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Is the product pqr divisible by 12?

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Is the product pqr divisible by 12?  [#permalink]

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New post 05 Apr 2016, 05:56
11
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A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

44% (00:49) correct 56% (00:45) wrong based on 160 sessions

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Re: Is the product pqr divisible by 12?  [#permalink]

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New post 05 Apr 2016, 06:53
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 .

Answer E
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Re: Is the product pqr divisible by 12?  [#permalink]

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New post 07 Apr 2016, 10:00
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.

Hence, answer is (E).
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Is the product pqr divisible by 12?  [#permalink]

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New post Updated on: 15 Feb 2019, 10:57
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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

Answer: E

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Brent
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Originally posted by GMATPrepNow on 25 May 2018, 06:53.
Last edited by GMATPrepNow on 15 Feb 2019, 10:57, edited 1 time in total.
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Re: Is the product pqr divisible by 12?  [#permalink]

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New post 25 May 2018, 07:04
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
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Re: Is the product pqr divisible by 12?  [#permalink]

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New post 29 May 2018, 09:33
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.

Answer: E
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Is the product pqr divisible by 12?  [#permalink]

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New post 23 Jun 2019, 11:30
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

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Is the product pqr divisible by 12?   [#permalink] 23 Jun 2019, 11:30
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