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# If n is an even integer and <n> denotes that the product of all the

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Intern
Joined: 10 Aug 2017
Posts: 17
GMAT 1: 720 Q48 V41
If n is an even integer and <n> denotes that the product of all the  [#permalink]

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Updated on: 05 Dec 2019, 06:37
3
00:00

Difficulty:

45% (medium)

Question Stats:

64% (01:40) correct 36% (02:02) wrong based on 87 sessions

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If n is an even integer and <n> denotes that the product of all the even positive integers to n. For example, <n> = 2 * 4 * 6 * 8 * .... * n. What is the greatest prime factor of <20> + <22>?

A. 19
B. 21
C. 23
D. 27
E. 31

Got this question from my offline GMAT prep course I signed up for last week.. Can anybody help me actually solve this problem please??
Also, how can I tag this post properly?

Originally posted by HappyQuakka on 28 Aug 2017, 05:39.
Last edited by Bunuel on 05 Dec 2019, 06:37, edited 3 times in total.
Edited the question and moved to PS forum.
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Joined: 26 Feb 2016
Posts: 3265
Location: India
GPA: 3.12
Re: If n is an even integer and <n> denotes that the product of all the  [#permalink]

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28 Aug 2017, 05:49
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1
Hey HappyQuakka,

Since <n> = 2*4*6*8*10*12*.... n
<20> = 2*4*6*8*10*12.... 20
<22> = 2*4*6*8*10*12.... 22

Therefore <20> + <22> = 2*4*6*8*10*12.... 20 + 2*4*6*8*10*12.... 20*22 = 2*4*6*8*10*12.... 20(1+22) = 2*4*6*8*10*12.... 20*23

Hence the greatest prime factor must be 23(Option C)

Hope that helps!
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##### General Discussion
Intern
Joined: 21 Nov 2016
Posts: 40
Re: If n is an even integer and <n> denotes that the product of all the  [#permalink]

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29 Aug 2017, 01:35
1
Luckisnoexcuse wrote:
HappyQuakka wrote:
If n is an even integer and <n> denotes that the product of all the positive integers to n. For example, <n> = 2 * 4 * 6 * 8 * .... * n. What is the greatest prime factor of <20> + <22>?

A. 19
B. 21
C. 23
D. 27
E. 31

Got this question from my offline GMAT prep course I signed up for last week.. Can anybody help me actually solve this problem please??
Also, how can I tag this post properly?

<20> + <22> = <20> (1 + 22) = <20> * 23

C

I guess the question stem here should say "<n> denotes that the product of all the positive EVEN integers to n" only then we can solve it the way you have done. Please correct me if I am wrong
Math Expert
Joined: 02 Sep 2009
Posts: 61484
Re: If n is an even integer and <n> denotes that the product of all the  [#permalink]

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28 Aug 2017, 06:13
HappyQuakka wrote:
If n is an even integer and <n> denotes that the product of all the positive integers to n. For example, <n> = 2 * 4 * 6 * 8 * .... * n. What is the greatest prime factor of <20> + <22>?

A. 19
B. 21
C. 23
D. 27
E. 31

Got this question from my offline GMAT prep course I signed up for last week.. Can anybody help me actually solve this problem please??
Also, how can I tag this post properly?

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Hope it helps.

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Re: If n is an even integer and <n> denotes that the product of all the  [#permalink]

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28 Aug 2017, 06:53
HappyQuakka wrote:
If n is an even integer and <n> denotes that the product of all the positive integers to n. For example, <n> = 2 * 4 * 6 * 8 * .... * n. What is the greatest prime factor of <20> + <22>?

A. 19
B. 21
C. 23
D. 27
E. 31

Got this question from my offline GMAT prep course I signed up for last week.. Can anybody help me actually solve this problem please??
Also, how can I tag this post properly?

<20> + <22> = <20> (1 + 22) = <20> * 23

C
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Luckisnoexcuse
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Re: If n is an even integer and <n> denotes that the product of all the  [#permalink]

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13 Oct 2019, 21:36
HappyQuakka wrote:
If n is an even integer and <n> denotes that the product of all the positive integers to n. For example, <n> = 2 * 4 * 6 * 8 * .... * n. What is the greatest prime factor of <20> + <22>?

A. 19
B. 21
C. 23
D. 27
E. 31

Got this question from my offline GMAT prep course I signed up for last week.. Can anybody help me actually solve this problem please??
Also, how can I tag this post properly?

<n> = 2*4*6*8*10*12*...*n
=> <20> = 2*4*6*8*10*12...*20
and <22> = <20>*22
Thus, <20> + <22> = <20>(1+22)=<20>*23
None of the terms in <20> is a prime number, except 2, so 23 is the greatest prime factor of <20> + <22>.

Therefore, the correct answer is option C.
Re: If n is an even integer and <n> denotes that the product of all the   [#permalink] 13 Oct 2019, 21:36
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