Find all School-related info fast with the new School-Specific MBA Forum

 It is currently 27 Apr 2015, 10:41

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# Help with 2 maths questions from GMATPrep please.

Author Message
TAGS:
Manager
Joined: 29 Sep 2006
Posts: 57
Followers: 0

Kudos [?]: 1 [0], given: 0

Help with 2 maths questions from GMATPrep please. [#permalink]  09 Dec 2006, 06:49
1
This post was
BOOKMARKED
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
Joined: 01 May 2006
Posts: 1805
Followers: 8

Kudos [?]: 98 [0], given: 0

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
Joined: 29 Sep 2006
Posts: 57
Followers: 0

Kudos [?]: 1 [0], given: 0

Thanks but..... [#permalink]  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
Joined: 01 May 2006
Posts: 1805
Followers: 8

Kudos [?]: 98 [0], given: 0

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
Joined: 20 Feb 2006
Posts: 373
Followers: 1

Kudos [?]: 1 [0], given: 0

Re: Help with 2 maths questions from GMATPrep please. [#permalink]  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
Joined: 01 May 2006
Posts: 1805
Followers: 8

Kudos [?]: 98 [0], given: 0

Re: Help with 2 maths questions from GMATPrep please. [#permalink]  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
Joined: 12 Jul 2006
Posts: 117
Followers: 1

Kudos [?]: 11 [0], given: 0

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.
_________________

I think I can. I think I can. I think I can.

Senior Manager
Joined: 20 Feb 2006
Posts: 373
Followers: 1

Kudos [?]: 1 [0], given: 0

Once again, thanks Fig!!
Manager
Joined: 24 Jun 2006
Posts: 62
Followers: 1

Kudos [?]: 3 [0], given: 0

Explanation Needed [#permalink]  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
SVP
Joined: 01 May 2006
Posts: 1805
Followers: 8

Kudos [?]: 98 [0], given: 0

Re: Explanation Needed [#permalink]  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 ?
Director
Joined: 28 Dec 2005
Posts: 922
Followers: 2

Kudos [?]: 37 [0], given: 0

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

=> x-2 = 13 = x = 15
Senior Manager
Joined: 20 Feb 2006
Posts: 373
Followers: 1

Kudos [?]: 1 [0], given: 0

Re: Help with 2 maths questions from GMATPrep please. [#permalink]  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
Similar topics Replies Last post
Similar
Topics:
5 Math Questions from GMATPrep that I need help 1 30 Jul 2007, 16:22
A math question from GMATPrep 3 19 Apr 2007, 18:32
1 Need Your Help with some MathQuestions from GMATPrep 9 16 Apr 2007, 17:07
Display posts from previous: Sort by