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If k is an integer such that 56 < k < 66, what is the value

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If k is an integer such that 56 < k < 66, what is the value [#permalink] New post 06 Dec 2012, 06:56
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If k is an integer such that 56 < k < 66, what is the value of k ?

(1) If k were divided by 2, the remainder would be 1.
(2) If k + 1 were divided by 3, the remainder would be 0.
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Re: If k is an integer such that 56 < k < 66, what is the value [#permalink] New post 06 Dec 2012, 06:59
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If k is an integer such that 56 < k < 66, what is the value of k ?

(1) If k were divided by 2, the remainder would be 1 --> k is an odd number, thus it could be 57, 59, 61, 63, or 65. Not sufficient.

(2) If k + 1 were divided by 3, the remainder would be 0 --> k is 1 less than a multiple of 3, thus it could be 59, 62, or 65. Not sufficient.

(1)+(2) k could still take more than one value: 59 or 65. Not sufficient.

Answer: E.
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Re: If k is an integer such that 56 < k < 66, what is the value [#permalink] New post 21 Oct 2013, 18:53
Bunuel wrote:
If k is an integer such that 56 < k < 66, what is the value of k ?

(1) If k were divided by 2, the remainder would be 1 --> k is an odd number, thus it could be 57, 59, 61, 63, or 65. Not sufficient.

(2) If k + 1 were divided by 3, the remainder would be 0 --> k is 1 less than a multiple of 3, thus it could be 59, 62, or 65. Not sufficient.

(1)+(2) k could still take more than one value: 59 or 65. Not sufficient.

Answer: E.



Hi Bunuel

Could you please explain the last part , I am still not able to figure out how E is the answer


Regards
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Re: If k is an integer such that 56 < k < 66, what is the value [#permalink] New post 21 Oct 2013, 20:56
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DivyanshuRohatgi wrote:
Bunuel wrote:
If k is an integer such that 56 < k < 66, what is the value of k ?

(1) If k were divided by 2, the remainder would be 1 --> k is an odd number, thus it could be 57, 59, 61, 63, or 65. Not sufficient.

(2) If k + 1 were divided by 3, the remainder would be 0 --> k is 1 less than a multiple of 3, thus it could be 59, 62, or 65. Not sufficient.

(1)+(2) k could still take more than one value: 59 or 65. Not sufficient.

Answer: E.



Hi Bunuel

Could you please explain the last part , I am still not able to figure out how E is the answer


Regards


From (1) k can be: 57, 59, 61, 63, or 65.
From (2) k can be: 59, 62, or 65.

Thus k can be 59, or 65. Two different answers. Hence not sufficient.
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Re: If k is an integer such that 56 < k < 66, what is the value [#permalink] New post 19 Dec 2014, 12:43
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Re: If k is an integer such that 56 < k < 66, what is the value [#permalink] New post 20 Jan 2016, 07:11
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Re: If k is an integer such that 56 < k < 66, what is the value [#permalink] New post 20 Jan 2016, 21:23
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Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

If k is an integer such that 56 < k < 66, what is the value of k ?

(1) If k were divided by 2, the remainder would be 1.
(2) If k + 1 were divided by 3, the remainder would be 0.


In the original condition, there is 1 variable(k), which should match with the number of equations. So you need 1 equation. For 1) 1 equation, for 2) 1 equation, which is likely to make D the answer.
For 1), k=2t+1=57,59,61...., which is not unique and not sufficient.
For 2), k+1=3m, k=3m-1=59, 62, 65, which is not unique and not sufficient.
When 1) & 2), n=59,65, which is not unique and not sufficient. Therefore, the answer is E.


 For cases where we need 1 more equation, such as original conditions with “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 59 % chance that D is the answer, while A or B has 38% chance and C or E has 3% chance. Since D is most likely to be the answer using 1) and 2) separately according to DS definition. Obviously there may be cases where the answer is A, B, C or E.
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Re: If k is an integer such that 56 < k < 66, what is the value [#permalink] New post 20 Jan 2016, 23:55
k is an integer such that 56 < k < 66 which means k=(57,58,59,60,61,62,63,64,65)
Now
Statement 1
If k were divided by 2, the remainder would be 1. which means k is odd so possible values of k=(57,59,61,63,65), not sufficient

Statement 2
If k + 1 were divided by 3, the remainder would be 0 so the possible values of k+1 are 60,63,66 so possible values of k=(59,62,65), insufficient

Combining 1 and 2
we still get 2 values 59 and 65 so insufficient

Answer is E

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Re: If k is an integer such that 56 < k < 66, what is the value   [#permalink] 20 Jan 2016, 23:55
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