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

Question

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%

Bunuel · Answer

Mean of X is (-4-1+0+6+9)/5=2;

In order the increase to be minimal we should replace two smallest elements of X, which are -4 and -1, with two smallest primes, which are 2 and 3. Hence our new set will be {2, 3, 0, 6, 9} --> new mean is (2+3+0+6+9)/5=4.

Percent increase=(4-2)/2*100=100%.

Answer: D.

pappueshwar · Answer

hi Bunuel,

request to let me if two smallest primes numbers can be negative?

Bunuel · Answer

Only positive numbers can be primes, so the smallest prime is 2.

Hope it helps.

PareshGmat · Answer

1 is not a prime number, got to know it now..... was considering it & made the answer wrong

LogicGuru1 · Answer

Current mean is = \frac{(-4)+(-1)+(0)+(6)+(9)}{5} = \frac{(-5+15)}{5} = \frac{10}{5} = 2

Since we have to find the minimum increase , we should add the smallest distinct prime 2,3
New mean is = \frac{(0)+(2)+(3)+(6)+(9)}{5} = \frac{20}{5} = 4

Percent change =  \frac{(New -Old}{Old})* 100 = \frac{4-2}{2}*100

Percent change =  \frac{2}{2}* 100 = 100  %

Answer is D

BrentGMATPrepNow · Answer

As others have demonstrated, the average of set X increases from   2   to   4  
Many students will incorrectly conclude that we have a 200% increase, since   4   is equal to 2 times   2  .
This is not the case. 
 Percent increase = 100( new  -  old )/ old 
 So, in this case, percent increase = 100( 4  -  2 )/ 2 
= 200/2
= 100

Cheers,
Brent

paidlukkha · Answer

Bunuel 
answer will change if I have 5 & 2 or say 2 & 11, isn't it?
just curious...

abhimahna · Answer

Yes, it will change but notice that we have to determine the minimum change and for that we are taking the lowest possible values as 2 and 3.

anairamitch1804 · Answer

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.

Arishas · Answer

I think D. 
Mean in the initial set is 2 (-4-2+0+6+9)/5. We should replace the smallest elements -4 and -1 with prime numbers also the smallest in order to have minimum percentage increase. So we get new set (2,3,0,6,9) with mean 4. So the minimum % increase is 100%

Sent from my SM-A310F using  GMAT Club Forum mobile app

Bunuel · Answer

Merging topics. Please refer to the discussion above.

Nunuboy1994 · Answer

minimize set   = 20/5= 4

old set   = 10/5 =2

4-2/2 = 1

D

bumpbot · Answer

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

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

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