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When positive integer y is divided by 51, the remainder is x. What is

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When positive integer y is divided by 51, the remainder is x. What is [#permalink]

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When positive integer y is divided by 51, the remainder is x. What is the remainder when y is divided by 17?

(1) When y is divided by 34 the remainder is zero.
(2) x = 17
[Reveal] Spoiler: OA

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Re: When positive integer y is divided by 51, the remainder is x. What is [#permalink]

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New post 20 Apr 2016, 07:41
IMO D

if y is divisible by 34 the it is also divisible by 17 as 34 is multiple of 17

also y=51K+x, 51x is divisible by 17 and x is is 17

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Re: When positive integer y is divided by 51, the remainder is x. What is [#permalink]

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New post 20 Apr 2016, 22:25
When positive integer y is divided by 51, the remainder is x. What is the remainder when y is divided by 17?

(1) When y is divided by 34 the remainder is zero.
(2) x = 17

Given - y is divided by 51, the remainder is x.

y = 51Q+x (Q is an integer) or y = 17 (3Q) + X. ; have to find out the remainder when y is divided by 17.

Statement 1:

y is a multiple of 34. Values that suit this are: 0, 34, 102 etc. All of these are divisible by 17 (as 34 = 17 x 2).

Hence sufficient as remainder for each of the values is 0.

Statement 2:

x = 17.

From the question stem we have y = 17 (3Q) + x. i.e. y = 17 (3Q) + 17.

This means that y = 17 (3Q+1). Always a multiple of 17.

Sufficient.

Answer D.

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Re: When positive integer y is divided by 51, the remainder is x. What is [#permalink]

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New post 12 Aug 2017, 22:14
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Kudos [?]: 287 [0], given: 0

Re: When positive integer y is divided by 51, the remainder is x. What is   [#permalink] 12 Aug 2017, 22:14
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