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For every even positive integer m, f(m) represents the produ [#permalink]
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11 Mar 2014, 03:20
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The Official Guide For GMAT® Quantitative Review, 2ND EditionFor every even positive integer m, f(m) represents the product of all even integers from 2 to m, inclusive. For example, f(12) = 2 x 4 x 6 x 8 x 10 x 12. What is the greatest prime factor of f(24) ? (A) 23 (B) 19 (C) 17 (D) 13 (E) 11 Problem Solving Question: 149 Category: Arithmetic Properties of numbers Page: 81 Difficulty: 600 GMAT Club is introducing a new project: The Official Guide For GMAT® Quantitative Review, 2ND Edition  Quantitative Questions ProjectEach week we'll be posting several questions from The Official Guide For GMAT® Quantitative Review, 2ND Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution. We'll be glad if you participate in development of this project: 1. Please provide your solutions to the questions; 2. Please vote for the best solutions by pressing Kudos button; 3. Please vote for the questions themselves by pressing Kudos button; 4. Please share your views on difficulty level of the questions, so that we have most precise evaluation. Thank you!
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Re: For every even positive integer m, f(m) represents the produ [#permalink]
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11 Mar 2014, 04:38
For every even positive integer m, f(m) represents the product of all even integers from 2 to m, inclusive. For example, f(12) = 2 x 4 x 6 x 8 x 10 x 12. What is the greatest prime factor of f(24) ? (A) 23 (B) 19 (C) 17 (D) 13 (E) 11 Sol: f(24)= 2*4*6**....*24 or 2^12 (1*2*3*4*5*6....12) The greatest prime factor will be 11 Ans is E
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Re: For every even positive integer m, f(m) represents the produ [#permalink]
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11 Mar 2014, 06:06
All numbers are even. The only even prime is 2. For larger primes, we need a number with an odd factor. Consider 6, 10,...,22. The prime factorization of 22 is 2*11. The answer is E.



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Re: For every even positive integer m, f(m) represents the produ [#permalink]
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11 Mar 2014, 20:21
Answer = (E) 11 f(24) = 2 x 4 x 6 x 8 x 10 x 12 x 14 x 16 x 18 x 20 x 22 x 24 22 = 2 * 11 So 11 is the largest prime factor, Answer = E
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15 Mar 2014, 10:25



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25 Jul 2014, 01:33
We have f(24) = 2 x 4 x 6 x 8 x 10 x 12 x 14 x 16 x 18 x 20 x 22 x 24
Now the greatest prime factor of the product will be the greatest prime factor of one of the numbers above.
22 = 2 x 11 Hence greatest prime factor = 11.
Ans. E



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Re: For every even positive integer m, f(m) represents the produ [#permalink]
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24 Jul 2015, 05:57
Very easy,..think simply. The highest number can be divided by a highest prime is 22/11. so 11 is the answer GIve Kudos if you like my solution



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Re: For every even positive integer m, f(m) represents the produ [#permalink]
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27 Jan 2017, 08:07
Bunuel wrote: SOLUTION
For every even positive integer m, f(m) represents the product of all even integers from 2 to m, inclusive. For example, f(12) = 2 x 4 x 6 x 8 x 10 x 12. What is the greatest prime factor of f(24) ?
(A) 23 (B) 19 (C) 17 (D) 13 (E) 11
f(24) = 2*4*6*8*10*12*14*16*18*20*22*24 = 2^12*(1*2*3*4*5*6*7*8*9*10*11) > the greatest prime factor is 11.
Answer: E. Best answer hands down. By the way ... does anybody know what should be the take away message from this question?



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Re: For every even positive integer m, f(m) represents the produ [#permalink]
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02 Feb 2017, 12:10
Bunuel wrote: The Official Guide For GMAT® Quantitative Review, 2ND EditionFor every even positive integer m, f(m) represents the product of all even integers from 2 to m, inclusive. For example, f(12) = 2 x 4 x 6 x 8 x 10 x 12. What is the greatest prime factor of f(24) ? (A) 23 (B) 19 (C) 17 (D) 13 (E) 11 We are given that for every even positive integer m, f(m) represents the product of all even integers from 2 to m inclusive. Thus, f(24) = 2 x 4 x 6 x 8 x 10 x 12 x 14 x 16 x 18 x 20 x 22 x 24. If we were to break each value into primes, we would see that the greatest prime factor is contained in 22 (which equals 2 x 11). Thus, the largest prime factor in f(24) is 11. Answer: E
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For every even positive integer m, f(m) represents the produ [#permalink]
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Updated on: 03 Apr 2017, 11:34
Check out the options: Whatever the answer is, it should be a multiple of 2. (2* prime no.) (1) 23*2= 46 (out of range) (2) 19*2= 38 (out of range) (3) 17*2= 34 (out of range) (4) 13*2= 26 (out of range) (5) 11*2= 22 (Correct answer)
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Last edited by Shiv2016 on 03 Apr 2017, 11:34, edited 2 times in total.



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Re: For every even positive integer m, f(m) represents the produ [#permalink]
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03 Apr 2017, 11:02
My approach:
f(24) = 2 x 4 x 6 x 8 x 10 x12 x 14 x 16 x 18 x 20 x 22 x 24 f(24) = 2 x 2² x2 x 3 x 2³ x 2 x 5 x 2² x 3 x 2 x 7 x 2⁴ x 2 x 3² x 2² x 5 x 2 x 11 x 2³ x 3
Answer is E. 11



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Re: For every even positive integer m, f(m) represents the produ [#permalink]
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06 Apr 2017, 10:00
Bunuel wrote: For every even positive integer m, f(m) represents the product of all even integers from 2 to m, inclusive. For example, f(12) = 2 x 4 x 6 x 8 x 10 x 12. What is the greatest prime factor of f(24) ?
(A) 23 (B) 19 (C) 17 (D) 13 (E) 11
We are given that for every even positive integer m, f(m) represents the product of all even integers from 2 to m, inclusive. We need to determine the greatest prime factor of f(24). f(24) = 2 x 4 x 6 x … x 20 x 22 x 24 We see from the even multiples from 2 to 24, that 22 (which is 2 x 11) produces the largest prime factor of 11. Answer: E
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