Value of x

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GmatKiss: Legendary Member; Posts: 2789; Joined: Tue Jul 26, 2011 12:19 amFollowed by: 43 members; Location: Chennai, India; Thanked: 206 times; GMAT Score:640

by GmatKiss » Wed Aug 17, 2011 10:16 am

What is the value of x?

1)x-y=1
2)xy=12

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Source: Beat The GMAT — Data Sufficiency | Wed Aug 17, 2011 10:16 am

gmatboost: Master | Next Rank: 500 Posts; Posts: 312; Joined: Tue Aug 02, 2011 3:16 pmFollowed by: 33 members; Location: New York City; Thanked: 130 times; GMAT Score:780

by gmatboost » Wed Aug 17, 2011 12:36 pm

Systems of equations in which one equation is

x + y = k or x - y = k
and the other is
xy = p

Always lead to quadratic equations, which almost always have two solutions for each variable.
Don't fall for the "obvious" positive answer for x.
And don't assume that this falls under the "two equations two variables -> sufficient" category.
The equation xy = p is NOT linear, so that idea doesn't apply here.

In this case,
xy = 12
[spoiler](y+1)y = 12[/spoiler]
[spoiler]y^2 + y - 12 = 0[/spoiler]
[spoiler](y + 4)(y - 3) = 0[/spoiler]
[spoiler]y = -4 or y = 3[/spoiler]
[spoiler]x = -3 or x = 4 Insufficient[/spoiler]

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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 » Thu Aug 18, 2011 5:37 am

GmatKiss wrote:What is the value of x?

1)x-y=1
2)xy=12

None of the statements individually is sufficient to determine the value of x. So let us consider both of them together. From statement 1, y = (x - 1)

Hence, xy = x(x - 1) = 12
The above quadratic equation will yield two values of x and we cannot determine any unique value of x.

The correct answer is E.

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gmatboost: Master | Next Rank: 500 Posts; Posts: 312; Joined: Tue Aug 02, 2011 3:16 pmFollowed by: 33 members; Location: New York City; Thanked: 130 times; GMAT Score:780

by gmatboost » Mon Aug 22, 2011 9:51 am

This is generally true but occasionally it isn't:

x(x-6) = -9 and any other equation that is derived from "perfect square = 0" has only one solution.

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