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# What is the sum of the digits of the positive integer n

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What is the sum of the digits of the positive integer n [#permalink]

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26 Jul 2008, 00:43
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62% (02:02) correct 38% (00:52) wrong based on 215 sessions

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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) y^4 is a two-digit odd integer.

OPEN DISCUSSION OF THIS QUESTION IS HERE: what-is-the-sum-of-the-digits-of-the-positive-integer-n-104241.html
[Reveal] Spoiler: OA

Last edited by Bunuel on 05 Sep 2014, 22:01, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
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Re: What is the sum of the digits of the positive integer n [#permalink]

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26 Jul 2008, 00:51
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GMBA85 wrote:
judokan 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

Is Statement 2 y^4

If it is y^4

Combining both the statements we get y = 3

This implies that N has to be divisible by 9. All 2 digit factors of 9 have the sum of their digits as 9.
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Re: What is the sum of the digits of the positive integer n [#permalink]

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26 Jul 2008, 06:19
GMBA85 wrote:
judokan 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

Is Statement 2 y^4

Yes, y^2, sorry for the typo.

WIll post OA later
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Re: What is the sum of the digits of the positive integer n [#permalink]

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05 Sep 2014, 21:17
judokan 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

ans is E .. bcz y^4 = odd it means

y^4 can be 11,13 and yes 81 also which many people thought so maultiples values of y^4 = odd
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Re: What is the sum of the digits of the positive integer n [#permalink]

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05 Sep 2014, 21:34
statement 1 : n is divisible by the square of the prime number y.

y can be 2,3,5 or 7. so n can be a multiple of 4,9,25 or 49. No definite answer

statement 2 : y^4 is a two-digit odd integer

statement is clearly insufficient

1 + 2 combined,

only y=3 can satisfy both conditions. so n is a multiple of 9 and n<99
Therefore n could be 9,18,27,36,45.....90
sum of digits for all the possibilities is 9. so combined statements are sufficient.

Ans- C
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Re: What is the sum of the digits of the positive integer n [#permalink]

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05 Sep 2014, 22:02
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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 --> clearly insufficient, as no info about y.

2) y^4 is a two-digit odd integer --> also insufficient, as no info about n, but from this statement we know that if y is an integer then y=3 (y must be odd in order y^4 to be odd and it cannot be less than 3 or more than 3 since 1^4 and 5^4 are not two digit numbers).

(1)+(2) Since from (1) y=integer then from (2) y=3, so n is divisible by 3^2=9. Number to be divisible by 9 sum of its digits must be multiple of 9, as n is two-digit number <99 then the sum of its digits must be 9 (18, 27, 36, ..., 90.). Suffiicient.

OPEN DISCUSSION OF THIS QUESTION IS HERE: what-is-the-sum-of-the-digits-of-the-positive-integer-n-104241.html
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Re: What is the sum of the digits of the positive integer n   [#permalink] 05 Sep 2014, 22:02
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