Help with 2 maths questions from GMATPrep please. : Quant Question Archive [LOCKED]
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# Help with 2 maths questions from GMATPrep please.

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Manager
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09 Dec 2006, 06:49
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Please can someone explain how to approah and solve the following two problems:

1. (1/4)^m x (1/5)^18 = 1/2(10)^35. What is m?

2. 2^x - 2^x-2 = 3(2^13)

All help would be really appreciated.

Thanks
SVP
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09 Dec 2006, 07:24
They are from a kind of classical GMAT questions The way to solve them is to reshape the equations in order to identify elements from the left and from the right sides

a^x * b^y = a^4 * b^45

1) (1/4)^m x (1/5)^18 = 1/2(10)^35

(1/4)^m x (1/5)^18 = 1/2(10)^35
<=> (1/2)^(2*m) x (1/5)^18 = 1/2(1/(5*2))^-35
<=> (1/2)^(2*m) x (1/5)^18 = (1/2)^-34*(1/5)^-35

=> 2*m = -34
<=> m = -17
Manager
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09 Dec 2006, 07:37
Thanks for your reply. Is there any chance you could explain it in a bit more detail as I'm having difficulty understand how you arrived at the final number.

If you now of any good maths workouts for GMAT questions involving exponents and square roots can you let me know as these two areas are probably my weakest.

I'm looking for a score of 680+ and this was the first question I had in the GMAT prep so I'm assuming it is a middle difficulty question.

Once again thanks
SVP
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09 Dec 2006, 08:00
Ok.... I can detail more

(1/4)^m x (1/5)^18 = 1/2(10)^35

Step 1
(10)^35 = ( (1/10)^-1 )^35 = (1/10)^(-1*35) = (1/10)^(-35) : Following this rule : (a^x)^y = a^(x*y)

Step 2
(1/10)^(-35) = (1/(5*2))^(-35) = (1/5 * 1/2)^(-35) = (1/5)^(-35) * (1/2)^(-35) : Following this rule : (a*b)^x = (a^x)*(b^x)

Step 3
1/2 * (1/2)^(-35) = (1/2)^(-34) : Following this rule : (a^x) * (a^y) = a^(x+y)

Step 4
(1/4)^(m) = ( 1/(2^2) )^(m)= ( (1^2/2^2) )^(m) = ( (1/2)^2 )^(m) Following this rule : a^x / b^x = (a/b)^x

Step 5
( (1/2)^2 )^(m) = ( 1/2 )^(2*m) : Same rule as the step 1 : (a^x)^y = a^(x*y)

And finally, by identification, we select the same constants and their powers :
( 1/2 )^(2*m) = (1/2)^(-34)
=> 2*m = -34 : we equal the powers

About your request, I have no idea concerning such online materials .... Perhaps other guys, any one to give an hand pls?
Senior Manager
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09 Dec 2006, 10:41
GMAT? wrote:
Please can someone explain how to approah and solve the following two problems:

1. (1/4)^m x (1/5)^18 = 1/2(10)^35. What is m?

2. 2^x - 2^x-2 = 3(2^13)

All help would be really appreciated.

Thanks

I'm having trouble with the 2nd one:

2^x - 2^x-2 = 3(2^13) = 3(2^13)
2^x (1 - 1^(-2)) = 3(2^13)
2^x (0)???? = 3*2(2^13)

What's the OA?
SVP
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09 Dec 2006, 10:44
GMAT? wrote:
Please can someone explain how to approah and solve the following two problems:

1. (1/4)^m x (1/5)^18 = 1/2(10)^35. What is m?

2. 2^x - 2^x-2 = 3(2^13)

All help would be really appreciated.

Thanks

I'm having trouble with the 2nd one:

2^x - 2^x-2 = 3(2^13) = 3(2^13)
2^x (1 - 1^(-2)) = 3(2^13)
2^x (0)???? = 3*2(2^13)

What's the OA?

Actually, the bold face should be a factorisation of 2^(x-2).

2^(x-2)*(2^2 -1) = 3(2^13)
<=> 3*2^(x-2) = 3(2^13)
=> x-2 = 13
<=> x = 15

Last edited by Fig on 09 Dec 2006, 11:59, edited 1 time in total.
Manager
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09 Dec 2006, 11:30
GMAT? - you could use the search function on GMAT club to find examples of exponent questions. Be sure to search the Math forum for "exponents" and you'll see a bunch of problems (and explanations) come up. They helped me with this type of problem. I'm not sure about other materials.
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09 Dec 2006, 17:32
Once again, thanks Fig!!
Manager
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10 Dec 2006, 10:34
Fig,

Can you please explain how do (1/5)^18 and 1/5^-35 cancel out on both the sides in the firsdt problem
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10 Dec 2006, 12:02
mitul wrote:
Fig,

Can you please explain how do (1/5)^18 and 1/5^-35 cancel out on both the sides in the firsdt problem

Ahhh... Absolutetly ... So what do u think?

I have m = -17 - 53*ln(5)/ln(4) .... Is a typo present ?
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10 Dec 2006, 15:57

2^x - 2^(x-2) = 2^(x-2) * (2^2 - 1) = 2^(x-2) * 3

=> x-2 = 13 = x = 15
Senior Manager
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10 Dec 2006, 16:14
GMAT? wrote:
Please can someone explain how to approah and solve the following two problems:

1. (1/4)^m x (1/5)^18 = 1/2(10)^35. What is m?

2. 2^x - 2^x-2 = 3(2^13)

All help would be really appreciated.

Thanks

I've seen this question before but in the form:

(1/4)^18 x (1/5)^m= 1/2(10)^35 which is much easier to solve and the 1/4^18 cancels out with the 2^36

However I cant seem to solve the one posted - is it a typo?
Re: Help with 2 maths questions from GMATPrep please.   [#permalink] 10 Dec 2006, 16:14
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