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P and Q are natural numbers. Is P divisible by 12?

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P and Q are natural numbers. Is P divisible by 12?  [#permalink]

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New post Updated on: 30 Sep 2018, 04:11
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P and Q are natural numbers. Is P divisible by 12?

(1) 17P + 24Q = 543
(2) P is eight more than seven times of Q and Q is odd.

Originally posted by aa008 on 30 Sep 2018, 01:16.
Last edited by Bunuel on 30 Sep 2018, 04:11, edited 1 time in total.
Renamed the topic and edited the question.
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Re: P and Q are natural numbers. Is P divisible by 12?  [#permalink]

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New post 30 Sep 2018, 02:09
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P and Q are natural numbers. Is P divisible by 12?

1) 17P+24Q=543
So 17P=543-24Q
Since Q is a positive integer, 17P = odd-even=odd
Therefore P is odd and not divisible by 12
Sufficient

2) P is eight more than seven times of Q and Q is odd.
P=7Q+8 and Q is Odd
So P= 7*odd+even=odd
Thus P is odd and not divisible by 12
Sufficient

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3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


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Re: P and Q are natural numbers. Is P divisible by 12?  [#permalink]

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New post 30 Sep 2018, 09:09
aa008 wrote:
P and Q are natural numbers. Is P divisible by 12?

(1) 17P + 24Q = 543
(2) P is eight more than seven times of Q and Q is odd.

chetan2u´s solution is simple and perfect (and valid for any integers P and Q). Nothing to add.

I would like to comment on the question stem, only.

"Natural numbers" are commonly defined in Mathematics in two ways:

A) 0, 1, 2, 3, 4, ... that is, as a synonym for nonnegative integers
B) 1, 2, 3, 4, ... that is, as a synonym for positive integers

Perhaps because of these two different (but both usual) possibilities, the term is simply not used in the GMAT.

Regards,
Fabio.
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Re: P and Q are natural numbers. Is P divisible by 12?  [#permalink]

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New post 01 Oct 2018, 00:49
Heyaa008 the question is a good quality question. Can you mention the source of the question if possible?
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Re: P and Q are natural numbers. Is P divisible by 12?  [#permalink]

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New post 01 Oct 2018, 01:31
a70 wrote:
Heyaa008 the question is a good quality question. Can you mention the source of the question if possible?



i got it from TIME, Coaching institute for CAT,gmat, and various other exams.
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Re: P and Q are natural numbers. Is P divisible by 12? &nbs [#permalink] 01 Oct 2018, 01:31
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P and Q are natural numbers. Is P divisible by 12?

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