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Manager
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For every positive even integer n, the function h(n) is defined to be
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14 Dec 2018, 08:55
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67% (01:41) correct 33% (02:00) wrong based on 74 sessions
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For every positive even integer n, the function h(n) is defined to be the product of all even integers from 2 to n, inclusive. For instance, h(10)= 2x4x6x8x10. What is the greatest prime factor of h(94)+h(96)? a) 89 b) 91 c) 93 d) 97 e) 99
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Re: For every positive even integer n, the function h(n) is defined to be
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14 Dec 2018, 10:48
h(94) = 2*4*6*....*94 = 2(1*2*3*...*47) = 2*47! h(96) = 2*4*6*.....*96 = 2(1*2*3*...*48) = 2*48! h(94)+h(96) = 47!(2+96) = 47!(97) Hence the largest prime factor is 97. D is the answer.
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Re: For every positive even integer n, the function h(n) is defined to be
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15 Dec 2018, 03:42
For every positive even integer n, the function h(n) is defined to be the product of all even integers from 2 to n, inclusive. For instance, h(10)= 2x4x6x8x10. What is the greatest prime factor of h(94)+h(96)? \(h(94)+h(96) = 2*4*.....*94+2*4*......94*96 = (2*4*.....94)(1+96) = (2*4*.....94)*97\) 97 is a prime number so it is the greatest prime factor Answer D
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Re: For every positive even integer n, the function h(n) is defined to be
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19 Dec 2018, 02:56
Afc0892 wrote: h(94) = 2*4*6*....*94 = 2(1*2*3*...*47) = 2*47! h(96) = 2*4*6*.....*96 = 2(1*2*3*...*48) = 2*48! h(94)+h(96) = 47!(2+96) = 47!(97) Hence the largest prime factor is 97.
D is the answer. 47! (2+96) is not equal to 47! (97). However, it is equal to 47! (98). But from this we can't sufficiently conclude that 97 is a factor of the two numbers. Liked the thinking though!! Best, gota900
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Re: For every positive even integer n, the function h(n) is defined to be
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19 Dec 2018, 02:59
gota900 wrote: Afc0892 wrote: h(94) = 2*4*6*....*94 = 2(1*2*3*...*47) = 2*47! h(96) = 2*4*6*.....*96 = 2(1*2*3*...*48) = 2*48! h(94)+h(96) = 47!(2+96) = 47!(97) Hence the largest prime factor is 97.
D is the answer. 47! (2+96) is not equal to 47! (97). However, it is equal to 47! (98). But from this we can't sufficiently conclude that 97 is a factor of the two numbers. Liked the thinking though!! Best, gota900 Hey gota900, yes its 97*47!. Made a silly mistake while typing the answer ? Posted from my mobile device
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Re: For every positive even integer n, the function h(n) is defined to be
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19 Dec 2018, 03:08
Afc0892 wrote: gota900 wrote: Afc0892 wrote: h(94) = 2*4*6*....*94 = 2(1*2*3*...*47) = 2*47! h(96) = 2*4*6*.....*96 = 2(1*2*3*...*48) = 2*48! h(94)+h(96) = 47!(2+96) = 47!(97) Hence the largest prime factor is 97.
D is the answer. 47! (2+96) is not equal to 47! (97). However, it is equal to 47! (98). But from this we can't sufficiently conclude that 97 is a factor of the two numbers. Liked the thinking though!! Best, gota900 Hey gota900, yes its 97*47!. Made a silly mistake while typing the answer ? Posted from my mobile deviceI know that it is 47! (97). Thats why the OA is D. But a little mistake in the factoring yields 98 in your answer. Not 97, thats why I liked your thinking, but the very last step went wrong. Let me show you what I mean: 2*47! + 2*48!  so far, so good! The factoring which would yield the desired outcome, however, should be this: 2*47! (1+2*48) 94! (1+96) 94! (97) OA: D Agreed? Best, gota900
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Re: For every positive even integer n, the function h(n) is defined to be
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31 Dec 2018, 12:03
Hello!
Can someone please give an alternative solution instead of binomial theorem?
Thank you very much!



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Re: For every positive even integer n, the function h(n) is defined to be
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31 Dec 2018, 21:15
jfranciscocuencag wrote: Hello!
Can someone please give an alternative solution instead of binomial theorem?
Thank you very much! H(94) = 2*4*6....*94 H(96) = 2*4*6....*94*96 = H(94)*96 H(94) + H(96) = H(94) + H(94)*96 = H(94) { 1 + 96 } = H(94) * 97 = 2*4*.....*94*97 Hence greatest prime factor is 97
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Re: For every positive even integer n, the function h(n) is defined to be
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01 Jan 2019, 08:52
This is how i have solved. h(94) = 2*4*6*8........94 = 2^47 ( 1 * 2 * 3 * 4 ......47) .........(i) h(96) = 2*4*6*8........96 =2^48 ( 1 * 2 * 3 * 4 ......48 ) .........(ii) adding above two equation and taking 2^47 ( 1 * 2 * 3 * 4 ......47) common , we get >2^47 ( 1 * 2 * 3 * 4 ......47) (1 + \(2*48\)) > 2^47 ( 1 * 2 * 3 * 4 ......47) (97) Thus 97 is our answer. Hope it helps.
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Re: For every positive even integer n, the function h(n) is defined to be
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01 Jan 2019, 08:52






