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When integer b is divided by 13, the remainder is 6. Which of the foll

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When integer b is divided by 13, the remainder is 6. Which of the foll [#permalink]

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New post 17 Aug 2016, 12:13
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When integer b is divided by 13, the remainder is 6. Which of the following cannot be an integer?

A) 13b/52
B) b/26
C) b/17
D) b/12
E) b/6

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Re: When integer b is divided by 13, the remainder is 6. Which of the foll [#permalink]

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New post 17 Aug 2016, 12:18
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Re: When integer b is divided by 13, the remainder is 6. Which of the foll [#permalink]

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New post 17 Aug 2016, 18:34
Is there another way to approach this problem

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Re: When integer b is divided by 13, the remainder is 6. Which of the foll [#permalink]

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New post 18 Aug 2016, 02:22
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habil wrote:
Is there another way to approach this problem

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According to Bunuel's solution, since "b" is not divisible by 13, "b" will not be divisible by any integer which has 13 as factor so that b/26 (i.e., 2 * 13) cannot result in an integer.

For option A, 13b/52, even though the denominator has 13 as factor, this is cancelled out by the 13 in the numerator, resulting in an integer.

Alternatively, you can also plug in numbers:

b
6
19 (= 6 + 13)
32 (= 19 + 13)
45 (= 32 + 13)
58 (= 45 + 13)
71 (= 58 + 13)
84 (= 71 + 13)
97 (= 84 + 13)
110 (= 97 + 13)
123 (= 110 + 13)
136 (= 123 + 13)
149 (= 136 + 13)
.
.
. etc

You realise that 6 and 84 are divisible by 6; 84 is divisible by 12; 136 is divisible by 17; but none of the numbers for integer "b" are divisible by 13 or an integer with 13 as a factor!

So b/26 will not result in an integer.

Hope this helps.
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Re: When integer b is divided by 13, the remainder is 6. Which of the foll [#permalink]

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New post 18 Aug 2016, 04:24
habil wrote:
Is there another way to approach this problem

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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
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Re: When integer b is divided by 13, the remainder is 6. Which of the foll [#permalink]

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New post 24 Jan 2018, 17:31
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?
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Re: When integer b is divided by 13, the remainder is 6. Which of the foll [#permalink]

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New post 24 Jan 2018, 20:29
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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
_________________

Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html


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Re: When integer b is divided by 13, the remainder is 6. Which of the foll   [#permalink] 24 Jan 2018, 20:29
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When integer b is divided by 13, the remainder is 6. Which of the foll

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