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# For every even positive integer m, f(m) represents the product of all

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For every even positive integer m, f(m) represents the product of all  [#permalink]

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11 Mar 2014, 03:20
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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

The Official Guide For GMAT® Quantitative Review, 2ND Edition

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Re: For every even positive integer m, f(m) represents the product of all  [#permalink]

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11 Mar 2014, 03:24
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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.

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Re: For every even positive integer m, f(m) represents the product of all  [#permalink]

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11 Mar 2014, 20:21
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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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Re: For every even positive integer m, f(m) represents the product of all  [#permalink]

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11 Mar 2014, 04:38
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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 product of all  [#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 product of all  [#permalink]

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25 Jul 2014, 01:33
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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 product of all  [#permalink]

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24 Jul 2015, 05:57
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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 product of all  [#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.

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 product of all  [#permalink]

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02 Feb 2017, 12:10
1
Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

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.

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.

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Re: For every even positive integer m, f(m) represents the product of all  [#permalink]

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Updated on: 03 Apr 2017, 11:34
3
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)

Originally posted by Shiv2016 on 03 Apr 2017, 07:10.
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 product of all  [#permalink]

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03 Apr 2017, 11:02
1
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 product of all  [#permalink]

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06 Apr 2017, 10:00
1
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.

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# Jeffrey Miller

Head of GMAT Instruction

Jeff@TargetTestPrep.com
122 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

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Re: For every even positive integer m, f(m) represents the product of all  [#permalink]

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31 May 2019, 06:03
$$f(24) = 2*4*6*8*10*12*14*16*18*20*22*24$$

$$f(24)$$ = 2^12$$*(1*2*3*4*5*6*7*8*9*10*11*12)$$

The greatest prime factor in f(24) is 11.

The correct answer is E
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Re: For every even positive integer m, f(m) represents the product of all   [#permalink] 31 May 2019, 06:03
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# For every even positive integer m, f(m) represents the product of all

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