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# M11-34

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Math Expert
Joined: 02 Sep 2009
Posts: 51280

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15 Sep 2014, 23:45
00:00

Difficulty:

5% (low)

Question Stats:

88% (01:01) correct 12% (00:59) wrong based on 108 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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Math Expert
Joined: 02 Sep 2009
Posts: 51280

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15 Sep 2014, 23:45
1
1
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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Intern
Joined: 14 Jan 2012
Posts: 9

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25 Sep 2014, 12:17
2
In my view it would be sensible to add the restriction that n>1. Otherwise n=1 is the least value.
Math Expert
Joined: 02 Sep 2009
Posts: 51280

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26 Sep 2014, 00:15
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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Manager
Joined: 22 Aug 2012
Posts: 73
Concentration: Technology
GMAT 1: 710 Q47 V40

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03 Nov 2015, 02:54
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

Regards
Jonas
Math Expert
Joined: 02 Sep 2009
Posts: 51280

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03 Nov 2015, 05:20
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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Manager
Joined: 22 Aug 2012
Posts: 73
Concentration: Technology
GMAT 1: 710 Q47 V40

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03 Nov 2015, 05:56
Hi Bunuel

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

Cheers
Intern
Joined: 29 Jul 2013
Posts: 1
Location: India
GMAT Date: 02-28-2014
GPA: 3.2
WE: Human Resources (Computer Software)

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25 Jul 2016, 04:59
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
Math Expert
Joined: 02 Sep 2009
Posts: 51280

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25 Jul 2016, 05:19
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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Intern
Joined: 26 Aug 2015
Posts: 34
Concentration: Strategy, Economics
GMAT 1: 570 Q40 V28
GMAT 2: 740 Q49 V41

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25 Jul 2016, 05:27
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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Send some kudos this way if I was helpful! !

Intern
Joined: 19 May 2016
Posts: 29
Location: United States
Concentration: Strategy, Human Resources
GMAT 1: 710 Q46 V41
GMAT 2: 730 Q49 V41
GMAT 3: 680 Q46 V37
WE: Operations (Manufacturing)

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25 Jul 2016, 07:06
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
Joined: 02 Sep 2009
Posts: 51280

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25 Jul 2016, 07:44
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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Senior Manager
Joined: 21 Jan 2015
Posts: 362
Location: India
Concentration: Strategy, Marketing
GMAT 1: 620 Q48 V28
GMAT 2: 690 Q49 V35
WE: Sales (Consumer Products)

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09 Aug 2018, 22:26
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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M11-34 &nbs [#permalink] 09 Aug 2018, 22:26
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# M11-34

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