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problem solving help again

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problem solving help again [#permalink] New post 24 Feb 2007, 15:41
thanks for the help on the last one....
since you were able to get that, could you help with this one?

(1/4)^n * (1/5)^18 = (1/20)^35
what is the value of n?
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 [#permalink] New post 25 Feb 2007, 04:29
First of all, welcome to the GMATClub ! :D :)

Following your posts focussed on this sort of question, I would like to detail u the whole process :)

This question is a classical one of the GMAT :)... The hidden structure behind some flips or simplications is like this:

x^a * y^b = x^d * y^e with x != y

As in an equation, the right side is always equal to the left side, we can indenty and then equalize expression in x and in y :)

So,
o x^a must be equal to x^d
o y^b must be equal to y^e

Then,
o a=d
o b=e

That said, let us try to rewrite your problem in an equation to identify expressions from the left side to the ones from the right.

To continue the image, set x=1/4 and y=1/5 in your mind :)... We have to recreate x and y in the right side of the equation.

(1/4)^n * (1/5)^18 = (1/20)^35
= (1/4 * 1/5)^35
= (1/4)^35 * (1/5)^35

Thus, n=35.

But, u could see that (1/5)^18 cannot be equal to (1/5)^35 :)... That's where I think we have a typo in this question ;)... Because the GMAT would never ask u to solve it like this:

(1/4)^n * (1/5)^18 = (1/20)^35
<=> (1/4)^n = (1/4)^35 * (1/5)^17
<=> n * ln(1/4) = 35*ln(1/4) + 17*ln(1/5)
<=> n = 35 + 17*ln(5)/ln(4)

;)
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 [#permalink] New post 25 Feb 2007, 11:04
thanks fig! i thought it may have been a typo. I've been racking my brain on it...
  [#permalink] 25 Feb 2007, 11:04
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