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

Redeem

Primes & Divisibility

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Master | Next Rank: 500 Posts
Posts: 110
Joined: Thu Apr 05, 2012 8:48 am
Thanked: 3 times
Followed by:1 members

Primes & Divisibility

by shanice » Sun Apr 08, 2012 6:32 am
Hi guys,

Can someone please help me with the below questions?

1)[u]Factor Foundation Rule (Manhattan Gmat)[/u]

[b]If a is a factor of b, and b is a factor of c, then a is a factor of c.[/b]
Meaning : Any integer is divisible by all of its factors and it is also divisible by all of the FACTORS of its factors.
Example : 72/12 = 6 (so, can I consider that a=12, b=72, c=6. Is my understanding correct?)

2) If x is an even integer, is x(x+1)(x+2) divisible by 4?
Answer is yes.


Thank you.
Top
Source: — Problem Solving |
User avatar
GMAT Instructor
Posts: 1248
Joined: Thu Mar 29, 2012 2:57 pm
Location: Everywhere
Thanked: 503 times
Followed by:192 members
GMAT Score:780

by Bill@VeritasPrep » Sun Apr 08, 2012 7:27 am
Your understanding is almost correct. In your example, it should be a=6, b=12, and c=72.

As for the question, to be divisible by 4, an integer must have two 2's as factors. Since x is even, (x+2) is also even, so x(x+1)(x+2) has two 2's and must be divisible by 4.
Join Veritas Prep's 2010 Instructor of the Year, Matt Douglas for GMATT Mondays

Visit the Veritas Prep Blog

Try the FREE Veritas Prep Practice Test
Top
User avatar
Master | Next Rank: 500 Posts
Posts: 342
Joined: Wed Jul 08, 2009 8:50 am
Thanked: 214 times
Followed by:19 members
GMAT Score:740

by Birottam Dutta » Sun Apr 08, 2012 9:48 am
As an addition to the above problem, you may also note the following:

x(X+1)(x+2) is always divisible by 24 if x is even.

Try and figure this out as well. The easiest way to do this is to assume values of x and try. Even without assuming the values, you can arrive at the answer.

Think about it!
Top
Master | Next Rank: 500 Posts
Posts: 110
Joined: Thu Apr 05, 2012 8:48 am
Thanked: 3 times
Followed by:1 members

by shanice » Sun Apr 08, 2012 7:14 pm
Yes, you're right, Dutta. It worked.

Thank you Bill and Dutta.
Top
Post new topic Post Reply
• Page 1 of 1