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What is the value of xy ?

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What is the value of xy ?  [#permalink]

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New post 16 Feb 2017, 11:20
3
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A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

55% (01:29) correct 45% (01:20) wrong based on 172 sessions

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What is the value of xy?

(1) y – 1 = x
(2) x^2 + x – 6 = 0

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Joined: 28 Jan 2017
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Re: What is the value of xy ?  [#permalink]

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New post 16 Feb 2017, 11:42
Restating:

1) y=x+1
2) (x+3)*(x-2)=0 ==> x=-3 or x = 2

If x=-3 then y= -2 and x*y= +6
If x= 2 then y= 3 and x*y= +6

Same result in both cases
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Re: What is the value of xy ?  [#permalink]

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New post 16 Feb 2017, 11:49
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Top Contributor
duahsolo wrote:
What is the value of xy?

(1) y – 1 = x
(2) x² + x – 6 = 0


Target question: What is the value of xy?

Statement 1: y – 1 = x
This statement doesn't FEEL sufficient (namely because we have 1 equation with 2 variables), so I'll TEST some values.
There are several values of x and y that satisfy statement 1. Here are two:
Case a: x = 0 and y = 1. In this case, xy = (0)(1) = 0
Case b: x = 1 and y = 2. In this case, xy = (1)(2) = 2
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Aside: For more on this idea of plugging in values when a statement doesn't feel sufficient, you can read my article: http://www.gmatprepnow.com/articles/dat ... lug-values

Statement 2: x² + x – 6 = 0
Since we have no information about y, there's no way to determine the value of xy
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 tells us that: y – 1 = x

Statement 2 tells us that x² + x – 6 =
Factor: (x + 3)(x - 2) = 0
Solve to get: x = -3 or x = 2

It SEEMS like these 2 different values of x will yield 2 different values for xy.
Let's see if that's the case.

If x = -3, then y = -2 (since statement 1 tells us that y - 1 = x). In this case, xy = (-3)(-2) = 6
If x = 2, then y = 3 (since statement 1 tells us that y - 1 = x). In this case, xy = (2)(3) = 6
So, when we COMBINE the statements, we get only ONE answer to the target question: xy = 6
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer: C

Cheers,
Brent
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Re: What is the value of xy ?  [#permalink]

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New post 08 Aug 2018, 10:57
Simple and easy approach.

Statement 1
\(y-1 = x\)
\(y = x+1\)
\(xy = x (x+1)\)
\(xy = x^2 +x\)
INSUFFICIENT

Statement 2
\(x^2 + x - 6 = 0\)
\(x^2 + 3x - 2x - 6 = 0\)
\(x(x + 3) - 2(x + 3)\)
\((x + 3)(x - 2) = 0\)
\(x = -3 or x = 2\)
INSUFFICIENT

BOTH Statement 1 and 2

We know,
\(x^2 + x - 6 = 0\)
and
\(xy = x^2 + x\)
Therefore,
\(xy - 6 = 0\)
\(xy = 6\)
SUFFICIENT
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Re: What is the value of xy ?   [#permalink] 08 Aug 2018, 10:57
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