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# GMAT PREP Test 1 - Question 1

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Intern
Joined: 15 Oct 2009
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GMAT PREP Test 1 - Question 1 [#permalink]  02 Nov 2009, 08:25
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0% (00:00) correct 0% (00:00) wrong based on 0 sessions
So not a good start to my gmat journey. I have just finished reviewing exponents from mgmat and am still not sure how this answer is derived.

If 5^ 21 + 4^ 11 = 2 * 10^ n . What is N ?

The answer is n = 21 but i do not see this. Can someone help explain?

Thanks
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Senior Manager
Joined: 18 Aug 2009
Posts: 329
Followers: 8

Kudos [?]: 206 [0], given: 13

Re: GMAT PREP Test 1 - Question 1 [#permalink]  02 Nov 2009, 08:40
Please check if the question is correct.
Do you mean 5^21*4^11 = 2*10^n . What is N

If yes, then here is the explanation:
5^21*4^11 = 5^10*(5^11*4^11) = (5^10*2^11)*(10^11) = 2*10^21

Questions? Let me know.
Intern
Joined: 15 Oct 2009
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Re: GMAT PREP Test 1 - Question 1 [#permalink]  02 Nov 2009, 09:02
Quote:
Please check if the question is correct.
Do you mean 5^21*4^11 = 2*10^n . What is N

If yes, then here is the explanation:
5^21*4^11 = 5^10*(5^11*4^11) = (5^10*2^11)*(10^11) = 2*10^21

Yes i believe that should be 5^21*4^11.

So i understand the factoring of 5^10 but, i dont see how this comes to be
Quote:
(5^10*2^11)*(10^11) = 2*10^21
. What happened to the 4^11 and how is this piece incorporated
Quote:
=2*10^n
to solve for N?
Senior Manager
Joined: 18 Aug 2009
Posts: 329
Followers: 8

Kudos [?]: 206 [1] , given: 13

Re: GMAT PREP Test 1 - Question 1 [#permalink]  02 Nov 2009, 09:15
1
KUDOS
sac8513 wrote:
So i understand the factoring of 5^10 but, i dont see how this comes to be
Quote:
(5^10*2^11)*(10^11) = 2*10^21
. What happened to the 4^11 and how is this piece incorporated
Quote:
=2*10^n
to solve for N?

Ok, lets go stpe by step:

5^21*4^11 = 5^10*(5^11*4^11); Here we split 5^21 into 5^10*5^11.
5^10*(5^11*2^11*2^11); Here we split 4^11 as 2^11*2^11.
(5^10*2^11)*(5^11*2^11); Hope this step is clear
(5^10*2^10*2)*(10^11); Split 2^11 into 2*2^10 and 5^11*2^11 = (5*2)^11 = 10^11
(10^10*2)*(10^11); Here 5^10*2^10 = (5*2)^10 = 10^10
2*(10^21); Here 10^10*10^11 = 10^21

Now we know that 5^ 21 + 4^ 11 = 2 * 10^ n.
That means 2*10^21 = 2 * 10^ n
So n = 21.

Hope this is clear now. Questions? Shoot....
Intern
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Re: GMAT PREP Test 1 - Question 1 [#permalink]  02 Nov 2009, 09:34
Ahhh very interesting. I definitely see it now. So these higher exponent problems need to be factored down as much as possible to create those commonalities...

Thank you very much

As mentioned this was the first problem that appeared in my practice test. What level problem would you say this is? Could these exponent questions be more difficult?
Senior Manager
Joined: 18 Aug 2009
Posts: 329
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Kudos [?]: 206 [1] , given: 13

Re: GMAT PREP Test 1 - Question 1 [#permalink]  02 Nov 2009, 10:01
1
KUDOS
sac8513 wrote:
Ahhh very interesting. I definitely see it now. So these higher exponent problems need to be factored down as much as possible to create those commonalities...

Thank you very much

As mentioned this was the first problem that appeared in my practice test. What level problem would you say this is? Could these exponent questions be more difficult?

I would rate this as 500-600 difficulty level. At times such problems can become pain in the xxx, but can be solved using correct approach. Nothing is difficult if the correct approach is employed

Well, consider KUDOS if you liked my explanation
Re: GMAT PREP Test 1 - Question 1   [#permalink] 02 Nov 2009, 10:01
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