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The least number which should be added to 28523 so that the sum is exa

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Intern
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Joined: 19 Dec 2016
Posts: 47
Location: India
Concentration: Technology, Leadership
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The least number which should be added to 28523 so that the sum is exa  [#permalink]

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New post 17 Jul 2017, 13:44
00:00
A
B
C
D
E

Difficulty:

(N/A)

Question Stats:

67% (02:07) correct 33% (00:00) wrong based on 3 sessions

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The least number which should be added to 28523 so that the sum is exactly divisible by 3, 5, 7 and 8 is

A. 41
B. 42
C. 32
D. 37
E. 45

kudo please if you liked the ques.

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Re: The least number which should be added to 28523 so that the sum is exa  [#permalink]

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New post 17 Jul 2017, 15:16
The question basically asks, when 28523 is divided by 8*7*5*3, a remainder will be there. Now what is the minimum number that should be added to 28523 so that it becomes completely divisible by 8*7*5*3.

8*7*5*3 = 840
Remainder when 28532 is divided by 840 = 803

So the minimum number to be added is 840-803 = 37

Answer is D
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Re: The least number which should be added to 28523 so that the sum is exa  [#permalink]

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New post 17 Jul 2017, 16:53
The approach above is great (though not something you'll likely need to use on a GMAT question). Alternatively, if we know 28523 + k is divisible by both 5 and 8, then it must be divisible by 40, so it must have a units digit of zero. If 28523 + k has a units digit of zero, and k is positive, then k must have a units digit of 7, so only answer D can be right. We don't actually need to use the fact that the sum is divisible by 3 or 7.

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Re: The least number which should be added to 28523 so that the sum is exa   [#permalink] 17 Jul 2017, 16:53
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