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
How would you solve it?
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Is the question : Represents the product of all +ve even integers less than or equal to n?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
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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.
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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i think the q is complete and correct....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.
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
I understood the part you wrote prior to the portion I quoted, but how did you go from "(<20>)*22 to <20>*23?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.
Why did you add 1?
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its just taking out the common thingchipbmk wrote:I understood the part you wrote prior to the portion I quoted, but how did you go from "(<20>)*22 to <20>*23?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.
Why did you add 1?
<20>+22*<20>;taking<20> as a common out , the expression will be <20>[1+22]=<20>*23
HTH
It does not matter how many times you get knocked down , but how many times you get up