Problem Solving

prachi18oct wrote:If M is a negative integer and K is a positive integer, which of the following could be the standard deviation of the set
{-7,-5,-3,M,0,1,3,K,7} ?
1. -1.5
2, -1
3. 0
A) 1 only
b) 2 only
c) 3 only
d) 1 & 3 only
e) None

K+M-4/9 = Mean
now K = { 4,5,6}
M can be ={ -3,-2,-1}
I could not proceed from here ... picking up these numbers to put in S.D formula is just way too time taking.
I am sure there must be a quicker way !
Experts please help.

Hi prachi18oct,

The question is not of the GMAT standard. Since Standard deviation is always positive, options A, B and D are ruled out.

SD can either be positive or 0.

Two things are not clear from the question narration: 1. Are the integers in the set {-7,-5,-3,M,0,1,3,K,7} arranged in the ascending order? The way they are arranged, it suggests that they; however, we cannot assume this. The question must tell it. 2. Are M and K unique? As per your work (K = {4,5,6}, M = { -3,-2,-1}), only K is unique.

Having said that there is no need to know whether K and M are placed in an order in the set or they are unique. The SD of the set cannot be 0 since there are many unequal numbers in the set, making SD a positive number. Since there no option as a positive number, the correct answer is none.

The correct answer: E

Hope this helps!

Relevant book: Manhattan Review GMAT Sets & Statistics Guide

-Jay
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