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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 11 Jan 2017, 03:29
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Kudos [?]: 128669 [0], given: 12181

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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 11 Jan 2017, 04:07
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Bunuel wrote:
When integer b is divided by 13, the remainder is 6. Which of the following cannot be an integer?

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


b is not divided evenly by 13.

26 = 2*13

Answer B

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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 12 Jan 2017, 14:24
Assume B = 19,32,45
A, 13B / 12 : No Integer
B, B/26 : No Integer
C, B/17 : Cannot be an Integer
D, B/12 : No
E, B/6 : No
??
Pls explain. Thanks
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Kudos [?]: 33 [0], given: 101

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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 12 Jan 2017, 15:24
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Bunuel wrote:
When integer b is divided by 13, the remainder is 6. Which of the following cannot be an integer?

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


Assume the number to be 13b + 6

Of the given numbers, only option B has a multiple of 13 in the denominator
But our number can never be a multiple of 13

Hence b/26 cannot be an integer.

Correct Option: B
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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 16 Jan 2017, 17:52
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Bunuel wrote:
When integer b is divided by 13, the remainder is 6. Which of the following cannot be an integer?

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


If, when b is divided by 13, the remainder is 6, then that means b = 13q + 6 for some integer q. Let’s analyze each answer choice to see whether the given expression can produce an integer.

A) 13b/12

We need to see if 13(13q + 6)/12 could equal an integer for some integer value of q. We can choose q = 6. If q = 6, then 13q + 6 = 84, which is is divisible by 12; hence 13(84)/12 is an integer.

B) b/26

Could (13q + 6)/26 result in an integer for some integer value of q? Notice that 26 is exactly 2 times 13. So, for any integer value of q, 13q will either be divisible by 26 (if q is even) or produce a remainder of 13 (if q is odd). Adding 6 to 13q, the expression will either produce a remainder of 6 or 19, but will never produce a remainder of zero. Therefore, (13q + 6)/26 = b/26 can never equal an integer.

Answer: B
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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 26 Jan 2017, 10:29
ScottTargetTestPrep wrote:
Bunuel wrote:
When integer b is divided by 13, the remainder is 6. Which of the following cannot be an integer?

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


If, when b is divided by 13, the remainder is 6, then that means b = 13q + 6 for some integer q. Let’s analyze each answer choice to see whether the given expression can produce an integer.

A) 13b/12

We need to see if 13(13q + 6)/12 could equal an integer for some integer value of q. We can choose q = 6. If q = 6, then 13q + 6 = 84, which is is divisible by 12; hence 13(84)/12 is an integer.

B) b/26

Could (13q + 6)/26 result in an integer for some integer value of q? Notice that 26 is exactly 2 times 13. So, for any integer value of q, 13q will either be divisible by 26 (if q is even) or produce a remainder of 13 (if q is odd). Adding 6 to 13q, the expression will either produce a remainder of 6 or 19, but will never produce a remainder of zero. Therefore, (13q + 6)/26 = b/26 can never equal an integer.

Answer: B



Fot the option (A), if we take q=7 or q=5 then the expression 13(13q+6)/12 will not be an integer. Then, shouldn't the option 'A' be also taken into consideration ?

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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 12 Aug 2017, 08:43
If B is not divided by 13, B can never be divided by its multiple (26, 39, 52....).
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Re: When integer b is divided by 13, the remainder is 6. Which of the foll   [#permalink] 12 Aug 2017, 08:43
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When integer b is divided by 13, the remainder is 6. Which of the foll

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