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# If r and s are nonzero integers, is r/s an integer ?

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Math Expert
Joined: 02 Sep 2009
Posts: 51185
If r and s are nonzero integers, is r/s an integer ?  [#permalink]

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03 Oct 2018, 02:58
00:00

Difficulty:

35% (medium)

Question Stats:

76% (01:14) correct 24% (02:10) wrong based on 87 sessions

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If r and s are nonzero integers, is r/s an integer ?

(1) r - 1 = (s + 1)(s - 1)
(2) r - s = 20

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If r and s are nonzero integers, is r/s an integer ?  [#permalink]

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Updated on: 04 Oct 2018, 12:30
Bunuel wrote:
If r and s are nonzero integers, is r/s an integer ?

(1) r - 1 = (s + 1)(s - 1)
(2) r - s = 20

It is basically asking if r is divisible by s, in another words is r a multiple of s?

r - 1 = s^2 - 1
r = s^2

r/s = s^2/s = s which is an integer.

Sufficient

r - s = 20

If r = 25 and s = 5 then yes 25/5 = 5 integer

But if r = 26 and s = 6 we get no 26/6 = 13/3 not integer.

insufficient.

Posted from my mobile device

Originally posted by Salsanousi on 03 Oct 2018, 03:09.
Last edited by Salsanousi on 04 Oct 2018, 12:30, edited 1 time in total.
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Re: If r and s are nonzero integers, is r/s an integer ?  [#permalink]

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03 Oct 2018, 03:11
From statement 1:

r-1 = $$s^2$$ - $$1^2$$

r = $$s^2$$ or s = +r or -r.

So r/s is an integer.
Sufficient.

From statement 2:
r-s = 20.

Insufficient.

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Re: If r and s are nonzero integers, is r/s an integer ? &nbs [#permalink] 03 Oct 2018, 03:11
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