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A function * is defined for all even positive integers n as the number 05 Dec 2019, 01:33
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58% (01:26) correct 42% (01:32) wrong based on 351 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


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A function * is defined for all even positive integers n as the number 05 Dec 2019, 02:24
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Bunuel
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


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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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A function * is defined for all even positive integers n as the number 05 Dec 2019, 03:01
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Bunuel
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


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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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A function * is defined for all even positive integers n as the number 08 Dec 2019, 08:03
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Bunuel
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


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\(48=2^4*3^1\)
Total factors=(4+1)*(1+1)=10
Even factors excluding 48 will be Total- [1,3,48]
10-3
=7
D:)
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A function * is defined for all even positive integers n as the number 28 Dec 2022, 23:07
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Bunuel
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

Show more

Formula

48=\(2^4*3^1\)
Number of factors: (4+1)(1+1)=10
Odd factors = (1+1) or 2, so even factors = 10-2 or 8.
If we take out 48, the remaining factors are 7.


Calculate the factors
48 being a small and friendly integer, we can find the factors directly
48 can be written as
1*48
2*24
3*16
4*12
6*8

Even factors other than 48 = 2,4,6,8,12,16,24, that is 7 in number.
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A function * is defined for all even positive integers n as the number 22 May 2024, 10:45
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