Kezia9 wrote:

chetan2u wrote:

habil wrote:

Is there another way to approach this problem

Posted from my mobile device

Hi

The logic is same as suggested by Bunuel..

Let the number be b as given..

b =13y+6....

Now substitute b as 13y +6 in all choices and you will get the ans

Hi, I didnot understand. I know b= 13y+6, when I substitute the value of b in the options I still get a fraction. How do I conclude b is an integer?? Can you please assist?

Hi...

When you substitute b as 13y+6, you get INTEGER in following way..

1) b/6....(13y+6)/6=13y/6 + 6/6... So when y is 0, 13y/6 and 6/6 both will give you 0 as Remainder so it will be integer at b=6

2) b/12...(13y+6)/12.. when y is 6.. 13y+6=13*6+6=6(13+1)=6*14=6*2*7=12*7.. so div by 12

3) 13b/52...13(13y+6)/52..whenever y is multiple of 2 but not 4..

13(13*2+6)/52=13*(32)/52=13*4*8/52=52*8/52=8

4) b/17...(13y+6)/17..when y is 10..(13*10+6)/17=136/17=8..

But you may not require all this if you know why b/26 is not an integer..

b/26=(13y+6)/26=13y/26 +6/26..

Now 13y/26 will leave a Remainder of 13 when y is odd and 0 when y is even..

But 6/26 will always leave 6 as Remainder.

Total remainder can be two

1) 13+6=19

2) 0+6=6

Thus there will always be a Remainder of 19 or 6, hence b/26 will never be an integer

Hope this helps

_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372

2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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