Manhattan CAT Question

[blue.vikasbhardwaj]

Q)
Set R contains five numbers that have an average value of 55. If the median of the set is equal to the mean, and the largest number in the set is equal to 20 more than three times the smallest number, what is the largest possible range for the numbers in the set?

78
77 1/5
66 1/7
55 1/7
52

The correct Answer is 78

Solution :

Please help me point out where is my approach going wrong

Mean = Median in case of an Arithmetic Progression Series

So let the five numbers be a-2d,a-d,a,a+d and a+2d and therefore the Maximum range will be 4d

Given Average(Mean) = 55 , implies that Median = 55 ; a = 55

As per the question a + 2d = 20 + 3(a-2d)
-2a + 8d = 20
4d = 10 + a
Since a = 55 , implies 4d = 65

And hence the Maximum Range is 65 .

[jnelson0612]

blue,
Will you please repost this in the CAT math forum? Here is the link: manhattan-gmat-cat-math-f32.html

This forum is for GMAT Prep questions.

Once it has been moved, I'll delete it from here and someone will help you in that forum.

Thank you,