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M05-01

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M05-01  [#permalink]

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New post 15 Sep 2014, 23:24
1
00:00
A
B
C
D
E

Difficulty:

  5% (low)

Question Stats:

93% (00:36) correct 7% (00:40) wrong based on 369 sessions

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Re M05-01  [#permalink]

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New post 15 Sep 2014, 23:24
2
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Re: M05-01  [#permalink]

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New post 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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New post 31 Jul 2019, 22:11
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New post 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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Re: M05-01  [#permalink]

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New post 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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Re: M05-01  [#permalink]

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New post 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

Answer: C
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Re: M05-01  [#permalink]

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New post 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

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

M05-01

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