b and c are 3 different integers.

a*b*c=55

Statement 1:

a=5 then b*c=11
b or c can be 1 or 11.

Not sufficient.

Statement 1:

b=11 then a*c=5
a or c can be 1 or 5.

Not sufficient.

Combined: we find unique values of a b and c

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Re: M05-01   [#permalink] 09 May 2020, 08:32

# M05-01

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