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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 Updated on: 15 Jul 2019, 02:58
3
4
00:00
A
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D
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Difficulty:

  55% (hard)

Question Stats:

56% (01:37) correct 44% (01:33) wrong based on 122 sessions

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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

Source: Nova GMAT
Difficulty Level: 700

Originally posted by vikasp99 on 04 Mar 2017, 08:11.
Last edited by SajjadAhmad on 15 Jul 2019, 02:58, edited 1 time in total.
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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 04 Mar 2017, 09:49
3
2 ways to solve this problem.

1. manually count all even factors except 48

2. use prime factorization =>
48 = 2^4 * 3^1
For an even factor, power of prime factor 2 must be at least 1 and power of prime factor 3 can be 0 or 1

thus, prime fact 2 can take 1,2,3 and 4 (4 choices) as powers and 3 can take 0 or 1 (2 choices)

total even factors = 4 * 2 =8, since n is not allowed as a factor
answer is 8 - 1 = 7
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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 04 Mar 2017, 11:04
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vikasp99 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


Use factorization -

The factors of 48 are:1, 2, 3, 4, 6, 8, 12, 16, 24, 48

So, except 48, there are 7 factors, answer must be (D) 7
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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 30 Sep 2018, 06:33
Bunuel could you please show a detailed method using factorization?
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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 04 Oct 2018, 21:33
The total 10 factors are 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48. But we need only even factors (leaving out 1 and 3), and don't need n itself (leaving out 48), which gives us a total of (10 - 3) = 7 factors.
Is my understanding correct?
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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 12 Nov 2018, 00:33
Total - odd - Number itself
10 - (3^0 and 1) - 1(Number is 48 or only one factor out of 48)
= 10-2-1 = 7
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Re: A function * is defined for all even positive integers n as the number   [#permalink] 12 Nov 2018, 00:33
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