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M11-34

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Math Expert
Joined: 02 Sep 2009
Posts: 58402

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16 Sep 2014, 00:45
00:00

Difficulty:

5% (low)

Question Stats:

88% (01:03) correct 12% (00:59) wrong based on 110 sessions

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The remainder when positive integer $$n$$ ($$n>1$$) is divided by 25 is 1 and the remainder when $$n$$ is divided by 7 is also 1. What is the least value of $$n$$?

A. 76
B. 101
C. 126
D. 151
E. 176

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Posts: 58402

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16 Sep 2014, 00:45
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Official Solution:

The remainder when positive integer $$n$$ ($$n>1$$) is divided by 25 is 1 and the remainder when $$n$$ is divided by 7 is also 1. What is the least value of $$n$$?

A. 76
B. 101
C. 126
D. 151
E. 176

Notice that $$n-1$$ is divisible by both 7 and 25. So, the least value of $$n-1$$ is the least common multiple of 7 and 25 which is $$7*25=175$$. Hence $$n-1=175$$ and $$n=176$$.

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25 Sep 2014, 13:17
2
In my view it would be sensible to add the restriction that n>1. Otherwise n=1 is the least value.
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26 Sep 2014, 01:15
Boycot wrote:
In my view it would be sensible to add the restriction that n>1. Otherwise n=1 is the least value.

You are right. Edited. Thank you.
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03 Nov 2015, 03:54
Hi Bunuel

Should we be looking for the least common multiple of n-1 or n?

Also could the the answer not be 76?

n = 25 * K +1
Possible values 1, 26, 51, 76

n = 7 * K +1
Possible values 1,8,15,22,29,36,43,50,57,64,71,76

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Jonas
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03 Nov 2015, 06:20
Jonas84 wrote:
Hi Bunuel

Should we be looking for the least common multiple of n-1 or n?

Also could the the answer not be 76?

n = 25 * K +1
Possible values 1, 26, 51, 76

n = 7 * K +1
Possible values 1,8,15,22,29,36,43,50,57,64,71,76

Regards
Jonas

76 give the remainder of 7 when divided by 7. There should be 78 instead of 71.
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03 Nov 2015, 06:56
Hi Bunuel

Absolutely right. My bad. Guess my mind badly wanted the result to be 76.

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Joined: 29 Jul 2013
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25 Jul 2016, 05:59
You don't have to mention n>1. The moment the question says positive integer, it's implied that n>1

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25 Jul 2016, 06:19
saurabhnehra wrote:
You don't have to mention n>1. The moment the question says positive integer, it's implied that n>1

Posted from my mobile device

Not true. Positive integers are integers more than or equal to 1: $$\geq 1$$. The stem exclude possibility of n being 1.
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25 Jul 2016, 06:27
saurabhnehra wrote:
You don't have to mention n>1. The moment the question says positive integer, it's implied that n>1

Posted from my mobile device

Not really, positive integer is n>0, in that case the answer could be 1 (although if it is not in the answer choices that would discard it). To have another possible "lower value" than the one in the options diminishes the quality of the question as a whole.

1/25 = 0*(25) + 1

1/7 = 0*(7) + 1

1 is a possible value that satisfies both options.

Posted from my mobile device

Posted from my mobile device
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25 Jul 2016, 08:06
Bunuel wrote:
The remainder when positive integer $$n$$ ($$n>1$$) is divided by 25 is 1 and the remainder when $$n$$ is divided by 7 is also 1. What is the least value of $$n$$?

A. 76
B. 101
C. 126
D. 151
E. 176

Hi Banuel,

Thanks for this! What does the M11-34 refer to? What is the source of this question if you don't mind me asking?

Thank you.
Math Expert
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Posts: 58402

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25 Jul 2016, 08:44
toby001 wrote:
Bunuel wrote:
The remainder when positive integer $$n$$ ($$n>1$$) is divided by 25 is 1 and the remainder when $$n$$ is divided by 7 is also 1. What is the least value of $$n$$?

A. 76
B. 101
C. 126
D. 151
E. 176

Hi Banuel,

Thanks for this! What does the M11-34 refer to? What is the source of this question if you don't mind me asking?

Thank you.

M11-34 is the ID of the question in GMAt Club Test. The source is GMAT Club.
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09 Aug 2018, 23:26
Ans: E
I solved this question working backwards from the options. We need to find least value N from which when 1 is reduced (N-1) it becomes multiple of both 25 and 7.
working backward:
N-1 divisible by 25 divisible by 7
75 Y N
100 Y N
125 Y N
150 Y N
175 Y Y ---- Ans.
Note: if we just look at the N-1 we will know in first instant without solving much that these are divisible by because they all end up with Unit digit 0 or 5. so we actually need to know which one is divisible by 7.

Bunuel wrote:
The remainder when positive integer $$n$$ ($$n>1$$) is divided by 25 is 1 and the remainder when $$n$$ is divided by 7 is also 1. What is the least value of $$n$$?

A. 76
B. 101
C. 126
D. 151
E. 176

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