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# For every even positive integer m, f(m) represents the produ

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Math Expert
Joined: 02 Sep 2009
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For every even positive integer m, f(m) represents the produ  [#permalink]

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11 Mar 2014, 02:20
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Difficulty:

15% (low)

Question Stats:

80% (01:26) correct 20% (01:37) wrong based on 965 sessions

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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

Problem Solving
Question: 149
Category: Arithmetic Properties of numbers
Page: 81
Difficulty: 600

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

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11 Mar 2014, 02:24
1
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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.

Similar questions to practice:
for-every-positive-even-integer-n-the-function-h-n-is-126691.html
for-every-positive-even-integer-n-the-function-h-n-149722.html
for-any-integer-p-p-is-equal-to-the-product-of-all-the-int-112494.html
x-is-the-product-of-all-even-numbers-from-2-to-50-inclusive-156545.html
if-a-and-b-are-odd-integers-a-b-represents-the-product-of-144714.html
the-function-f-m-is-defined-for-all-positive-integers-m-as-108309.html
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Re: For every even positive integer m, f(m) represents the produ  [#permalink]

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11 Mar 2014, 19:21
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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 produ  [#permalink]

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11 Mar 2014, 03:38
1
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, 05:06
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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Joined: 02 Sep 2009
Posts: 52108
Re: For every even positive integer m, f(m) represents the produ  [#permalink]

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15 Mar 2014, 09:25
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.

Similar questions to practice:
for-every-positive-even-integer-n-the-function-h-n-is-126691.html
for-every-positive-even-integer-n-the-function-h-n-149722.html
for-any-integer-p-p-is-equal-to-the-product-of-all-the-int-112494.html
x-is-the-product-of-all-even-numbers-from-2-to-50-inclusive-156545.html
if-a-and-b-are-odd-integers-a-b-represents-the-product-of-144714.html
the-function-f-m-is-defined-for-all-positive-integers-m-as-108309.html
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Re: For every even positive integer m, f(m) represents the produ  [#permalink]

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25 Jul 2014, 00:33
1
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, 04:57
4
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, 07:07
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.

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, 11:10
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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For every even positive integer m, f(m) represents the produ  [#permalink]

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Updated on: 03 Apr 2017, 10:34
2
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)
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Originally posted by Shiv2016 on 03 Apr 2017, 06:10.
Last edited by Shiv2016 on 03 Apr 2017, 10:34, 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, 10:02
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

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

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06 Apr 2017, 09:00
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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Re: For every even positive integer m, f(m) represents the produ  [#permalink]

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26 Apr 2018, 14:08
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