Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

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...

Re: Power question [#permalink]
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.

Re: Power question [#permalink]
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

Re: Power question [#permalink]
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.

Re: Power question [#permalink]
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.

gmatclubot

Re: Power question
[#permalink]
03 Oct 2007, 23:03

I couldn’t help myself but stay impressed. young leader who can now basically speak Chinese and handle things alone (I’m Korean Canadian by the way, so...