BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

Need help with OG13 quant q116

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Newbie | Next Rank: 10 Posts
Posts: 1
Joined: Sat Sep 20, 2014 9:36 am

Need help with OG13 quant q116

by cml907 » Sat Sep 20, 2014 3:18 pm
The question reads "If p is the product of the integers from 1 to 30, inclusive, what is the greatest integer for k for which 3^k is a factor of p?"
a) 10
b) 12
c) 14
d) 16
e) 18

I am kind of comfortable with the explanation of finding all the multiples of 3 between 1 and 30 but I don't understand how you can sum the number of factors of 3 (see problem explanation on pg 225) to get k. How do you know that the number for k will be a factor of p with this solution method?

Any help is appreciated! Thanks so much!
Top
Source: — Problem Solving |

GMAT/MBA Expert

User avatar
Elite Legendary Member
Posts: 10392
Joined: Sun Jun 23, 2013 6:38 pm
Location: Palo Alto, CA
Thanked: 2867 times
Followed by:511 members
GMAT Score:800

by [email protected] » Sat Sep 20, 2014 4:51 pm
Hi cml907,

These types of questions are based on a math concept called "prime factorization", which basically means that any integer greater than 1 is either prime OR the product of a bunch of primes.

Here's a simple example:

24 = (2)(2)(2)(3)

Now, when it comes to this question, we're asked to multiply all the integers from 1 to 30, inclusive and find the greatest integer K for which 3^K is a factor of this really big number.

Here's a simple example with a smaller product:
1 to 6, inclusive...
(1)(2)(3)(4)(5)(6)

Then numbers 1, 2, 4 and 5 do NOT have any 3's in them, so we can essentially ignore them:
3 = one 3
6 = (2)(3) = one 3
Total = two 3's

So 3^2 is the biggest "power of 3" that goes into the product of 1 to 6, inclusive.

Using that same idea, we need to find all of the 3's in the product of 1 to 30, inclusive. Here though, you have to be careful, since there are probably MORE 3's than immediately realize:

3 = one 3
6 = one 3
9 = (3)(3) = two 3s
12 = one 3
15 = one 3
18 = (2)(3)(3) = two 3s
21 = one 3
24 = one 3
27 = (3)(3)(3) = three 3s
30 = one 3

Total = 14 3's

Final Answer: C

GMAT assassins aren't born, they're made,
Rich
Contact Rich at [email protected]
Image
Top
Post new topic Post Reply
• Page 1 of 1