Number System

what is the source of this question?

It dont appear like GMAT question.

manu.pant wrote:Find the greatest number of 4 digits which when divided by 10,11, 15, 22, leaves 3,4,8 & 15 as remainder respectively.

a) 9907
b) 9903
c) 9893
d) None

i think the answer is C

to get a remainder "3" when divided by 10, the no has to end on a 3! eg: 93,103,113...
so we can eliminate the first option completely!

now we have to check only for option B or option C

look at option B, does leave the remainder 3 when divided by 10.
will it leave a remainder 4 when divided by 11? by looking itself we can say no. because 99 is divisible by 11 and a 0 follows it so remainder is not 4!

this option is not possible

finally option C. satisfies remainder 3 when divided by 10, when divided by 11 does give the remainder 4
check it out by simple division.
when divided by 15 will give remainder 8 and when divided by 22 does give remainder of 15

so effectively in this question Process of elimination could be used and you narrow it down to solving just one part of it.

i hope this helps!

Raunak[spoiler

oh yes it does....thnx....but wanted to find a more generalized...by LCM/HCF method....

@selango: source of the ques.... Quantitative Aptitude.... Arun Sharma...

selango wrote:what is the source of this question?

It dont appear like GMAT question.

Correct - definitely not a GMAT question, don't worry about it (unless you just want a number properties challenge that's beyond the scope of the test).