Problem involving exponents

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bnd2: Newbie | Next Rank: 10 Posts; Posts: 2; Joined: Fri May 21, 2010 6:54 am

by bnd2 » Sun Jul 18, 2010 11:10 am

Hi everyone! I have been lurking for quite a bit and love this site!

I was wondering if anyone would be able to explain this problem to me as I am not understanding the correct answer (or how to arrive to the correct answer).

If (1/5)^m (1/4)^18 = 1/2(10)^35, then m =

a. 17
b. 18
c. 34
d. 35
e. 36

The correct answer is 35, but I can't seem to figure out why. Any help would be greatly appreciated.

Thanks,

Beth

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Source: Beat The GMAT — Problem Solving | Sun Jul 18, 2010 11:10 am

singhpreet1: Senior | Next Rank: 100 Posts; Posts: 95; Joined: Tue Jun 08, 2010 11:27 am; Thanked: 7 times

by singhpreet1 » Sun Jul 18, 2010 11:17 am

bnd2 wrote:Hi everyone! I have been lurking for quite a bit and love this site!

I was wondering if anyone would be able to explain this problem to me as I am not understanding the correct answer (or how to arrive to the correct answer).

If (1/5)^m (1/4)^18 = 1/2(10)^35, then m =

a. 17
b. 18
c. 34
d. 35
e. 36

The correct answer is 35, but I can't seem to figure out why. Any help would be greatly appreciated.

Thanks,

Beth

lets take this step by step

(1/5)^m(1/4)^18=(1/2)^35 can be re-written as (1/5)^m(1/2)^36 right?

(1/5)(1/2)(1/2)^35

(1/10)(1/2)^35 or 1/2(10)^35

so m=35.

i hope i dint make a mistake anywhere.

Preet

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aloneontheedge: Senior | Next Rank: 100 Posts; Posts: 97; Joined: Thu Jan 28, 2010 2:07 am; Thanked: 9 times

by aloneontheedge » Sun Jul 18, 2010 11:21 am

bnd2 wrote:Hi everyone! I have been lurking for quite a bit and love this site!

I was wondering if anyone would be able to explain this problem to me as I am not understanding the correct answer (or how to arrive to the correct answer).

If (1/5)^m (1/4)^18 = 1/2(10)^35, then m =

a. 17
b. 18
c. 34
d. 35
e. 36

The correct answer is 35, but I can't seem to figure out why. Any help would be greatly appreciated.

Thanks,

Beth

5^-m*2^-36 = 2^-1(2*5)^-35
since bases are same powers can be added
5^-m*2^-36 = 2^-36*5^-35
5^-m = 5^ -35
therefore m =35
hope it is clear. If not plz let me know

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bnd2: Newbie | Next Rank: 10 Posts; Posts: 2; Joined: Fri May 21, 2010 6:54 am

by bnd2 » Sun Jul 18, 2010 11:28 am

Preet, when I first looked at yours I was still all WTF.

aloneontheedge, thank you thank you thank you.

I understood Preet's explanation after seeing yours. It makes a lot more sense now.

These questions seem to trip me up because I do not tend to think to break down something like 1/4 into (1/2)(1/2). I really need to drill that into my head.

You guys are my savior. Thanks so much

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aloneontheedge: Senior | Next Rank: 100 Posts; Posts: 97; Joined: Thu Jan 28, 2010 2:07 am; Thanked: 9 times

by aloneontheedge » Sun Jul 18, 2010 11:32 am

bnd2 wrote:Preet, when I first looked at yours I was still all WTF.

aloneontheedge, thank you thank you thank you.

I understood Preet's explanation after seeing yours. It makes a lot more sense now.

These questions seem to trip me up because I do not tend to think to break down something like 1/4 into (1/2)(1/2). I really need to drill that into my head.

You guys are my savior. Thanks so much

whenever you encounter exponents problems,try to break down the elements into prime factors.
bit of practice,u will on the track

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singhpreet1: Senior | Next Rank: 100 Posts; Posts: 95; Joined: Tue Jun 08, 2010 11:27 am; Thanked: 7 times

by singhpreet1 » Sun Jul 18, 2010 8:35 pm

bnd2 wrote:Preet, when I first looked at yours I was still all WTF.

aloneontheedge, thank you thank you thank you.

I understood Preet's explanation after seeing yours. It makes a lot more sense now.

These questions seem to trip me up because I do not tend to think to break down something like 1/4 into (1/2)(1/2). I really need to drill that into my head.

You guys are my savior. Thanks so much

another takeaway from such questions is the answer to these will mostly be the highest exponent power, because we will try and fit every other exponent power to match that. but to be doubly sure, you should always solve it.

i encountered big problems with these questions with such questions forever, but BTG has been really kind to me.

Preet

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tyrath25: Junior | Next Rank: 30 Posts; Posts: 10; Joined: Mon Jul 19, 2010 1:04 pm; Location: Chicago

by tyrath25 » Tue Jul 20, 2010 1:02 pm

I hate to say it... I still don't get it...

I kind of grasp the left side of the equation, break the 1/4 down to (1/2)^18(1/2)^18 = (1/2)^36 - got it. No clue what's happening on the right side of the equation.

Is there a lower level of this sort of problem I can look at and learn from? Take the test in 6 days - this would probably be something good to know...

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singhpreet1: Senior | Next Rank: 100 Posts; Posts: 95; Joined: Tue Jun 08, 2010 11:27 am; Thanked: 7 times

by singhpreet1 » Tue Jul 20, 2010 9:46 pm

tyrath25 wrote:I hate to say it... I still don't get it...

I kind of grasp the left side of the equation, break the 1/4 down to (1/2)^18(1/2)^18 = (1/2)^36 - got it. No clue what's happening on the right side of the equation.

Is there a lower level of this sort of problem I can look at and learn from? Take the test in 6 days - this would probably be something good to know...

if nothing else makes sense and you dont have time, re-read my last post.

in this question: If (1/5)^m (1/4)^18 = 1/2(10)^35, then m =

a. 17
b. 18
c. 34
d. 35
e. 36

the highest exponential power we have is 35, therefore 99out of 100 that is the answer you are looking for, even without solving.

hope you do well on the test.

Preet

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