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

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Manager
Joined: 02 Jun 2015
Posts: 191
Location: Ghana
When integer b is divided by 13, the remainder is 6. Which of the foll  [#permalink]

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17 Aug 2016, 11:13
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65% (hard)

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55% (02:16) correct 45% (02:35) wrong based on 108 sessions

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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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17 Aug 2016, 11:18
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duahsolo wrote:
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

b is not a multiple of 13 thus it cannot be a multiple of 26 either (26 = 2*13).

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Joined: 12 Mar 2016
Posts: 9
Re: When integer b is divided by 13, the remainder is 6. Which of the foll  [#permalink]

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

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Manager
Joined: 02 Jun 2015
Posts: 191
Location: Ghana
Re: When integer b is divided by 13, the remainder is 6. Which of the foll  [#permalink]

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18 Aug 2016, 01:22
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habil wrote:
Is there another way to approach this problem

Posted from my mobile device

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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18 Aug 2016, 03:24
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
_________________

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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Manager
Joined: 04 Oct 2017
Posts: 77
Re: When integer b is divided by 13, the remainder is 6. Which of the foll  [#permalink]

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24 Jan 2018, 16:31
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?
Math Expert
Joined: 02 Aug 2009
Posts: 7212
Re: When integer b is divided by 13, the remainder is 6. Which of the foll  [#permalink]

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24 Jan 2018, 19:29
1
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

GMAT online Tutor

Re: When integer b is divided by 13, the remainder is 6. Which of the foll &nbs [#permalink] 24 Jan 2018, 19:29
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# When integer b is divided by 13, the remainder is 6. Which of the foll

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