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divisible by 2, 5 and 7

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divisible by 2, 5 and 7

by sanju09 » Sat Jun 19, 2010 12:55 am
If n is a positive integer divisible by 2, 5 and 7, which of the following is true?

I. n^2 + 100 is divisible by 100
II. n + 28 is divisible by 14
III. n^2 + 1 is divisible by 2

(A) I and II only
(B) II and III only
(C) I and III only
(D) I, II and III
(E) None
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by amising6 » Sat Jun 19, 2010 1:02 am
sanju09 wrote:If n is a positive integer divisible by 2, 5 and 7, which of the following is true?

I. n^2 + 100 is divisible by 100
II. n + 28 is divisible by 14
III. n^2 + 1 is divisible by 2

(A) I and II only
(B) II and III only
(C) I and III only
(D) I, II and III
(E) None
I. n^2 + 100 is divisible by 100
if n is divisible by 2,5,7
then n^2 will be divisible by 4,25,49
let say for example take 70 which is divisble by 2,5,7 so 70^2=4900 is divisble by 4,25,49

so n^2 will be divisble by 4and 25 so we can say it will be divisible by 100
n^2 + 100 will also be divisible by 100

II. n + 28 is divisible by 14
n is divisble by 2 ,7 so n will also be divisble by 14
n+28 will also be divisible by 14 as 28 is divisble by 14

III. n^2 + 1 is divisible by 2
now n is divisble by 2,5,7 the square would also be divisble by 2,5,7
and it will be even but the moment 1 is added it becomes odd and hence not divisble by 2

so answer A
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