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A function * is defined for all even positive integers n as the number
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Updated on: 15 Jul 2019, 02:58
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
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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
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04 Mar 2017, 09:49
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
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04 Mar 2017, 11:04
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, 48So, 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
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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
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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
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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) = 1021 = 7
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Re: A function * is defined for all even positive integers n as the number
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12 Nov 2018, 00:33






