GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 03 Jun 2020, 22:08 ### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # M05-01

Author Message
TAGS:

### Hide Tags

Math Expert V
Joined: 02 Sep 2009
Posts: 64242

### Show Tags

1 00:00

Difficulty:   5% (low)

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

### HideShow timer Statistics

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

_________________
Math Expert V
Joined: 02 Sep 2009
Posts: 64242

### Show Tags

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 $$c = 1$$.

_________________
Intern  B
Joined: 23 Dec 2015
Posts: 3

### Show Tags

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: 64242

### Show Tags

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.
_________________
Tutor D
Joined: 16 May 2019
Posts: 744

### Show Tags

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.
Intern  Joined: 17 Apr 2020
Posts: 1

### Show Tags

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.

Posted from my mobile device
Senior Manager  P
Joined: 30 Oct 2019
Posts: 385
Location: United Kingdom
Concentration: General Management, Technology
GPA: 4

### Show Tags

(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

VP  V
Joined: 18 Dec 2017
Posts: 1377
Location: United States (KS)
GMAT 1: 600 Q46 V27 ### Show Tags

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

_________________
The Moment You Think About Giving Up, Think Of The Reason Why You Held On So Long

Why You Don’t Deserve A 700 On Your GMAT

Learn from the Legend himself: All GMAT Ninja LIVE YouTube videos by topic
You are missing on great learning if you don't know what this is: Project SC Butler Re: M05-01   [#permalink] 09 May 2020, 08:32

# M05-01

Moderators: chetan2u, Bunuel  