Problem Solving

Hi tanvis1120,

For these types of questions, you have some options when it comes to approaching the "math" behind the question. As long as you're not breaking any of the rules that the prompt describes, you can use whatever examples you want (to help you prove what the correct answer is). You have to be careful about your assumptions though; here, you got a bit lucky, because the ideas behind this prompt involve numbers that are NOT necessarily sequential.

We're asked for the largest possible range of this group of 7 numbers, which means that we have to make the largest value as large as possible and make the smallest value as small as possible (and by extension, make everything as small as possible too).

First, let's deal with the median, which equals 23 (when the numbers are ordered, the "middle number" is 23):

_ _ _ 23 _ _ _

This means that the 3 numbers to the "left" of the 23 can be 23 or less and the the 3 numbers to the "right" of the 23 can be 23 or more.

We also know that the average is 23, which means that the sum of the 7 numbers = sum/7 = 23.......sum = 161

We have one more piece of info to implement: the largest number is 15 more than 4 times the smallest number:

X = smallest number
4X + 15 = largest number

X _ _ 23 _ _ (4X+15)

To make the largest number as large as possible, we have to make EVERYTHING ELSE as small as possible. Here's how to do it:

X X X 23 23 23 (4X+15)

Summing all of these values gives us:

7X + 84 = 161
7X = 77
X = 11

So, the smallest number = 11 and the largest number = 4(11)+15 = 59

The range = 59 - 11 = 48

Final Answer: D

GMAT assassins aren't born, they're made,
Rich