Powers of 5 - ACTUAL NAME OF MGMAT CAT PROBLEM.

[vish1234]

Powers of 5

hi All,

This is the name of the mgmat cat questions.

If 5^x = y, what is x?

(1) y2 = 625
(2) y3 = 15,625

If we know y, we can solve for x. Thus, we can rephrase the question, "What is y?"

(1) SUFFICIENT: If y2 = 625, we know that y = 25 or -25. However, since 5x will be positive no matter what x is, and 5x = y, then y must be positive. Thus, y must be 25. If y is 25, we know that x = 2.

My question was regarding the 1st solution given in the mgmat cat.

How can you say that 5 ^x will be positive no matter what x is. why could it not be negative. ?

Thanks

[StaceyKoprince]

5^x represents 5 multiplied some number of times. 5 is a positive number, so no matter how many times you multiply it, a positive times a positive is always a positive. The only way to make it negative would be to start with a negative base (say, -5) and then raise that to an odd power, eg (-5)^3.

If x is negative, then it doesn't turn 5^x into a negative number; rather, it turns into a fraction. eg 5^(-1) = 1/5.

Do make sure you know all of your exponent rules before you take the test - these are very commonly tested rules.

[vish1234]

thanks a lot stacy, i was aware of those rules, did not click , got confused within the two minutes of time frame. U are awesome and I have seen ure name a million times on beat the gmat.

Thanks

Vimal Shah

[StaceyKoprince]

No problem! It's very easy to get turned around / confused during the 2 minutes, so one of the things you should study is: what do I do when I don't know what to do? Or what do I do when I know I'm confused?

It's going to happen on the test, no matter how good you get! So figure out what process you'll use to (a) make sure you don't get sucked into spending WAY too much time and (b) make an educated guess.