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Manager  Joined: 08 Oct 2010
Posts: 179
Location: Uzbekistan
Schools: Johnson, Fuqua, Simon, Mendoza
WE 3: 10
Which is the least number that must be subtracted from 1856 so that  [#permalink]

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7 00:00

Difficulty:   55% (hard)

Question Stats: 69% (02:41) correct 31% (02:49) wrong based on 106 sessions

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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
Retired Moderator Joined: 02 Sep 2010
Posts: 724
Location: London
Re: Which is the least number that must be subtracted from 1856 so that  [#permalink]

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1
1
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.

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Current Student Joined: 08 Jun 2013
Posts: 32
Which is the least number that must be subtracted from 1856 so that  [#permalink]

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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?
Math Expert V
Joined: 02 Sep 2009
Posts: 58427
Re: Which is the least number that must be subtracted from 1856 so that  [#permalink]

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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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