gmat preparation courses

It is currently Tue Dec 12, 2017 12:03 pm

All times are UTC - 5 hours [ DST ]




Post new topic Reply to topic  [ 2 posts ] 
Author Message
 Post subject: GMAT Number Theory
PostPosted: Mon May 13, 2013 10:38 am 
Offline

Joined: Sun May 30, 2010 3:15 am
Posts: 424
The product of the squares of two positive integers is 400. How many pairs of positive integers satisfy this condition?
A. 0
B. 1
C. 2
D. 3
E.4

(D) 400 = 2 × 2 × 2 × 2 × 5 × 5
Combine the prime factors in pairs.

400 = (2 × 2) × (2 × 2) × (5 × 5)
Now brake the factorization into two parts, each one will be a square.
The possible combinations are:
400 = (2 × 2) × [(2 × 2) × (5 × 5)]
400 = [(2 × 2) × (2 × 2)] × (5 × 5)
But don't forget that 400 = 1 × 400, where 1 = 1². So we also have:
400 = (1 × 1) × [(2 × 2) × (2 × 2) × (5 × 5)]

Thus all the possible combinations of the factors that make the product of two squares are the following:
1² × 20² = 400
2² × 10² = 400
4² × 5² = 400

There are three possible pairs that fit the criterion. The correct answer is D.
---------
The answer should be E. 4 , because your explanation has missed the possibility of 20² × 20² . It is not mentioned that the numbers should be distinct.


Top
 Profile  
 
 Post subject: Re: GMAT Number Theory
PostPosted: Mon May 13, 2013 10:38 am 
Offline

Joined: Sun May 30, 2010 2:23 am
Posts: 498
Quote:
The answer should be E. 4 , because your explanation has missed the possibility of 20² × 20² . It is not mentioned that the numbers should be distinct.
20² × 20² = 400 × 400 = 160,000 , NOT 400.


Top
 Profile  
 
Display posts from previous:  Sort by  
Post new topic Reply to topic  [ 2 posts ] 

All times are UTC - 5 hours [ DST ]


Who is online

Users browsing this forum: No registered users and 5 guests


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:  
cron
Powered by phpBB © 2000, 2002, 2005, 2007 phpBB Group