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

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?

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources