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

Question

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

shrouded1 · Accepted Answer

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)

urfrndniks · Answer

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?

Bunuel · Answer

______________
Yes, that;s correct.

JoeKan1234 · Answer

Let X be the number

1856 - X =336Q + 4

X = 1852 - 336Q

To minimize X, maximize Q

Max. value of Q = 5

So Min. value of X = 1852 - 336*5 = 172

qwerty0311bc · Answer

My thought process:
to subtract a number from 1856 so that the remainder when divided by 7, 12, 16 is 4.

Since we have 12 and 16 as divisors and remainder is 4 I figured out the final number must be even, since multiples of 12, 16 are even and when we add 4 to them to count for remainder the value still is even.
so we need to subtract even from 1856 to get another even.
out of 5 options 3 are odd and when subtract odd numbers from 1856 we get final odd number which isn't what we concluded from top. hence eliminate a,b,d.
remaining c,e. substitute and check.
divide (1856-140)/7 to check if we get remainder 4. the answer is no.
bingo hence the answer is e.

BrushMyQuant · Answer

Which is the least number that must be subtracted from 1856 so that the remainder when divided by 7, 12, 16 is 4?

As remainder is same when the number is divided by 7, 12 and 16
=> Number = Multiple of GCD(7, 12, 16) + 4 = 336*k + 4 (where k is an integer)
 Watch  this video  to MASTER LCM AND GCD  ]

Multiple of 336 close to 1856 = 336 * 5 = 1680
=> Number = 1680 + 4 = 1684

=> We need to subtract 1856 - 1684 = 172

So,  Answer will be E 
Hope it helps!

Watch the following video to MASTER Remainders

https://www.youtube.com/watch?v=P0S6j2uTaj4

bumpbot · Answer

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

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