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sac8513
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GMAT PREP Test 1 - Question 1 02 Nov 2009, 09:25
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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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GMAT PREP Test 1 - Question 1 02 Nov 2009, 09:40
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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.
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sac8513
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GMAT PREP Test 1 - Question 1 02 Nov 2009, 10:02
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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
Show more

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
Show more
. What happened to the 4^11 and how is this piece incorporated
Quote:
=2*10^n
Show more
to solve for N?
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GMAT PREP Test 1 - Question 1 02 Nov 2009, 10:15
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sac8513

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?
Show more

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....
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GMAT PREP Test 1 - Question 1 02 Nov 2009, 10:34
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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?
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GMAT PREP Test 1 - Question 1 02 Nov 2009, 11:01
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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?
Show more

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 ;)



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Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Problem Solving (PS) Forum
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Thank you for understanding, and happy exploring!
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