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

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

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New post 03 Oct 2018, 02:58
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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
Spoiler: OA

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

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New post 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.

A is the answer choice.

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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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New post 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.

A is the answer.
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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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