urgent quick math question

[solb22]

Quick math question:

Should I reduce a fraction BEFORE finding the remainder:

for example: 5/10...would that have a remainder of 5, or 1 (because 5/10=1/2)

this makes a difference. Take question 19 in Advanced Quant by MGMAT (pg235)

19. If j and k are positive integers such that 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 answered E, because if j is a multiple of 10 then I reduced the fraction first. Answer is C, which would imply (rather require) you don't reduce your fraction.

If you do say C, I'm going to reply that your prob. right but then why don't you consider 6/3 as a remainder of 3? Hey, no reducing first!

This is the stupidest test ever! And this is coming from someone whose scoring 50-51Q on the GMATpreps etc. I don't care what the adcom says, but this test gives no indication of mathematical ability. I spent a week getting inequality answers wrong, only to find out complex numbers aren't on the test (making proofs wrong)!

[solb22]

Just figured out my own question while in the shower

You don't reduce.

Every number can be written as a linear combination of another number.

a=bt+r

If you want to know if a/b

a/b=t+c

Now for our 5/10 case, 10=(0*10)+5

So the remainder is r. You can use this to prove there exists an infinite number of primes.

[jnelson0612]

It's amazing how the shower can provide inspiration. :-)