Skip to Main Content

Source: Official Guide for the GMAT 13th Ed. Problem Solving; #91 Official Guide for the GMAT 2015 14th Ed. Problem Solving; #91


If Q is an odd number and

If Q is an odd number and the median of Q consecutive integers is 120, what is the largest of these integers?

4 Explanations



Can we plug in an odd number into the equation Q=3 OR 1 and get answer choice A as the correct answer?


Dec 6, 2016 • Comment

Sam Kinsman

Hi Sonika,

Yes, we can find the answer by plugging in numbers. However, we would need to work with each answer choice, to see which one works.

For example, if Q=3, we would have three integers: 119, 120, 121. The largest integer would be 121.

We would then plug Q=3 into each answer choice, to see which answer choice gives us a result of 121. A does that, so A must be correct.

Dec 7, 2016 • Reply


hichem elkateb

why the highest number equal to 120 plus n
and lowest number is 120 - n here n numbers below 20 not 120 - n same for the highest number

Mar 7, 2016 • Comment

Cydney Seigerman, Magoosh Tutor

Hi Hichem :)

While it seems like Mike says 20 instead of 120 at about 0:30 in the explanation, he is referring to the median of 120 at that point. Since 120 is the median of a set with an odd number of values, we know that 120 will be the middle number when we write the values in ascending order. For that reason, if there are n numbers above 120, there must also be n numbers below 120.

I hope this helps :)

Mar 8, 2016 • Reply

hichem elkateb

Thank you :D

Mar 12, 2016 • Reply

Cydney Seigerman, Magoosh Tutor

You're very welcome! Happy studying :)

Mar 13, 2016 • Reply


Deethu Krishnan

Consider {3, 4, 5} median is an even number like the set we have here in this question and the first number is odd. Substitute the values in the answer choice.. A gives the right answer choice.. but instead of 120 in the choice consider 4 as the median..

Jul 4, 2015 • Comment

Jonathan , Magoosh Tutor

Hi Deethu. Yes, changing 120 to a different integer doesn't change how the problem works. But 120 shouldn't be difficult to work with either, since we are simply counting consecutive integers after it. 119, 120, 121, for example, are just as easy to work with.

Jul 10, 2015 • Reply


Gravatar Mike McGarry, Magoosh Tutor

Dec 28, 2013 • Comment

Add Your Explanation

You must have a Magoosh account in order to leave an explanation.

Learn More About Magoosh

Official GMAT Material

Official Guide for GMAT Review 2016

Official Guide for the GMAT 13th Ed.

Official Guide for the GMAT 2015 14th Ed.

Nova's GRE Prep

Official Guide for the GMAT 12th Ed.

Revised GRE PDF 2nd Ed.

Section 5.3 Problem Solving

Section 5.3 Problem Solving

Improve Your Score

Magoosh GMAT is an affordable online course for studying the GMAT.

Learn More About Magoosh

Share Post