Data Sufficiency

What is the sum of the digits of the positive integer n where n < 99?

1) n is divisible by the square of the prime number y.

2) y4 is a two-digit odd integer.

OA is C but I need some clarification.

After taking both statements together, we can only conclude y = 3.
But we have no information on n.

Is it because n will always be a multiple of 9 that its sum of digits will be 9?

kartikshah wrote:What is the sum of the digits of the positive integer n where n < 99?

1) n is divisible by the square of the prime number y.

2) y4 is a two-digit odd integer.

OA is C but I need some clarification.

After taking both statements together, we can only conclude y = 3.
But we have no information on n.

Is it because n will always be a multiple of 9 that its sum of digits will be 9?

Yes because after combining both the statements we can find the value of y, which has to be 3.
and since n is divisible by 3^2 (from the first statement) the sum of the digits of n will always be 9.

Why B is not sufficient to answer the question.

y^4 will be only 3^4 =81 less then 99.


Nawneet

gmattest001 wrote:Why B is not sufficient to answer the question.

y^4 will be only 3^4 =81 less then 99.


Nawneet

Because y=3 doesn't tell us anything about n. We need to determine what is sum of digits of "n".

Statement 1. N = ay2 (y is a prime number)
N has different value for y = 3, 5, 7 etc. Hence, Insufficient.
Statement 2. y4 is a two digit odd integer.
y= 3.
But we don't know the relation between 'n' and 'y' in statement 2. Hence, Insufficient.
Statement 1 & 2 together. Using the results of statement 1 and 2, we get,
n = ay2 and y = 3
n = 9a
So, n is a no divisible by 9. Any two digit no divisible by 9 has sum of its digits = 9.
Hence, Sufficient.