Equation Systems

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yellowho: Master | Next Rank: 500 Posts; Posts: 233; Joined: Wed Aug 22, 2007 3:51 pmFollowed by: 2 members; Location: New York; Thanked: 7 times

by yellowho » Sat Feb 26, 2011 7:17 pm

If you are given an two equations one LINEAR and one NOT-LINEAR can you solve for it? I know it gives multiple answers but in the context of DS. When you see it do you still have to solve and check or is that sufficient to say the choice is insufficient?

Ex: (Totally made up by me)

If x+y=-5, What is the value of X and Y?

1) xy=6

2) x-y=4

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Source: Beat The GMAT — Data Sufficiency | Sat Feb 26, 2011 7:17 pm

Night reader: Legendary Member; Posts: 1337; Joined: Sat Dec 27, 2008 6:29 pmFollowed by: 10 members; Thanked: 127 times

by Night reader » Sat Feb 26, 2011 7:34 pm

I prefer killing DS till end

my strategy here would be to start from st(2): (x-y=4)+(x+y=-5) --> 2x=-1, x=-1/2; y=-4.5 Sufficient
then st(1) (x+y)^2=25, 2xy=12, x^2+y^2=25-12, x^2+y^2=13 Not Sufficient as there can be mod x and mod y answers i.e. -ve /+ve

yellowho wrote:If you are given an two equations one LINEAR and one NOT-LINEAR can you solve for it? I know it gives multiple answers but in the context of DS. When you see it do you still have to solve and check or is that sufficient to say the choice is insufficient?

Ex: (Totally made up by me)

If x+y=-5, What is the value of X and Y?

1) xy=6

2) x-y=4

in general quadratic equations have more than one answer unless it's just (x+c)^2=0, then only x=-c

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

by Anurag@Gurome » Sat Feb 26, 2011 8:24 pm

(1) x(-x - 5) = 6 or x^2 + 5x + 6 = 0 or (x + 2)(x + 3) = 0 gives 2 values of x and hence two values of y. Since we don't get a unique answer, so (1) is NOT SUFFICIENT.

(2) We have two linear equations and two variables. So, they can be solved to get values of x and y. Hence, (2) is SUFFICIENT.

The correct answer is B.

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