Is xy < 6? : GMAT Data Sufficiency (DS)
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# Is xy < 6?

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30 Jan 2014, 22:44
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The Official Guide For GMAT® Quantitative Review, 2ND Edition

Is xy < 6?

(1) x < 3 and y < 2.
(2) 1/2 < x < 2/3 and y^2 < 64.

Data Sufficiency
Question: 68
Category: Algebra Inequalities
Page: 157
Difficulty: 600

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Re: Is xy < 6? [#permalink]

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30 Jan 2014, 22:44
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SOLUTION

Is xy < 6?

(1) x < 3 and y < 2 --> now, if both $$x$$ and $$y$$ are equal to zero then $$xy=0<6$$ and the answer will be YES but if both $$x$$ and $$y$$ are small enough negative numbers, for example -10 and -10 then $$xy=100>6$$ and the answer will be NO. Not sufficient.

(2) $$\frac{1}{2}<x<\frac{2}{3}$$ and $$y^2<64$$, which is equivalent to $$-8<y<8$$ --> even if we take the boundary values of $$x$$ and $$y$$ to maximize their product we'll get: $$xy=\frac{2}{3}*8\approx{5.3}<6$$, so the answer to the question "is $$xy<6$$?" will always be YES. Sufficient.

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Re: Is xy < 6? [#permalink]

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30 Jan 2014, 23:46
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Statement (1)

We are given x < 3 and y < 2 ; no lower bound specified for either of the variables.
x and y could be x=-3 and y=-2 we get xy=6 or they could be very small negative numbers then xy would be much greater than 6.
On the other hand x=1 y=1 which results in xy=1 which is smaller than 6 so Statement (1) is not sufficient

Statement (2)

y^2 < 64 can be rewritten as -8< y <8 ,
Since x is positive, we can test the extremes without worrying about changing the direction of the inequality sign
-8*(2/3) < xy < 8*(2/3)

-5.3333 < xy < 5.333
So we can answer the question "Is xy<6" with the Statement (2) ALONE.

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Last edited by code19 on 01 Feb 2014, 13:04, edited 1 time in total.
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Re: Is xy < 6? [#permalink]

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01 Feb 2014, 09:22
SOLUTION

Is xy < 6?

(1) x < 3 and y < 2 --> now, if both $$x$$ and $$y$$ are equal to zero then $$xy=0<6$$ and the answer will be YES but if both $$x$$ and $$y$$ are small enough negative numbers, for example -10 and -10 then $$xy=100>6$$ and the answer will be NO. Not sufficient.

(2) $$\frac{1}{2}<x<\frac{2}{3}$$ and $$y^2<64$$, which is equivalent to $$-8<y<8$$ --> even if we take the boundary values of $$x$$ and $$y$$ to maximize their product we'll get: $$xy=\frac{2}{3}*8\approx{5.3}<6$$, so the answer to the question "is $$xy<6$$?" will always be YES. Sufficient.

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Re: Is xy < 6?   [#permalink] 01 Feb 2014, 09:22
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# Is xy < 6?

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