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# If {x} is the product of all even integers from 1 to x inclusive, what

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Joined: 02 Sep 2009
Posts: 49206
If {x} is the product of all even integers from 1 to x inclusive, what  [#permalink]

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02 Oct 2017, 23:47
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55% (hard)

Question Stats:

55% (00:56) correct 45% (01:33) wrong based on 67 sessions

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If {x} is the product of all even integers from 1 to x inclusive, what is the greatest prime factor of {22} + {20}?

A. 23
B. 20
C. 11
D. 5
E. 2

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Re: If {x} is the product of all even integers from 1 to x inclusive, what  [#permalink]

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02 Oct 2017, 23:52
Bunuel wrote:
If {x} is the product of all even integers from 1 to x inclusive, what is the greatest prime factor of {22} + {20}?

A. 23
B. 20
C. 11
D. 5
E. 2

{x} = Product of all EVEN integers from 1 to x

{22} + {20} = (2*4*6*8*10*12*14*16*18*20*22) + (2*4*6*8*10*12*14*16*18*20) = (2*4*6*8*10*12*14*16*18*20) * (22+1) = (2*4*6*8*10*12*14*16*18*20) * (23)

The greatest Prime factor of the result = 23

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Re: If {x} is the product of all even integers from 1 to x inclusive, what  [#permalink]

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05 Oct 2017, 10:16
Bunuel wrote:
If {x} is the product of all even integers from 1 to x inclusive, what is the greatest prime factor of {22} + {20}?

A. 23
B. 20
C. 11
D. 5
E. 2

{22} = 22 x 20 x 18 x 16 x … 4 x 2

{20} = 20 x 18 x 16 x … 4 x 2

{22} + {20} = (22 x 20 x 18 x 16 x … 4 x 2) + (20 x 18 x 16 x … 4 x 2)

From the two terms above, we pull out the common factor of (20 x 18 x 16 x … 4 x 2), yielding:

{22} + {20} = 20 x 18 x 16 x … 4 x 2 x (22 + 1)

{22} + {20} = 20 x 18 x 16 x … 4 x 2 x 23

We see that the greatest prime factor is 23.

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Re: If {x} is the product of all even integers from 1 to x inclusive, what &nbs [#permalink] 05 Oct 2017, 10:16
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