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Is the positive integer r a multiple of the positive integer s?

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Bunuel
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Is the positive integer r a multiple of the positive integer s? [#permalink] New post   15 Jul 2019, 00:56
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62% (01:16) correct 38% (01:40) wrong based on 123 sessions
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Is the positive integer r a multiple of the positive integer s?

(1) r + 2s is a multiple of s.
(2) 2r + s is a multiple of s.
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A
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Kinshook
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Re: Is the positive integer r a multiple of the positive integer s? [#permalink] New post   15 Jul 2019, 01:09
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Bunuel wrote:
Is the positive integer r a multiple of the positive integer s?

(1) r + 2s is a multiple of s.
(2) 2r + s is a multiple of s.


Q:Is the positive integer r a multiple of the positive integer s?

#1: r + 2s is a multiple of s.
Since 2s is a multiple of s => r is a multiple of s
SUFFICIENT

#2: 2r + s is a multiple of s.
Since s is a multiple of s => 2r is a multiple of s
Take for example 24(2*12) is a multiple of 24 but 12 is not a multiple of 24.
It is not necessary that r is a multiple of s
NOT SUFFICIENT.

IMO A
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MariemeDieng
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Re: Is the positive integer r a multiple of the positive integer s? [#permalink] New post   25 Jul 2019, 08:46
Kinshook wrote:
Bunuel wrote:
Is the positive integer r a multiple of the positive integer s?

(1) r + 2s is a multiple of s.
(2) 2r + s is a multiple of s.


Q:Is the positive integer r a multiple of the positive integer s?

#1: r + 2s is a multiple of s.
Since 2s is a multiple of s => r is a multiple of s
SUFFICIENT

#2: 2r + s is a multiple of s.
Since s is a multiple of s => 2r is a multiple of s
Take for example 24(2*12) is a multiple of 24 but 12 is not a multiple of 24.
It is not necessary that r is a multiple of s
NOT SUFFICIENT.

IMO A




Did you say 12 is not a multiple of 24?? How come it isn't?
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Re: Is the positive integer r a multiple of the positive integer s? [#permalink] New post   26 Jul 2019, 08:16
Using 1 only
\((r+2s)/s\) should be an integer
this can only be possible if \(r/s\) is an integer. Hence r is a multiple of the positive integer s. Remove C and E.

Using 2 only

\((2r+s)/s\) should be an integer
this can be possible even if \(2r/s\) even if \(r=3 and s=2\) or if r is a multiple of the positive integer s. Insufficient.

Answer is A
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Is the positive integer r a multiple of the positive integer s? [#permalink] New post   27 Jul 2019, 00:40
MariemeDieng wrote:
Kinshook wrote:
Bunuel wrote:
Is the positive integer r a multiple of the positive integer s?

(1) r + 2s is a multiple of s.
(2) 2r + s is a multiple of s.


Q:Is the positive integer r a multiple of the positive integer s?

#1: r + 2s is a multiple of s.
Since 2s is a multiple of s => r is a multiple of s
SUFFICIENT

#2: 2r + s is a multiple of s.
Since s is a multiple of s => 2r is a multiple of s
Take for example 24(2*12) is a multiple of 24 but 12 is not a multiple of 24.
It is not necessary that r is a multiple of s
NOT SUFFICIENT.

IMO A





Did you say 12 is not a multiple of 24?? How come it isn't?


Multiples of 24 are 24,48,72 etc.. 24 is a multiple of 12 but 12 is not a multiple of 24

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Re: Is the positive integer r a multiple of the positive integer s? [#permalink] New post   28 Aug 2019, 12:21
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Hi everyone,

Is the positive integer r a multiple of the positive integer s?

(1) r + 2s is a multiple of s.
Can be written as: r+2s=sk where k is a positive integer
r=sk-2s=s*(k-2)
Since k-2 is an integer r is a multiple of s
Statement 1 is sufficient


(2) 2r + s is a multiple of s.
Can be written as 2r+s=ks where k is a positive integer
r=s*(k-s)/2
Now r is a multiple of s if s or (k-s) can be divided by 2.
Since we cannot verify this information statement 2 is insufficient.


Statement a only is sufficient to answer this question
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Re: Is the positive integer r a multiple of the positive integer s? [#permalink] New post   07 Jan 2022, 20:11
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Re: Is the positive integer r a multiple of the positive integer s? [#permalink]
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