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Which is the least number that must be subtracted from 1856 so that

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Which is the least number that must be subtracted from 1856 so that  [#permalink]

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New post 18 Oct 2010, 02:05
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Which is the least number that must be subtracted from 1856 so that the remainder when divided by 7, 12, 16 is 4?

a) 137
b) 1361
c) 140
d) 157
e) 172
Spoiler: OA
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Re: Which is the least number that must be subtracted from 1856 so that  [#permalink]

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New post 18 Oct 2010, 02:38
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feruz77 wrote:
Which is the least number that must be subtracted from 1856 so that the remainder when divided by 7, 12, 16 is 4?
a) 137
b) 1361
c) 140
d) 157
e) 172

pls. help with solution method!?


First we need to figure out what numbers are exactly divisible by 7,12,16. This will be the set {LCM,LCMx2,LCMx3,...}
LCM(7,12,16) = 48*7 = 336
The numbers which will leave remainder 4 will be {336+4, 336x2 +4, 336x3 +4,...}
The largest such number less than or equal to 1856 is 336x5+4 or 1684
To obtain this you need to subtract 172.

Answer is (d)
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Which is the least number that must be subtracted from 1856 so that  [#permalink]

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New post 24 Sep 2016, 05:27
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Bunuel

I solved this with POE, subtracting each option from the original number and dividing it by 7, 12, 16. Solved it under 2 mins though.
A) 1856 - 137 = 1719 ; 1719/7 gives remainder 4 but dividing by 12 it fails, leave it
B) 1856 - 1361 = 495 ; 495/7 fails remainder is 5, leave it
C) 1856 - 140 = 1716; 1716/7 , fails remainder is not 4
D) 1856 - 157 = 1699; 1699/7, fails remainder is not 4
E) 1856-172 = 1684; dividing by all three 7, 12 and 16 gives remainder 4 - CORRECT

Is this approach suitable?
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Re: Which is the least number that must be subtracted from 1856 so that  [#permalink]

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New post 25 Sep 2016, 03:02
urfrndniks wrote:
Bunuel

I solved this with POE, subtracting each option from the original number and dividing it by 7, 12, 16. Solved it under 2 mins though.
A) 1856 - 137 = 1719 ; 1719/7 gives remainder 4 but dividing by 12 it fails, leave it
B) 1856 - 1361 = 495 ; 495/7 fails remainder is 5, leave it
C) 1856 - 140 = 1716; 1716/7 , fails remainder is not 4
D) 1856 - 157 = 1699; 1699/7, fails remainder is not 4
E) 1856-172 = 1684; dividing by all three 7, 12 and 16 gives remainder 4 - CORRECT

Is this approach suitable?

______________
Yes, that;s correct.
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Re: Which is the least number that must be subtracted from 1856 so that  [#permalink]

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Re: Which is the least number that must be subtracted from 1856 so that   [#permalink] 11 Feb 2019, 21:18
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