Data Sufficiency

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

Looking for some assistance on above problem.

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.

It often helps to start a DS problem by thinking about what you'll need to solve.

Here, we need to know what Z is, and we need to know what N is.

S1 tells us Z, so we're halfway there.

S2 tells us N **IF** know Z. We don't know Z yet, but this is the other half!

Together, S1 gives us Z, and S2 uses Z to find N. From there, we're done - don't even bother calculating!