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

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

(A) (Q – 1)/2 + 120
(B) Q/2 + 119
(C) Q/2 + 120
(D) (Q + 119)/2
(E) (Q + 120)/2

To me this screams: pick a value for Q. Just make sure that you follow any rules outlined in the question. Always take your time to get things straight. That doesn’t mean sit and stare. Or obsessively re-read things. That means find the pace and level of detail that allows you to comprehend the question. Pause. Think. Digest.

## Let’s get to work!

So the median is 120, Q is an odd number, and there are Q consecutive integers. We’re looking for: the largest of these integers.

If 120 is the middle number (median) let’s just add one above and once below: 119 120 121

So, since Q represents the number of numbers, Q is 3. That value follows the rule: Q is odd.

## Plug back into the answer choices and look out for shortcuts (choices that clearly won’t match 121)

Now what? Now we do what we always do picking values and plug back into the answer choices. We need to sub in 3 for Q and output 121 (the largest of these integers).

You can rule out some of these without doing much since you can see fractions that clearly won’t work (B, C, E).

Then work out A and D.

D you can also eyeball. It’s way too small to equal 121.

It has to be A.

## Additional GMAT Statistics Example Questions!

Here’s a GMAT statistics puzzle (median/range) which will teach you how to work with a while bunch of unknowns. Also a good one to work on maximizing a value.

A set of 15 different integers has median of 25 and a range of 25. What is greatest possible integer that could be in this set?

Here’s a top shelf statistics, max/min question which we tackle in just about every GMAT preparation. it’s a great question to work on organizing a ton of variables. Also, it will help you understand how deal with a max/min scenario.

Seven pieces of rope have an average (arithmetic mean) length of 68 centimeters and a median length of 84 centimeters. If the length of the longest piece of rope is 14 centimeters more than 4 times the length of the shortest piece of rope, what is the maximum possible length, in centimeters, of the longest piece of rope?

Bread and butter GMAT statistics question. Not the most difficult but still very important. Be ready to interpret a chart/graph on test day. What isn’t challenging in practice can quickly become a swirling mess on GMAT day.

The table above shows the distribution of test scores for a group of management trainees. Which score interval contains the median of the 73 scores?

Great one to wrap your head around statistics concepts and how they can be tested on the GMAT. It’s a PS (problem solving) question but having this square will also help you on DS statistics questions.

Last month 15 homes were sold in Town X. The average (arithmetic mean) sale price of the homes was \$150,000 and the median sale price was \$130,000. Which of the following statements must be true?

Moderately challenging DS statistics range question from GMAT question of the day

And here’s a very challenging GMAT statistics range question from GMAT question of the day that requires algebra and number properties skills.

Good luck and happy studies!