GmatPrep #2 - exponents

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GmatPrep #2 - exponents [#permalink]

29 Mar 2009, 18:18

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I thought this was an interesting little problem.
I'll post the OA later.

If (400)(6000)=(240)(100^x), what is the value of x?

5
4
3
2
1

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Re: GmatPrep #2 - exponents [#permalink]

30 Mar 2009, 07:37

peraspera wrote:

I thought this was an interesting little problem.
I'll post the OA later.

If (400)(6000)=(240)(100^x), what is the value of x?

5
4
3
2
1

IMO: 2
Simplify to get the same base.
2400000=(240)(100^x)
(240)(100^2)=(240)(100^x)

Therefore x=2

Last edited by joyseychow on 02 Apr 2009, 01:30, edited 1 time in total.

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Re: GmatPrep #2 - exponents [#permalink]

31 Mar 2009, 18:11

Any other answers, with explanations?

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Re: GmatPrep #2 - exponents [#permalink]

06 Apr 2009, 19:20

Correct, the OA is D.

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Re: GmatPrep #2 - exponents [#permalink]

06 Apr 2010, 17:34

I actually just got this question in GMATprep#2 yesterday. Here's what I did.

Factor the four terms into primes:

(400)(6000)=(240)(100^x)

(2^4 5^2)(2^4 3^1 5^3)=(2^4 3^1 5^1)(2^2x 5^2x)

Combine to get, remember that (X^a)(X^b)=(X^a+b)

(2^8)(5^5)(3^1)=(2^4+2x)(5^1+2x)(3^1)

Cancel out the (3^1) to get:

(2^8)(5^5)=(2^4+2x)(5^1+2x)

Remember that there must be an equal number of exponents for each term on boths ides of the equation. Here there are eight 2's on the left side this means that there must be eight 2's on the right side, so 4+2x must equal 8.

4+2x=8
2x=4
x=2

D

You can use the same process for the exponents of 5 and you will arrive at the same answer.

Is there an easier/faster way to do this b/c this ate up alot of time during my test. especially b/c I had to factor out all the numbers.

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Re: GmatPrep #2 - exponents [#permalink]

07 Apr 2010, 10:01

I think this question is self explanatory.
By scanning the question itself we get that 4*6 = 24.
So the simple way is just multiply left hand side

400*6000 = 2400000
Dealing with 0 is always easy when it comes to exponents.
=> 240* 10000 = 240. 100^2

x = 2.

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Re: GmatPrep #2 - exponents [#permalink]

07 Apr 2010, 12:05

I think that the fastest way is aslo mads's and joyseychow's.
working with cero can simplify things

Re: GmatPrep #2 - exponents [#permalink] 07 Apr 2010, 12:05

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	GmatPrep #2 - exponents	peraspera	2	23 Mar 2009, 11:52
	GmatPrep #2 - exponents	peraspera	6	29 Mar 2009, 18:18

GmatPrep #2 - exponents

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