What is the minimum percentage increase in the mean of set X

[Anaira Mitch]

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%

Stuck with above problem looking for some guidance and assistance.

[GMATGuruNY]

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%

Current mean = sum/number = [-4 + (-1) + 0 + 6 + 9]/5 = 10/5 = 2.

The smallest elements in the set are -4 and -1.
To minimize the increase in the mean, the prime numbers chosen to replace -4 and -1 must be as small as possible.
Smallest distinct primes that could replace -4 and -1 are 2 and 3.
New mean = (new sum)/number = (2 + 3 + 0 + 6 + 9)/5 = 20/5 = 4.

From 2 to 4 is an increase of 100%.

The correct answer is D.

[Matt@VeritasPrep]

If we've got

(-4 + -1 + 0 + 6 + 9) / 3

and we're changing it to

(2 + 3 + 0 + 6 + 9) / 3

we're going from 10/3 to 20/3. That DOUBLES the mean, for an increase of 100%. (If you picked 200%, don't beat yourself up, that's an easy mistake to make. The new mean IS 200% of the old man, but it's also 100% GREATER THAN the old mean, which is what the question is asking for.)

[Anaira Mitch]

Thanks guys for your amazing solution on this problem.