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Tasha's Favorite Number
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Updated on: 27 Aug 2016, 06:29
Updated on: 27 Aug 2016, 06:29
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Question Stats:
55% (00:34) correct
44% (01:01) wrong based on 106 sessions
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Tasha's favorite number can be written as \(3^2*17^2\)
Quantity A |
Quantity B |
The number of distinct positive divisors of Tasha's favorite number |
9 |
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Re: Tasha's Favorite Number
[#permalink]
27 Aug 2016, 06:54
27 Aug 2016, 06:54
5
yasir9909 wrote:
Tasha's favorite number can be written as \(3^2*17^2\)
Quantity A |
Quantity B |
The number of distinct positive divisors of Tasha's favorite number |
9 |
Useful formula: If N = (p^a)(q^b)(r^c)..., where p, q, r,...(etc.) are prime numbers, then the total number of positive divisors of N is equal to (a+1)(b+1)(c+1)...
Example: 14000 = (2^4)(5^3)(7^1)
So, the number of positive divisors of 14000 = (4+1)(3+1)(1+1) = (5)(4)(2) = 40
Now onto the question......
QUANTITY A: we're given: (3^2)(17^2)
So, the number of positive divisors = (2+1)(2+1) = (3)(3) = 9
QUANTITY B: 9
Answer:
Show: ::
C
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General Discussion
Re: Tasha's Favorite Number
[#permalink]
27 Aug 2016, 06:28
27 Aug 2016, 06:28
1
Here is how I have solved it:
\(3^2*17^2 = 2601\)
Distinct positive divisors of 2601 = {1,3,9,17,51,153,289,867,2061}
So both these quantities are equal and answer is C.
\(3^2*17^2 = 2601\)
Distinct positive divisors of 2601 = {1,3,9,17,51,153,289,867,2061}
Quantity A |
Quantity B |
No of distinct positive divisors of 2601 = 9 |
9 |
So both these quantities are equal and answer is C.
