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The number 2135, when divided by a positive integer n, leaves a remain

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The number 2135, when divided by a positive integer n, leaves a remain [#permalink]

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The number 2135, when divided by a positive integer n, leaves a remainder r. What is the value of n?

(1) The number 2315, when divided by n, also leaves the same remainder r .
(2) The number 2585, when divided by n, also leaves the same remainder r .
[Reveal] Spoiler: OA

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Kudos [?]: 132619 [0], given: 12326

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Re: The number 2135, when divided by a positive integer n, leaves a remain [#permalink]

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New post 28 Jul 2017, 02:13
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Bunuel wrote:
The number 2135, when divided by a positive integer n, leaves a remainder r. What is the value of n?

(1) The number 2315, when divided by n, also leaves the same remainder r .
(2) The number 2585, when divided by n, also leaves the same remainder r .


Bunuel wrote:
The number 2135, when divided by a positive integer n, leaves a remainder r. What is the value of n?

(1) The number 2315, when divided by n, also leaves the same remainder r .
(2) The number 2585, when divided by n, also leaves the same remainder r .


2135
If
n= 2 then r = 1
n= 3 then r = 2
n= 4 then r = 3
n= 6 then r = 5
n= 8 then r = 1
n= 9 then r = 2

(1) 2315 = pn + r
if
n= 2 then r = 1
n= 3 then r = 2
n= 4 then r = 3

Not sufficient

(2) 2585
if
n=2 then r = 1
n=3 then r = 2

Not sufficient

On combining also not sufficient

E
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Re: The number 2135, when divided by a positive integer n, leaves a remain [#permalink]

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New post 22 Sep 2017, 00:07
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Theory: If two numbers, each divided by n, produce same remainder, then their difference will be multiple of n.

Stmt-1: The difference between 2135 and 2315 is 180. So, n could be any multiple of 10 between 10 and 180 inclusive. Not sufficient

Stmt-2: The difference between 2135 and 2585 is 450. So, n could be any multiple of 10 between 10 and 450 inclusive. Not sufficient

1+2: HCF of 180 and 450 is 90. So, n could be any multiple of 10 between 10 and 90 inclusive, i.e., 10, 20,...., 90. Not sufficient

Answer: E
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Re: The number 2135, when divided by a positive integer n, leaves a remain   [#permalink] 22 Sep 2017, 00:07
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