Source: Official Guide for GMAT Review 2016 Problem Solving; #112

1

# 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?

### 1 Explanation

1 Mike McGarry, Magoosh Tutor

Aug 14, 2015 • Comment

Amani Emeson

Hi Mike, Will be grateful if you could explain why the largest number in this set will be "120+n" if n is simply the number of entries above 120? Thanks.

Jul 17, 2016 • Reply

Cydney Seigerman, Magoosh Tutor

Hi Amani,

Great question! The largest number in the set is 120+n because of the fact that we have a list of consecutive integers. This means that there is a difference of 1 between every two numbers in the set. So, the number of entries from 120 to the largest number is equal to the difference between 120 and this largest number.

For example, let's say that n = 3, that there are 3 entries greater than 120. Because the entries are consecutive integers, we know that they are equal to

120
121
122
123

n = 3 and 120 + 3 = 123, the largest number in the set :)

I hope this clears up your doubts! If not, please let me know :)

Jul 23, 2016 • Reply

Amani Emeson

Hi! Yes, thanks, this clarifies. Clear this applies to an arithmetic sequence where the common difference is 1. I now assume that for any arithmetic sequence where the common difference 'd' is 2, 3, or4, etc., then I could multiply n x d and add that to the median to get the largest entry, e.g d=3 and n=4, then d x n=12 and the largest entry will be 120+12=132. Hope this is mathematically correct?

Jul 25, 2016 • Reply

Cydney Seigerman, Magoosh Tutor

Great, I'm glad my explanation helped! Yes, this method will work but only if there are an odd number of integers in the series. This is because for an odd number of terms, the median is the middle terms. However, for an even number of terms, the median is the average of the two middle terms. :)

Aug 2, 2016 • Reply

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