##### This topic has expert replies
Senior | Next Rank: 100 Posts
Posts: 73
Joined: 16 Sep 2008
Thanked: 2 times

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?

17
27
28
30
39

Master | Next Rank: 500 Posts
Posts: 148
Joined: 10 Dec 2008
Location: SF, CA
Thanked: 12 times
by lilu » Wed Mar 11, 2009 9:01 pm
I got confused with this as well.
https://www.beatthegmat.com/mgmat-exponents-t10402.html
the concepts for solving it are well explained in that thread.

### GMAT/MBA Expert

GMAT Instructor
Posts: 2583
Joined: 02 Jun 2008
Location: Toronto
Thanked: 1090 times
Followed by:355 members
GMAT Score:780

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.
If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com

• Page 1 of 1