Problem Solving

phoenix9801 wrote:Question:

You have a some sum of money in a investment portfolio and you know over the next ten years five years are going to be positive 5% returns and 5 years are going to be negative 5% returns. You want the most money at the end of the ten years and you have full choices of which order will happen. What order do you want them to happen????

Please show all work how you came to that answer or why your answer is correct... I feel its a tricky question. I though the order does not matter because it would come out to be the same number anyway.

Dear phoenix 99^2,
I'm happy to respond.

Are you familiar with the idea of using a multiplier for a percent increase or decrease? I discuss this in this blog:
https://magoosh.com/gmat/2012/understand ... -the-gmat/
First, 5% as a decimal is 0.05. Therefore, the multiplier for a 5% increase, a positive 5% return, is 1.05. If we multiply any quantity by 1.05, we are applying a 5% increase to it. Similarly, the multiplier for a 5% decrease, a negative 5% return, would be 1 - 0.05 = 0.95. If we multiply any quantity by 0.95, we are applying a 5% decrease to it.

If I understand your scenario correctly, we are multiplying five factors of 1.05 and five factors of 0.95, and of course, the order of multiplication does not matter at all. That's the commutative property of multiplication. Therefore, the order of the increases & decreases should not matter.

I guess I wonder if I am interpreting everything you said correctly. Also, you said, "I thought the order does not matter because it would come out to be the same number anyway." I guess I wonder on what basis you believe this initial hunch of yours is not correct.

Please let me know where you found this question and what they said about it.

Mike

phoenix9801 wrote:Thanks I understand better, but does it matter if we use a mixture of -5% and +5%????

Dear phoenix9801,
By "any order", I mean intermixed orders as well.

(1.05)*(1.05)*(1.05)*(1.05)*(1.05)*(0.95)*(0.95)*(0.95)*(0.95)*(0.95)
= (0.95)*(0.95)*(0.95)*(0.95)*(0.95)*(1.05)*(1.05)*(1.05)*(1.05)*(1.05)
= (1.05)*(0.95)*(1.05)*(0.95)*(1.05)*(0.95)*(1.05)*(0.95)*(1.05)*(0.95)
= (1.05)*(1.05)*(0.95)*(0.95)*(1.05)*(1.05)*(0.95)*(0.95)*(0.95)*(1.05)
= (1.05)*(1.05)*(1.05)*(0.95)*(0.95)*(1.05)*(1.05)*(0.95)*(0.95)*(0.95)
= etc.
These are five of the the 10C5 = 252 different arrangements we could have, and by the magic of the commutative & associative laws of multiplication, all 252 of these absolutely must be equal.

Does all this make sense?
Mike

Hi phoenix9801,

I'm curious about where this question originated. The GMAT will certainly ask you about percents (through ratio questions, interest rate formulas, etc.) and will also ask you about Number Properties (e.g. when multiplying numbers, the order does NOT matter), but the way this question is phrased is outside the scope of the exam. It's in your best interest to practice with realistic GMAT questions, so be wary about material that deviates so far from original source material.

GMAT assassins aren't born, they're made,
Rich