Difference in squares: MGMAT

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ru2008: Senior | Next Rank: 100 Posts; Posts: 58; Joined: Tue Aug 26, 2008 9:42 am

by ru2008 » Fri Sep 24, 2010 1:41 pm

If x and y are integers such that x < y < 0, what is x - y?

(1) (x + y)(x - y) = 5

(2) xy = 6

Please explain your answer as much as possible

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Source: Beat The GMAT — Data Sufficiency | Fri Sep 24, 2010 1:41 pm

this_time_i_will: Master | Next Rank: 500 Posts; Posts: 268; Joined: Wed Mar 17, 2010 2:32 am; Thanked: 17 times

by this_time_i_will » Fri Sep 24, 2010 7:18 pm

Sud be A.
A gives=> (x+y)(x-y)=5. We know 5 is a prime so the factors of 5 can only be 5 and 1 or -5 and -1.
But, if we take 5 and 1, then x+y = 5 and x-y = 1. (because x+y > x-y for positive x and y).
The only posisble integer solution for x and y cud be 3 and 2. But 3 and 2 are positive so this solution is ruled out.

so the factor of 5 are actually -5 and -1.
so x-y = -1 and x+y = -5.
Only integer possibility is x=-3 and y = -2

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