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A function * is defined for all even positive integers n as the number

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A function * is defined for all even positive integers n as the number  [#permalink]

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New post 05 Dec 2019, 01:33
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E

Difficulty:

  55% (hard)

Question Stats:

52% (01:51) correct 48% (01:30) wrong based on 48 sessions

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Concentration: Finance, Operations
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Re: A function * is defined for all even positive integers n as the number  [#permalink]

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New post 05 Dec 2019, 02:24
1
Bunuel wrote:
A function * is defined for all even positive integers n as the number of even factors of n other than n itself. What is the value of *(48) ?

(A) 3
(B) 5
(C) 6
(D) 7
(E) 8


Are You Up For the Challenge: 700 Level Questions


Explanation:

*n = Number of even factors of n other than n
= *48
Factors of 48 are: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
Number of even factors other than 48 = 7 (2,4,6,8,12,16,24)

IMO-D

:please Please give kudos, if you find my explanation Good Enough :please
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Re: A function * is defined for all even positive integers n as the number  [#permalink]

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New post 05 Dec 2019, 03:01
1
Bunuel wrote:
A function * is defined for all even positive integers n as the number of even factors of n other than n itself. What is the value of *(48) ?

(A) 3
(B) 5
(C) 6
(D) 7
(E) 8


Are You Up For the Challenge: 700 Level Questions



For any number N which can be written prime factorized and written like this = \(2^a * P^b * Q^c *....\) , (where 2, P, Q...are all prime numbers)

The total even factors including \(N = a * (b+1) * (c+1)....\)

In this case \(N = 48 = 2^4 * 3^1\)

Thus, total even factors including 48 will be \( 4* (1+1) = 8\)

However, we need even factors excluding the number, thus the answer will be \(8 - 1 = 7\).

Option D
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Re: A function * is defined for all even positive integers n as the number  [#permalink]

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New post 08 Dec 2019, 08:03
Bunuel wrote:
A function * is defined for all even positive integers n as the number of even factors of n other than n itself. What is the value of *(48) ?

(A) 3
(B) 5
(C) 6
(D) 7
(E) 8


Are You Up For the Challenge: 700 Level Questions

\(48=2^4*3^1\)
Total factors=(4+1)*(1+1)=10
Even factors excluding 48 will be Total- [1,3,48]
10-3
=7
D:)
GMAT Club Bot
Re: A function * is defined for all even positive integers n as the number   [#permalink] 08 Dec 2019, 08:03
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