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

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

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New post Updated on: 05 Dec 2019, 07:37
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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, 06:39.
Last edited by Bunuel on 05 Dec 2019, 07:37, edited 3 times in total.
Edited the question and moved to PS forum.
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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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New post 28 Aug 2017, 06:49
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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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Re: If n is an even integer and <n> denotes that the product of all the  [#permalink]

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New post 29 Aug 2017, 02:35
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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
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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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New post 28 Aug 2017, 07:13
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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P.S. Please follow the rules when posting a question.
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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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New post 28 Aug 2017, 07:53
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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Re: If n is an even integer and <n> denotes that the product of all the  [#permalink]

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New post 13 Oct 2019, 22:36
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.
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Re: If n is an even integer and <n> denotes that the product of all the   [#permalink] 13 Oct 2019, 22:36
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