Probability that their product (GMAT PREP 1)

This topic has expert replies
Master | Next Rank: 500 Posts
Posts: 435
Joined: Wed Nov 16, 2011 7:27 am
Thanked: 48 times
Followed by:16 members
If two of the four expressions x+y, x+5y, x-y, and 5x-y are chosen at random, what is the probability that their product will be of the form (x^2)-[(by)^2], where b is an integer?

1/2
1/3
1/4
1/5
1/6

Thanks!
A useful website I found that has every quant OG video explanation:

https://www.beatthegmat.com/useful-websi ... tml#475231

Junior | Next Rank: 30 Posts
Posts: 16
Joined: Sun Jul 22, 2012 7:08 am
Location: Famagusta
Thanked: 2 times

by javzprobz » Sat Aug 04, 2012 12:47 am
Hi,

Using the combination formula, we will know how many groupings of 2 of these 4 expression we can have:4!/(4-2)!2!=6

So, now, let's see how many of these 6 combinations are of the form of (x^2)-[(by)^2], which is (x+by)(x-by)...

(x+y)(x+5y): it's not of the form of (x+by)(x-by), so NO
(x+y)(x-y): it is of the form of (x+by)(x-by), so YES
(x+y)(5x-y): not of the form of (x+by)(x-by), so NO
(x+5y)(x-y): not of the form of (x+by)(x-by), so NO
(x+5y)(5x-y): not of the form of (x+by)(x-by), so NO
(x-y)(5x-y): not of the form of (x+by)(x-by), so NO

So only one of these 6 combinations is of the form of (x+by)(x-by)...

Therefore, the correct answer is E.

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 3835
Joined: Fri Apr 02, 2010 10:00 pm
Location: Milpitas, CA
Thanked: 1854 times
Followed by:523 members
GMAT Score:770

by Anurag@Gurome » Sat Aug 04, 2012 3:42 am
alex.gellatly wrote:If two of the four expressions x+y, x+5y, x-y, and 5x-y are chosen at random, what is the probability that their product will be of the form (x^2)-[(by)^2], where b is an integer?

1/2
1/3
1/4
1/5
1/6

Thanks!
(x + y)(x + 5y) = x^2 + 6xy + 5y^2: Not in the form x^2- (by)^2
(x + y)(5x - y) = 5x^2 + 4xy - y^2: Not in the form
(x + 5y)(x - y) = x^2 + 4xy - 5y^2: Not in the form
(x + 5y)(5x - y) = 5x^2 + 24xy - 5y^2: Not in the form
(x - y)(5x - y) = 5x^2 - 6xy + y^2: Not in the form
(x + y)(x - y) = x^2 - y^2: This is in the required form

Hence, the required probability is [spoiler]1/6[/spoiler].
Anurag Mairal, Ph.D., MBA
GMAT Expert, Admissions and Career Guidance
Gurome, Inc.
1-800-566-4043 (USA)

Join Our Facebook Groups
GMAT with Gurome
https://www.facebook.com/groups/272466352793633/
Admissions with Gurome
https://www.facebook.com/groups/461459690536574/
Career Advising with Gurome
https://www.facebook.com/groups/360435787349781/