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

 It is currently 16 Feb 2020, 13:17 ### 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.  # Is the product pqr divisible by 12?

Author Message
TAGS:

### Hide Tags

Math Expert V
Joined: 02 Sep 2009
Posts: 61189
Is the product pqr divisible by 12?  [#permalink]

### Show Tags

12 00:00

Difficulty:   65% (hard)

Question Stats: 43% (00:49) correct 57% (00:46) wrong based on 166 sessions

### HideShow timer Statistics

Is the product pqr divisible by 12?

(1) p is a multiple of 3
(2) q is a multiple of 4

_________________
Verbal Forum Moderator V
Status: Greatness begins beyond your comfort zone
Joined: 08 Dec 2013
Posts: 2450
Location: India
Concentration: General Management, Strategy
Schools: Kelley '20, ISB '19
GPA: 3.2
WE: Information Technology (Consulting)
Re: Is the product pqr divisible by 12?  [#permalink]

### Show Tags

1
(1) p is a multiple of 3
We have no information about q and r
Not sufficient
(2) q is a multiple of 4
We have no information about p and r
Not sufficient
Combining 1 and 2 , we get
p*q will be a multiple of 3*4 = 12
But we have no information whether r is an integer or not .
If r is an integer , then the product pqr will be divisible by 12 .
If p=3 , q = 4 and r = 1/12 , then product pqr = 3*4 * (1/12) = 1 , therefore product will not be divisible .

_________________
When everything seems to be going against you, remember that the airplane takes off against the wind, not with it. - Henry Ford
The Moment You Think About Giving Up, Think Of The Reason Why You Held On So Long
Intern  B
Joined: 20 Oct 2014
Posts: 37
GMAT 1: 740 Q49 V42
Re: Is the product pqr divisible by 12?  [#permalink]

### Show Tags

Bunuel wrote:
Is the product pqr divisible by 12?

(1) p is a multiple of 3
(2) q is a multiple of 4

In statement 1, we are not given any information about whether q and/or r are integers or even zero. Thus, statement 1 is insufficient.

Similarly, statement 2 does not provide any information about p and r. Hence, insufficient.

Combining both statements, we still do not know if r is an integer. If r is an integer, pqr will be divisible by 12 and if r is not an integer or r is zero, prq is not divisible by 12.

GMAT Club Legend  V
Joined: 11 Sep 2015
Posts: 4318
Is the product pqr divisible by 12?  [#permalink]

### Show Tags

Top Contributor
Bunuel wrote:
Is the product pqr divisible by 12?

(1) p is a multiple of 3
(2) q is a multiple of 4

Target question: Is the product pqr divisible by 12?
At first glance, it LOOKS like the correct answer is C.
However, we are not told whether ALL of the numbers (p, q and r ) are integers.
Sure, statements 1 and 2 indirectly tell us that p and q are divisible by 3 and 4, but r may or may not be an integer.

Given this, we can go straight to.....

Statements 1 and 2 combined
Statement 1 tells us that p² - q² = 128
Statement 2 tells us that p² - q² = 128
There are many values of p, q and r that satisfy BOTH statements. Here are two:
Case a: p = 3, q = 4 and r = 1. In this case, pqr = (3)(4)(1) = 12, which is divisible by 12. So, the answer to the target question is YES, pqr IS divisible by 12
Case b: p = 3, q = 4 and r = 0.5. In this case, pqr = (3)(4)(0.5) = 6, which is not divisible by 12. So, the answer to the target question is NO, pqr is NOT divisible by 12
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Cheers,
Brent
_________________

Originally posted by GMATPrepNow on 25 May 2018, 05:53.
Last edited by GMATPrepNow on 15 Feb 2019, 09:57, edited 1 time in total.
Manager  B
Joined: 02 Jul 2017
Posts: 67
Re: Is the product pqr divisible by 12?  [#permalink]

### Show Tags

1) p=3k ..not sufficient
2)q=4r..not sufficient where k and r are integers ..
combining1 & 2 ..we have no idea about r ..if it is integer pqr will be divisible by 12 else not ..hence answer is E
Target Test Prep Representative V
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 9415
Location: United States (CA)
Re: Is the product pqr divisible by 12?  [#permalink]

### Show Tags

Bunuel wrote:
Is the product pqr divisible by 12?

(1) p is a multiple of 3
(2) q is a multiple of 4

p is a multiple of 3

Knowing only that p is a multiple of 3 is not sufficient to answer the question. If q and r both = 1, then pqr is not divisible by 12; however, if q and r both = 12, then pqr is divisible by 12. Statement one alone is not sufficient to answer the question.

Statement Two Alone:

q is a multiple of 4

Knowing only that q is a multiple of 4 is not sufficient to answer the question. If p and r both = 1, then pqr is not divisible by 12; however, if p and r both = 12, then pqr is divisible by 12. Statement two alone is not sufficient to answer the question.

Statements One and Two Together:

Using both statements we see that pq is a multiple of 12. However, we are given no information about the value of r. If r = 1/2, then pqr is not divisible by 12; however, if r = 1, then pqr is divisible by 12. Thus, we still do not have enough information to answer the question.

_________________

# Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

VP  V
Joined: 20 Jul 2017
Posts: 1316
Location: India
Concentration: Entrepreneurship, Marketing
WE: Education (Education)
Is the product pqr divisible by 12?  [#permalink]

### Show Tags

1
Bunuel wrote:
Is the product pqr divisible by 12?

(1) p is a multiple of 3
(2) q is a multiple of 4

Important: Note that r is not given as an integer

(1) p is a multiple of 3

We need at least a multiple of 4
—> Insufficient

(2) q is a multiple of 4

We need at least a multiple of 3
—> Insufficient

Combining (1) & (2)

p*q is a multiple of 12. BUT we don’t know whether r is an integer or not

Case1: If r = 1/3 or 1/4 or 1/12 or 1/2
—> p*q*r will not be a multiple of 12

Case2: If r = 1 or 2 or 3 or any integer
—> p*q*r is a multiple of 12

IMO Option E

Pls Hit kudos if you like the solution

Posted from my mobile device Is the product pqr divisible by 12?   [#permalink] 23 Jun 2019, 10:30
Display posts from previous: Sort by

# Is the product pqr divisible by 12?  