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If when a certain integer x is divided by 5, the remainder is 2, then

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If when a certain integer x is divided by 5, the remainder is 2, then  [#permalink]

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New post 04 May 2011, 10:38
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If when a certain integer x is divided by 5, the remainder is 2, then each of the following could also be an integer EXCEPT:

A. x/17
B. x/10
C. x/6
D. x/3
E. x/11
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Re: If when a certain integer x is divided by 5, the remainder is 2, then  [#permalink]

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New post 04 May 2011, 18:29
carollu wrote:
if when a certain integer x is divided by 5, the remainder is 2, then each of the following could also be an integer EXCEPT:

a)x/17
b)x/10
c)x/6
d)x/3
e)x/11


The question tells us that x is not completely divisible by 5 (it leaves a remainder 2). If x is not divisible by 5, it certainly will not be divisible by 10 either because to be divisible by 10, it needs to be divisible by 5 as well as 2. Hence answer (B)

If you want to see examples how other options can be integers, let me give examples where x/5 gives a remainder 2:
x = 17; Completely divisible by 17
x = 12; Completely divisible by 6 and 3
x = 22; Completely divisible by 11
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Re: If when a certain integer x is divided by 5, the remainder is 2, then  [#permalink]

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New post 04 May 2011, 19:08
x = 5k + 2 = 2,12,17,22,27,32

From the list it's eveident that x/10 is the odd man out.

Answer - B
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Re: If when a certain integer x is divided by 5, the remainder is 2, then  [#permalink]

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New post 04 May 2011, 19:37
10 is a multiple of 5.The remainder is lesser than 10.
Hence if we divide the number by 10,remainder will always be 2.

Thus B.
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Re: If when a certain integer x is divided by 5, the remainder is 2, then  [#permalink]

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New post 05 May 2011, 03:14
Thanks guys! After reading your explanations, made me realized it was not difficult! It was really helpful!:)
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Re: If when a certain integer x is divided by 5, the remainder is 2, then  [#permalink]

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New post 05 May 2011, 05:40
Number is x=5n+2. Now 5n will always have 0 or 2 as last digit. When 2 is added to the 5n last digit of number x becomes 2 or 4. For any number to be divisible by 10, last digit should be 0.
Hence x/10 is not an integer
OA. B
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Re: If when a certain integer x is divided by 5, the remainder is 2, then  [#permalink]

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Re: If when a certain integer x is divided by 5, the remainder is 2, then &nbs [#permalink] 16 Apr 2018, 03:12
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