Register    Login    Search    Rss Feeds

Forums Home » Ask An Instructor » GMAT Math » GMAT Prep Math


 Page 1 of 1 [ 3 posts ] 



  Print view Print view Previous topic Previous topic | Next topic Next topic
 

if d is a positive integer and f is the product

Author Message
john_haddock
 Post subject: if d is a positive integer and f is the product
 Post Posted: Wed May 27, 2009 10:35 pm 
Offline
Course Students


Posts: 6
if d is a positive integer and f is the product of the first 30 integers what is the value of d?

(1) 10^d is a factor of f
(2) d>6
Top 
stock.mojo11
 Post subject: Re: q1
 Post Posted: Thu May 28, 2009 12:05 am 
Offline
Forum Guests


Posts: 42
john_haddock wrote:
if d is a positive integer and f is the product of the first 30 integers what is the value of d?

(1) 10^d is a factor of f
(2) d>6


Did you mean first 30 positive integers? Assuming thats what you meant, the answer is C

d > 6 Insuff

10 ^ d is a factor of f 10 is a factor and 10 ^ 2 is a factor too. Hence d = 1/2 or more Insuff

Combine. How many 10's are in 30!

3 10's (10,20,30)

Now 10 can also be 5 X 2. rather than counting 2's and 5's just count 5's as there can be only that many number of 10's

5,15,25 ( total of 4 5's) Note that there are two 5's in 25.

Hence the max number of 10's in 30! is 7. means 10 ^ 7 is a factor of 30! but d > 6 so d =7
Top 
RonPurewal
 Post subject: Re: q1
 Post Posted: Fri May 29, 2009 4:57 am 
Offline
ManhattanGMAT Staff


Posts: 7146
stock.mojo11 wrote:
Combine. How many 10's are in 30!

3 10's (10,20,30)

Now 10 can also be 5 X 2. rather than counting 2's and 5's just count 5's as there can be only that many number of 10's

5,15,25 ( total of 4 5's) Note that there are two 5's in 25.


this solution is good, in that it gets at the underlying structure of the problem (i.e., this problem is ultimately about prime factorizations).

however, it's unnecessarily try-hard.

here's all you have to do:
forget entirely about 10, 20, and 30, and ONLY THINK ABOUT PRIME FACTORIZATIONS.
(TAKEAWAY: this is the way to go in general - when you break something down into primes, you should not think in hybrid terms like this. instead, just translate everything into the language of primes.)

each PAIR OF A '5' AND A '2' in the prime factorization translates into a '10'.

there are seven 5's: one each from 5, 10, 15, 20, and 30, and two from 25.

there are waaaaaaayyyyy more than seven 2's.

therefore, 30! can accommodate as many as seven 10's before you run out of fives.

--

statement 2 is clearly insufficient.

statement 1, by itself, means that d can be anything from 1 to 7 inclusive.

together, d must be 7.

ans (c)
Top 
Display posts from previous:  Sort by  
 
 Page 1 of 1 [ 3 posts ] 





Who is online

Users browsing this forum: No registered users and 1 guest

 
 

 
You cannot post new topics in this forum
You cannot reply to topics in this forum
You cannot edit your posts in this forum
You cannot delete your posts in this forum
You cannot post attachments in this forum

Search for:
Jump to: