Problem Solving

alanforde800Maximus wrote:What is the minimum percentage increase in the mean of set X {-4, -1, 0, 6, 9} if its two smallest elements
are replaced with two different primes?

(A) 25% (B) 50% (C) 75% (D) 100% (E) 200%

Average (arithmetic mean) of set X = [(-4) + (-1) + 0 + 6 + 9]/5
= 10/5
= 2

NOTE: all prime numbers are always POSITIVE. So, we'll be replacing -4 and -1 with two positive numbers.
This will be sure to increase the average of set X.
So, to MINIMIZE this increase, we MINIMIZE the values of two replacement numbers (primes).
The two smallest primes are 2 and 3, so set X becomes: {2, 3, 0, 6, 9}

NEW average (arithmetic mean) of set X = (2 + 3 + 0 + 6 + 9)/5
= 20/5
= 4

So, the average of set X increased from 2 to 4

This represents a [spoiler]100%[/spoiler] increase.
Answer: D

ASIDE: many students will incorrectly conclude that we have a 200% increase, since 4 is equal to 2 times 2.

Percent increase = 100(new - old)/old
So, in this case, percent increase = 100(4 - 2)/2
= 200/2
= 100

Related video: https://www.gmatprepnow.com/module/gmat ... video/1078