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

Redeem

Maths coprime factors

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Master | Next Rank: 500 Posts
Posts: 124
Joined: Sun Mar 07, 2010 3:15 pm
Thanked: 1 times

Maths coprime factors

by francoisph » Fri Jun 04, 2010 1:20 pm
hi guys,

it is hard this question below

For every positive even integern, the function h(n) is defined to be the product of all the even integers from 2 to n, inclusive. If p is the smallest prime factor of h(100)+1, then p is
1. between 2 and 10
2. between 10 and 20
3. between 20 and 30
4. between 30 and 40
5. greater than 40
Top
Source: — Problem Solving |
User avatar
Master | Next Rank: 500 Posts
Posts: 362
Joined: Fri Oct 02, 2009 4:18 am
Thanked: 26 times
Followed by:1 members

by indiantiger » Fri Jun 04, 2010 3:13 pm
Search for h(100) in the forum

https://www.beatthegmat.com/mba/search-r ... 8&q=h(100)
"Single Malt is better than Blended"
Top
User avatar
GMAT Instructor
Posts: 1052
Joined: Fri May 21, 2010 1:30 am
Thanked: 335 times
Followed by:98 members

by Patrick_GMATFix » Tue Jun 08, 2010 6:42 am
This is a killer of a question but there are lots of discussions about it on the forum. The key to solving this question is knowing that the best way to prove that an expression is divisible by n is to demonstrate that the expression can be written as the product of n * integer. For example, 4!+6 is divisible by 3 because it can be written as the product of 3 * integer >> 4! + 6 = 3*(4*2*1 + 2)

On the other hand, one way to prove that an expression is not divisible by n is to demonstrate that the expression can be written as the sum of (multiple of n) + (non-multiple of n). For instance, 3p+7 cannot be a multiple of 3 (assuming p is an integer) because it equals a multiple of 3 + a non multiple of 3.

We can use this to prove that all numbers from 1 to 40 cannot be factors of h(100)+1.

The answer is E. You can see a detailed explanation and step-by-step video to solve this question at GMATPrep question 1282. To practice similar questions, set topic='Number Properties' and difficulty='700+' in the Drill Generator

Hope that helps,
-Patrick
  • Ask me about tutoring.
Top
Post new topic Post Reply
• Page 1 of 1