Adding exponents

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Adding exponents

by relaxin99 » Wed Mar 11, 2009 7:52 pm
I always have trouble with these type of questions....

5^28 + 3^11 = 5^q, what is q?

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by lilu » Wed Mar 11, 2009 9:01 pm
I got confused with this as well.
But here is a thread about this problem:
https://www.beatthegmat.com/mgmat-exponents-t10402.html
the concepts for solving it are well explained in that thread.

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Re: Adding exponents

by Ian Stewart » Thu Mar 12, 2009 5:10 am
relaxin99 wrote:I always have trouble with these type of questions....

5^28 + 3^11 = 5^q, what is q?

17
27
28
30
39
This question is very different from other questions that have a similar appearance. Normally in these kinds of questions, the bases are similar - they typically at least have divisors in common - which allows you to factor. That doesn't happen here; there's nothing convenient we can factor from 5^28 + 3^11.

The question does *not* ask for the value of q; it asks for an approximation of the value of q. There is no way for q to be a whole number here. I've never seen a similar question in official GMAT materials, so it isn't likely to be important on test day, but if the explanation in the link above is not convincing, we can be more rigorous.

We know: 5^28 + 3^11 = 5^q.

Now, 5^28 + 3^11 is certainly greater than 5^28, so q must be greater than 28. On the other hand,

5^28 + 5^28 + 5^28 + 5^28 + 5^28 = 5^29

so 5^28 + 3^11 is much smaller than 5^29, and q must be very close to 28.
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