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GMAT Prep question - really tough one - LCM, GCF factor etc.

Expert replies

by lunarpower » Sun Jul 05, 2009 3:58 am
@ navalpike
navalpike wrote:P=m+r
2s=2k+r
2s-2k=r
2(s-k)=r
your heart's in the right place, but this needs a little overhaul.

specifically:
"p = m + r" is wrong, unless 'm' goes into 'p' EXACTLY ONCE and then leaves a remainder. (for instance, if i want the remainder when i divide 200 by 6, i clearly can't write 200 = 6 + r; that will give an absolutely absurd remainder.)

still, you can use this method. here's the refinement:
in general, 'm' will divide into 'p' some integer number of times, say 'j', and leave a remainder.
therefore,
p = jm + r
2s = 2jk + r
2s - 2jk = r
then factor out the '2' and proceed as before.
Ron has been teaching various standardized tests for 20 years.

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by navalpike » Sun Jul 05, 2009 9:40 am
Ahhh, I can't believe I did that. Thanks for correcting me.

Ron, as my post stated above, do you know of a similar algebraic approach that we can apply to S2. As I mentioned, the first time around I got the question wrong and chose D because I failed to consider the right numbers for LCM 30.

Thanks,
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by lunarpower » Sun Jul 05, 2009 10:59 pm
navalpike wrote:Ahhh, I can't believe I did that. Thanks for correcting me.

Ron, as my post stated above, do you know of a similar algebraic approach that we can apply to S2. As I mentioned, the first time around I got the question wrong and chose D because I failed to consider the right numbers for LCM 30.

Thanks,
unfortunately, no, i can't think of a simple algebraic approach for numbers with a given LCM.
(you could try to write the numbers as something like 30/m and 30/n, but whatever you do with those numbers is going to be obnoxiously difficult. worse yet, the 'm' and 'n' in these expressions are the EXACT SAME numbers that you'll get if you just let 'm' and 'n' represent the factors themselves.)

this is how a LOT of gmat divisibility problems work, by the way. in fact, i'd say that, among divisibility problems, there are probably more problems that DON'T have simple all-algebraic solutions than problems that do have such solutions.
Ron has been teaching various standardized tests for 20 years.

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Pueden hacerle preguntas a Ron en castellano
Potete chiedere domande a Ron in italiano
On peut poser des questions à Ron en français
Voit esittää kysymyksiä Ron:lle myös suomeksi

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by gmat_for_life » Mon Apr 25, 2016 7:17 pm
Hello experts,

I was going through Ron's solution to this question. I realized that we have to pick numbers whose LCM is 30. Could you please let me know how to pick such numbers? Its easy to find the LCM when the numbers are given but to find those 2 numbers when the LCM is given is a bit confusing.

Regards,
Amit
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TTT

by moonavav » Mon Feb 12, 2018 2:28 am
It is quite simple.

The question asks us if the remainder is greater than one or not?

lets assume the remainder is 0 or 1.

Scenario 1 (remainder is zero):
This is not possible due to the fact that p is not divisible by m.

Scenario 2 (remainder is one):
This is not also possible because consecutive numbers can have a remainder of one. and since both numbers are even (GCF is 2), the remainder is greater than one.

As a result, Statement 1 is sufficient for answering the question.

Lets take Statement 2:
LCM is 30. Lets state all of possible numbers that m and p can have:
1 2 3 5 6 10 15 30

Well, 1 and 2 will be omitted (the question tells us m and p are greater than 2) and the others will remain:

if p=10 and m=6, the remainder will be greater than 1
and
if p=6 and m=5, the remainder will be one.

So statement 2 is insufficient for answering the problem and the answer will be A.

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