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Which of the following is NOT a factor of the product of the

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Which of the following is NOT a factor of the product of the [#permalink] New post 02 Oct 2007, 15:35
Which of the following is NOT a factor of the product of the first 50 positive multiples of 4?

a- 17 power of 2
b- 11 power of 4
c- 7 power of 6
d- 47 power of 12
e- 2 power of 124
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 [#permalink] New post 02 Oct 2007, 16:27
Is it D?

4*8*12*16...*200 = (2^2)^50 * 50! = 2^100 * 50!

47 is a prime number and it only occurs once in the first 50 multiples of 4 (47*4= 188).

a) there are 2 17's in the 50!. (17 and 34)
b) there are 4 11's in the 50!. (11, 22, 33, 44)
c) there are 6 7's in the 50!. (7,14,21,28,35,42)
e) same logic...
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Re: Power question [#permalink] New post 02 Oct 2007, 20:48
mozeh wrote:
Which of the following is NOT a factor of the product of the first 50 positive multiples of 4?

a- 17 power of 2
b- 11 power of 4
c- 7 power of 6
d- 47 power of 12
e- 2 power of 124


D should be it.

a- 2^17
b- 2^22
c- 2^7 x 3^7
d- 2^94 x 3^47
e- 124^2 = 2^(12x2) = 2^24

The product of the first 50 positive multiples of 4 = 4 x 50!

4 x 50! has 2^(25 +12+6+3+1) or 2^37
4 x 50! has 3^(16 +8+4+2+1) or 3^31

So, only D is not a factor of "The product of the first 50 positive multiples of 4 = 4 x 50!".
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Re: Power question [#permalink] New post 02 Oct 2007, 21:15
mozeh wrote:
Which of the following is NOT a factor of the product of the first 50 positive multiples of 4?

a- 17 power of 2
b- 11 power of 4
c- 7 power of 6
d- 47 power of 12
e- 2 power of 124


Also for D,

not A, cuz 4*17.....4*17*2, so the product must have 17^2
not B, cuz 4*11.....4*11*2....4*11*3.....4*11*4, so the product must have 11^4
not C, cuz 4*7...4*2*7...4*3*7...4*4*7...4*5*7...4*6*7
can not be D, cuz 4*47....there is only one 47 (and it is prime) among the first 50 positive multiples of 4.
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Re: Power question [#permalink] New post 02 Oct 2007, 21:44
Fistail wrote:
mozeh wrote:
Which of the following is NOT a factor of the product of the first 50 positive multiples of 4?

a- 17 power of 2
b- 11 power of 4
c- 7 power of 6
d- 47 power of 12
e- 2 power of 124


D should be it.

a- 2^17
b- 2^22
c- 2^7 x 3^7
d- 2^94 x 3^47
e- 124^2 = 2^(12x2) = 2^24

The product of the first 50 positive multiples of 4 = 4 x 50!

4 x 50! has 2^(25 +12+6+3+1) or 2^37
4 x 50! has 3^(16 +8+4+2+1) or 3^31


So, only D is not a factor of "The product of the first 50 positive multiples of 4 = 4 x 50!".


can you explain how you figured out the red parts? Thanks!!
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Re: Power question [#permalink] New post 02 Oct 2007, 22:12
beckee529 wrote:
Fistail wrote:
mozeh wrote:
Which of the following is NOT a factor of the product of the first 50 positive multiples of 4?

a- 17 power of 2
b- 11 power of 4
c- 7 power of 6
d- 47 power of 12
e- 2 power of 124


D should be it.

a- 2^17
b- 2^22
c- 2^7 x 3^7
d- 2^94 x 3^47
e- 124^2 = 2^(12x2) = 2^24

The product of the first 50 positive multiples of 4 = 4 x 50!

4 x 50! has 2^(25 +12+6+3+1) or 2^37
4 x 50! has 3^(16 +8+4+2+1) or 3^31


So, only D is not a factor of "The product of the first 50 positive multiples of 4 = 4 x 50!".


can you explain how you figured out the red parts? Thanks!!


the question seems wrong as it has 2 answers, D and E.

e. 2 power of 124 = 124^2 = (31x4)^2 = 31^2 x 2^4

so "The product of the first 50 positive multiples of 4 = 4 x 50!" cannot have E as its factor.

4 x 50! has a factor of 2^{(25 +12+6+3+1) + 2} or 2^49

50/2 = 25
50/4 = 12
50/8 = 6
50/16 = 3
50/32 = 1
so sum = 47.

