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How would you solve it?

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by gmatv09 » Sun Oct 25, 2009 8:34 am
<20> + <22>
(2 * 4 * 6 * 8 * 10 ....20) + (2 * 4* 6 * 8 * ... 22)

(2 * 4 * 6 * 8 * 10 .... 20) [1 + 22]
(2 * 4 * 6 * 8 * 10 .... 20) [23]

Hence ans 23
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Re: How would you solve it?

by sanjana » Sun Oct 25, 2009 9:28 pm
manelgirona wrote:The symbol <n> represents the product of all the positive integers less than or equal n. For example <8> = 8 x 6 x 4 x 2. What is the greatest prime factor of <20> + <22>?

a) 7
b) 11
c) 13
d) 19
e) 23

OA: E
Is the question : Represents the product of all +ve even integers less than or equal to n?
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by chris6 » Tue Oct 27, 2009 6:22 pm
Where are you getting the 1 from? I am coming up with 19.
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by chipbmk » Tue Oct 27, 2009 7:15 pm
Can someone please explain HOW you do this problem?

I do not see a clear explanation by anyone yet.
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by NikolayZ » Wed Oct 28, 2009 1:18 am
hey chipbmk !
If <n> represents the product of ALL integers equal or less then n. So, <n> might be rewritten as n! (factorial)

so 20!+22!=20!(1+21+22)=20!(44), thus, the largest prime will be indeed 19.

I suppose you just forgot to write that <n> represents the product of all even positive integers less than or equal to n.
If so
<20>=20*18*16*...*2(the largest and only prime here is 2)
<22>=22*(20*18*16*...*2), look, the product of all numbers except 22 equals <20>. so <22> can be rewritten into <22>=22*<20>
Hence, <20>+<22>=<20>+22*(<20>)=<20>(1+22)=<20>*23.
WE know that the largest prime in <20> is 2, hence our answer is 23.
Hope it is clear now.
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by xcusemeplz2009 » Wed Oct 28, 2009 2:25 am
NikolayZ wrote:hey chipbmk !
If <n> represents the product of ALL integers equal or less then n. So, <n> might be rewritten as n! (factorial)

so 20!+22!=20!(1+21+22)=20!(44), thus, the largest prime will be indeed 19.

I suppose you just forgot to write that <n> represents the product of all even positive integers less than or equal to n.
If so
<20>=20*18*16*...*2(the largest and only prime here is 2)
<22>=22*(20*18*16*...*2), look, the product of all numbers except 22 equals <20>. so <22> can be rewritten into <22>=22*<20>
Hence, <20>+<22>=<20>+22*(<20>)=<20>(1+22)=<20>*23.
WE know that the largest prime in <20> is 2, hence our answer is 23.
Hope it is clear now.
i think the q is complete and correct....
it is a typical GMAT type q where clues are hidden...
in the Q <n> is represented by an eg <8>=8*6*4*2


that means <n> is a product of even int..
under time pressure such small things can cause much damage...
It does not matter how many times you get knocked down , but how many times you get up
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by CrackGMAC » Wed Oct 28, 2009 5:46 am
Ya there is a confusion b/w even and odd (factorial)numbers here coz as question it should be all (ans 19) and as per defination of n <n> = 8*6*4*2 it should be 23.
Beat The GMAT
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by chipbmk » Wed Oct 28, 2009 6:55 am
NikolayZ wrote:hey chipbmk !

Hence, <20>+<22>=<20>+22*(<20>)=<20>(1+22)=<20>*23.
WE know that the largest prime in <20> is 2, hence our answer is 23.
Hope it is clear now.
I understood the part you wrote prior to the portion I quoted, but how did you go from "(<20>)*22 to <20>*23?

Why did you add 1?
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by xcusemeplz2009 » Wed Oct 28, 2009 9:05 am
chipbmk wrote:
NikolayZ wrote:hey chipbmk !

Hence, <20>+<22>=<20>+22*(<20>)=<20>(1+22)=<20>*23.
WE know that the largest prime in <20> is 2, hence our answer is 23.
Hope it is clear now.
I understood the part you wrote prior to the portion I quoted, but how did you go from "(<20>)*22 to <20>*23?

Why did you add 1?
its just taking out the common thing
<20>+22*<20>;taking<20> as a common out , the expression will be <20>[1+22]=<20>*23

HTH
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by chipbmk » Wed Oct 28, 2009 1:57 pm
its just taking out the common thing
<20>+22*<20>;taking<20> as a common out , the expression will be <20>[1+22]=<20>*23

HTH[/quote]

OOHHHH I get it now. So it is the same as saying

x+x(2) ==> x(2+1) ==> x(3)

Thanks!
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