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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: 52227
If r and s are nonzero integers, is r/s an integer ?  [#permalink]

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05 Sep 2017, 03:52
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Difficulty:

45% (medium)

Question Stats:

66% (01:06) correct 34% (01:29) wrong based on 94 sessions

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

(1) s = 3
(2) r – 5s = s^2

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

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05 Sep 2017, 03:58
Bunuel wrote:
If r and s are nonzero integers, is r/s an integer ?

(1) s = 3
(2) r – 5s = s^2

(1) no info abt r..not sufficient

(2) r – 5s = s^2
dividing by s both sides
r/s – 5 = s
now r/s = s+5 (since s is a non zero integer) r/s will be an integer
Sufficient

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

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28 Dec 2017, 20:36
(1) Insufficient: Only s =3 is given, as we dont know value of r.
(2) Sufficient :
r - 5s = s^2
r = s^2 + 5s
r = s ( s + 5)
r /s = ( s + 5)
Now, (s+5) we know is an integer as s is an integer. Therefore, r/s is an integer.
Re: If r and s are nonzero integers, is r/s an integer ? &nbs [#permalink] 28 Dec 2017, 20:36
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