If every member of set X {-14, -12, 17, 28, 41, Z} is multiplied by nu

.
X {-14, -12, 17, 28, 41, Z}
If all the numbers are multiplied by a constant, the mean will also increase by that constant.

1. Z=60

We get a mean of 20 here initially.
If the set is multiplied by 10, the new mean becomes 200, increasing the mean by 900%
If the set is multiplied by 2, the new mean becomes 40, increasing the mean by 100%

We must find an exact value of multiplier or mean to find the percent increase in mean.
Not Sufficient.

2. N = Z / M

(-14, -12, 17, 28, 41 + Z)/6 = M

60+Z=6M
N = Z / M; Z=NM

60+NM=6M.
Not Sufficient to find an exact mean or multiplier.
Not Sufficient.

Combining both;
60+NM=6M
NM=Z=60
60+60=6M
M = 120/6= 20
And
N = Z/M = 60/20=3

We know the multiplier.
Sufficient.

Ans: "C"

P.S.: The new mean will increase by 20% because the multiplier is 3. We wouldn't need "Z" if we knew the multiplier, however in this case; we needed Z to find the multiplier.