Remainder Question

[relansachin]

If j and k are positive integers where k > j, what is the value of the remainder when k is divided by j?

(1) There exists a positive integer m such that k = jm + 5.

(2) j > 5

I got answer for this question..can someone please testify...and provide explanation ?

[trang.kieu.phung]

If j and k are positive integers where k > j, what is the value of the remainder when k is divided by j?

(1) There exists a positive integer m such that k = jm + 5.

(2) j > 5

[1]: It is obvious that 5 is the remainder when k is divided by j

[2]: insuff because we don't know about k.

So, my answer is A.

[gokul_nair1984]

[1]: It is obvious that 5 is the remainder when k is divided by j

[2]: insuff because we don't know about k.

So, my answer is A.

Nope, the answer has to be C

Stem:If j and k are positive integers where k > j, what is the value of the remainder when k is divided by j?

(1) There exists a positive integer m such that k = jm + 5.

(2) j > 5

Let's plug in some numbers for Statement 1;

If k=6 and j=1;where m=1 then the remainder when you divide 6/1=0
If k=11 and j=6,where m=1 then the remainder when you divide 11/6=5 . Hence A is Not sufficient.


Coming to Statement 2,
Let k=7 ,j=6 => Remainder=1 or k=8,j=6 =>Remainder=2
This is clearly insufficient.


Combining both the equations we always get the remainder as 5 because jm will always be divisible by j, so you are left with 5

So C it is

[trang.kieu.phung]

Oops, I've made the mistake when assuming that the remainder is 5 according to (1): k = jm + 5, and this is apparently incorrect.

The reason is as follows:
k/j = (jm + 5)/j = m + 5/j

If 5 < j, then the remainder will be 5.
But when 5 > j, the remainder can't be 5.
The examples of gokul showed this (Thank you, gokul :D)

So, (1) is insuff.

(1) and (2) is suff.

[gokul_nair1984]

You're Welcome :)

[tim]

:)