Hi akash,

From the info given in the question we can deduce the following

M = (60+z)/6

Now if you multiply each number of the set by 'N' then

M = N(60+z)/6

Percentage change in M would be [M(new) - M(old)]/M(old) * 100%
This turns out to be

[N(60+z)/6 - (60+z)/6] / (60+z)/6
Factor out (60+z)/6 and you'll be left with N-1 (So you essentially need the value of N)

1) Z = 60
You can find the exact value of M from this. (No need to calculate though)
N is unknown, hence NOT Sufficient

2) N = Z/M
Z could have any value, hence NOT Sufficient

Combine both the statements and you have an exact value of M from Statement 1 and Statement 2 will give you a value of N

These two pieces of information are sufficient to calculate the percent change in N
Combined the statements are sufficient

OA : C

I would really appreciate if an expert could show a time efficient approach to this question.

akash singhal wrote:If every member of set X {-14, -12, 17, 28, 41, Z} is multiplied by number N, by what percent will the mean M of the set increase?
(1) Z = 60 (2) N = Z / M

If every value in Set X is multiplied by a factor of N=2, then the value of mean M will also be multiplied by a factor of N=2.
If every value in Set X is multiplied by a factor of N=3, then the value of mean M will also be multiplied by a factor of N=3.
If every value in Set X is multiplied by a factor of N=10, then the value of mean M will also be multiplied by a factor of N=10.
Implication:
If we know the value of N, we can determine by what percent mean M will increase.

Question stem, rephrased:
What is the value of N?

Statement 1: Z=60
Since every value in Set X is known, the value of M can be determined.
No information about N.
INSUFFICIENT.

Statement 2: N = Z/M
Since the values of Z and M are unknown, no way to determine the value of N.
INSUFFICIENT.

Statements combined:
Statement 1: Z=60 enables us to determine the value of M.
Statement 2: Z=60 and the value of M will enable us to determine the value of N.
SUFFICIENT.

The correct answer is C.