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Sum of the digits of the positive integer n where n < 99

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Sum of the digits of the positive integer n where n < 99

by kartikshah » Mon Jul 23, 2012 8:12 am
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?
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Source: — Data Sufficiency |
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by niketdoshi123 » Mon Jul 23, 2012 8:21 am
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.
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by gmattest001 » Mon Jul 23, 2012 10:00 am
Why B is not sufficient to answer the question.

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


Nawneet
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by eagleeye » Mon Jul 23, 2012 10:18 am
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".

:)
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by masoom j negi » Fri Dec 21, 2018 8:57 pm
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.
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