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For every integer n, n* is defined as the sum of all the distinct

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Bunuel
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For every integer n, n* is defined as the sum of all the distinct [#permalink] New post   29 Apr 2019, 23:25
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For every integer n, n* is defined as the sum of all the distinct factors of n. Which of the following is equal to 10*?

A. 5*
B. 15*
C. 17*
D. 18*
E. 100*
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C
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Archit3110
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For every integer n, n* is defined as the sum of all the distinct [#permalink] New post   Updated on: 01 May 2019, 01:31
Bunuel wrote:
For every integer n, n* is defined as the sum of all the distinct factors of n. Which of the following is equal to 10*?

A. 5*
B. 15*
C. 17*
D. 18*
E. 100*


factors of 10 ; 2,5,10
sum ; 17
IMO c

Originally posted by Archit3110 on 30 Apr 2019, 03:05.
Last edited by Archit3110 on 01 May 2019, 01:31, edited 2 times in total.
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Re: For every integer n, n* is defined as the sum of all the distinct [#permalink] New post   30 Apr 2019, 03:12
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The factors of 10 are 1,2,5,10. The Sum= 18

IMO, the answer should be D
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For every integer n, n* is defined as the sum of all the distinct [#permalink] New post   Updated on: 17 Aug 2019, 06:46
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let \(P= a^m * b^n * c^o\) ........
where a,b and c are distinct primes
Sum of factor of P= \(\frac{a^{m+1}- 1}{a-1} * \frac{b^{n+1}- 1}{b-1} * \frac{c^{o+1}- 1}{c-1}\) ...
10=2*5
sum of factors of 10= \(\frac{(2^2 -1)}{(2-1)} * \frac{(5^2 -1)}{(5-1)}= 3*6=18\)

Originally posted by nick1816 on 30 Apr 2019, 09:38.
Last edited by nick1816 on 17 Aug 2019, 06:46, edited 1 time in total.
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Re: For every integer n, n* is defined as the sum of all the distinct [#permalink] New post   30 Apr 2019, 10:14
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Guys i solved it this way.

Sum of factors of 10- 1+10+2+5= 18

Only 17 will give sum of factors 1+17= 18

Hope i’m correct.

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For every integer n, n* is defined as the sum of all the distinct [#permalink] New post   17 Aug 2019, 06:28
Hello Bunuel ,

Please correct me if i am wrong.

Distinct factors of 10 are 1,2,5,10
Hence the sum should be 18.

However, the OA is given as C(which is 17). Am i missing something here?

Thank you
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Re: For every integer n, n* is defined as the sum of all the distinct [#permalink] New post   17 Aug 2019, 06:35
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brains wrote:
For every integer n, n* is defined as the sum of all the distinct factors of n. Which of the following is equal to 10*?

A. 5*
B. 15*
C. 17*
D. 18*
E. 100*


Hello Bunuel ,

Please correct me if i am wrong.

Distinct factors of 10 are 1,2,5,10
Hence the sum should be 18.

However, the OA is given as C(which is 17). Am i missing something here?

Thank you


10* = the sum of all the distinct factors of 10 = 1 + 2 + 5 + 10 = 18.
17* = the sum of all the distinct factors of 17 = 1 + 17 = 18.

Option C shows 17*, not 17.
Option D shows 18*, not 18.

Hope it's clear.
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For every integer n, n* is defined as the sum of all the distinct [#permalink] New post   17 Aug 2019, 08:23
Bunuel wrote:
For every integer n, n* is defined as the sum of all the distinct factors of n. Which of the following is equal to 10*?

A. 5*
B. 15*
C. 17*
D. 18*
E. 100*


Given: For every integer n, n* is defined as the sum of all the distinct factors of n.

Asked: Which of the following is equal to 10*?

10 = 2*5
Distinct factors of 10 = {1,2,5,10}
Sum of distinct factors of 10 = 1+2+5+10 = 18
10* =18

Distinct factors of 17 = {1,17}
Sum of distinct factors of 17 = 1+17 = 18
17* =18
10* =18 = 17*

IMO C
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Re: For every integer n, n* is defined as the sum of all the distinct [#permalink] New post   14 Feb 2022, 09:21
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