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#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # A function * is defined for all even positive integers n as the number

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Math Expert V
Joined: 02 Sep 2009
Posts: 60480
A function * is defined for all even positive integers n as the number  [#permalink]

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Difficulty:   45% (medium)

Question Stats: 52% (01:50) correct 48% (01:31) wrong based on 42 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

Are You Up For the Challenge: 700 Level Questions

_________________
Senior Manager  G
Joined: 16 Feb 2015
Posts: 252
Location: United States
Concentration: Finance, Operations
Re: A function * is defined for all even positive integers n as the number  [#permalink]

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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 give kudos, if you find my explanation Good Enough Intern  B
Joined: 07 May 2019
Posts: 28
Re: A function * is defined for all even positive integers n as the number  [#permalink]

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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
Manager  G
Joined: 10 Dec 2017
Posts: 174
Location: India
Re: A function * is defined for all even positive integers n as the number  [#permalink]

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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:) Re: A function * is defined for all even positive integers n as the number   [#permalink] 08 Dec 2019, 08:03
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