4 x 50! has 3^(16 +8+4+2+1) or 3^31

thanks beckee529.
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Re: Power question [#permalink] New post 02 Oct 2007, 22:20
Fistail wrote:
beckee529 wrote:
Fistail wrote:
mozeh wrote:
Which of the following is NOT a factor of the product of the first 50 positive multiples of 4?

a- 17 power of 2
b- 11 power of 4
c- 7 power of 6
d- 47 power of 12
e- 2 power of 124


D should be it.

a- 2^17
b- 2^22
c- 2^7 x 3^7
d- 2^94 x 3^47
e- 124^2 = 2^(12x2) = 2^24

The product of the first 50 positive multiples of 4 = 4 x 50!

4 x 50! has 2^(25 +12+6+3+1) or 2^37
4 x 50! has 3^(16 +8+4+2+1) or 3^31


So, only D is not a factor of "The product of the first 50 positive multiples of 4 = 4 x 50!".


can you explain how you figured out the red parts? Thanks!!


the question seems wrong as it has 2 answers, D and E.

e. 2 power of 124 = 124^2 = (31x4)^2 = 31^2 x 2^4

so "The product of the first 50 positive multiples of 4 = 4 x 50!" cannot have E as its factor.

4 x 50! has a factor of 2^{(25 +12+6+3+1) + 2} or 2^49

50/2 = 25
50/4 = 12
50/8 = 6
50/16 = 3
50/32 = 1
so sum = 47.

4 x 50! has 3^(16 +8+4+2+1) or 3^31

thanks beckee529.


DOESN`T "the product of the first 50 positive multiples of 4" equal 4 x 8 x 12 x 16......? which is not the same as 4 x 50!=4 x 1 x 2 x 3 x 4 ......x 50
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Re: Power question [#permalink] New post 02 Oct 2007, 22:32
mozeh wrote:
Which of the following is NOT a factor of the product of the first 50 positive multiples of 4?

a- 17 power of 2
b- 11 power of 4
c- 7 power of 6
d- 47 power of 12
e- 2 power of 124


New explanation, in the previous post misread the answer choices,

D,

4*8*12*16...*200 = (2^2)^50 * 50! = 2^100 * 50!

a) 2^17--------> factor
b) 2^22--------> factor
c) 2^7 x 3^7---> 2^7 x 9 x 27 -----> factor, cuz 50! has both 9 and 27 as factors.
d) 2^94 x 3 ^47-----> 2^94 x 81^11 x 3^3---------> not factor, cuz 81^11 is not factor of 2^100 * 50!
e) 2^124----------> 2^200 x 2^24----->factor, cuz 50! has 25 even numbers, thus 50! is divisible by 2^25.
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 [#permalink] New post 03 Oct 2007, 09:35
E

124²= 31²x4² -> 31 is no factor of a multiple of 4
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Re: Power question [#permalink] New post 03 Oct 2007, 23:03
IrinaOK wrote:
DOESN`T "the product of the first 50 positive multiples of 4" equal 4 x 8 x 12 x 16......? which is not the same as 4 x 50!=4 x 1 x 2 x 3 x 4 ......x 50


Thanks, agreed.


IrinaOK wrote:
mozeh wrote:
Which of the following is NOT a factor of the product of the first 50 positive multiples of 4?

a- 17 power of 2
b- 11 power of 4
c- 7 power of 6
d- 47 power of 12
e- 2 power of 124


New explanation, in the previous post misread the answer choices,

D.

4*8*12*16...*200 = (2^2)^50 * 50! = 2^100 * 50!

a) 2^17--------> factor
b) 2^22--------> factor
c) 2^7 x 3^7---> 2^7 x 9 x 27 -----> factor, cuz 50! has both 9 and 27 as factors.
d) 2^94 x 3 ^47-----> 2^94 x 81^11 x 3^3---------> not factor, cuz 81^11 is not factor of 2^100 * 50!
e) 2^124----------> 2^200 x 2^24----->factor, cuz 50! has 25 even numbers, thus 50! is divisible by 2^25.





Again D and E.

4x8x12x16...x200 = (2^2)^50 x 50! = 2^100 x 50!

a) 2^17--------> factor
b) 2^22--------> factor
c) 2^7 x 3^7--------> factor cuz 50! has 3^31 as factor.
d) 2^94 x 3^47 --------> not factor cuz 3^47 is not factor of 2^100 x 50!
e) 124^2-----------> not factor cuz 50! has not two 31 as its factor. so it is also not correct.


now seems there is a typo in E of the question: it should be 124 power of 2 rather than 2 power of 124.
Re: Power question   [#permalink] 03 Oct 2007, 23:03
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