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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
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x and y are non-negative integers. If xy+2x+3y=0, then y=?  [#permalink]

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Question Stats: 81% (01:26) correct 19% (02:24) wrong based on 92 sessions

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[Math Revolution GMAT math practice question]

$$x$$ and $$y$$ are non-negative integers. If $$xy+2x+3y=0$$, then $$y=?$$

$$A. 0$$
$$B. 1$$
$$C. 2$$
$$D. 3$$
$$E. 4$$

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Re: x and y are non-negative integers. If xy+2x+3y=0, then y=?  [#permalink]

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MathRevolution wrote:
[Math Revolution GMAT math practice question]

$$x$$ and $$y$$ are non-negative integers. If $$xy+2x+3y=0$$, then $$y=?$$

$$A. 0$$
$$B. 1$$
$$C. 2$$
$$D. 3$$
$$E. 4$$

$$xy+2x+3y=0$$
i.e. $$xy+2x+3y+6-6 =0$$

i.e. $$x(y+2)+3(y+2)-6 =0$$

i.e. $$(y+2)*(x+3) =6$$
But 2*3 = 6

i.e. y = 0 and x = 0 is the only possible case we get because x and y are NON-NEGATIVE integers

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Re: x and y are non-negative integers. If xy+2x+3y=0, then y=?  [#permalink]

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xy+2x+3y=0 is possible only when both x and y are equal to 0.

So Answer must be A.
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Re: x and y are non-negative integers. If xy+2x+3y=0, then y=?  [#permalink]

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By carefully observing the equation, we can say that for all values of $$y\geq1$$ the RHS part fo the equation will be a negative value. So the only value that satisfies the equation is $$Zero$$.

OPTION : A
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x and y are non-negative integers. If xy+2x+3y=0, then y=?  [#permalink]

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MathRevolution wrote:
[Math Revolution GMAT math practice question]

$$x$$ and $$y$$ are non-negative integers. If $$xy+2x+3y=0$$, then $$y=?$$

$$A. 0$$
$$B. 1$$
$$C. 2$$
$$D. 3$$
$$E. 4$$

whenever the the phrase " non-negative" is used , pay special attention to Zero. It's test makers silent trick.

xy + 2x + 3y = 0

How?

If x = 0

xy = 0

2x = 0

but still we have 3y.

2 variables in this question.

say y = 0

xy = 0

3y = 0

but what's about 2x.

So, both x and y are 0 as ultimate result is 0.

Number plugging is helpful here. Back solving is also useful. But remember that ultimate result is 0 and u have 2 variables.

The best answer is A.
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Re: x and y are non-negative integers. If xy+2x+3y=0, then y=?  [#permalink]

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MathRevolution wrote:
[Math Revolution GMAT math practice question]

$$x$$ and $$y$$ are non-negative integers. If $$xy+2x+3y=0$$, then $$y=?$$

$$A. 0$$
$$B. 1$$
$$C. 2$$
$$D. 3$$
$$E. 4$$

NONNEGATIVE implies that we should test ZERO.
Let x=0.
Substituting x=0 into xy + 2x + 3y = 0, we get:
0*y + 2*0 + 3y = 0
3y = 0
y = 0

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Re: x and y are non-negative integers. If xy+2x+3y=0, then y=?  [#permalink]

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xx and yy are non-negative integers. If xy+2x+3y=0xy+2x+3y=0, then y=?y=?

A.0A.0
B.1B.1
C.2C.2
D.3D.3
E.4

Plug in for values of y only at y=0 we get is a even +ve integer value which is x=0
Math Revolution GMAT Instructor V
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GMAT 1: 760 Q51 V42 GPA: 3.82
Re: x and y are non-negative integers. If xy+2x+3y=0, then y=?  [#permalink]

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=>
$$xy+2x+3y=0$$
$$=> xy+2x+3y+6=6$$
$$=> (x+3)(y+2)=6$$
Since $$x$$ and $$y$$ are integers, $$x+3$$ and $$y+2$$ are integers.
The possible pairs $$(x+3,y+2)$$ are as follows:
$$( x+3, y+2 ) = (1,6), (2,3), (3,2), (6,1), (-1,-6), (-2,-3), (-3,-2)$$ and $$(-6,-1).$$
The corresponding pairs $$(x,y)$$ are:
$$(x,y) = (-2,4), (-1,2), (0,0), (3,-1), (-4,-8), (-5,-5), (-6,-4)$$ and $$(-9,-3).$$
The unique pair with non-negative $$x$$ and $$y$$ is $$(x,y)=(0,0).$$
Thus, $$y = 0.$$

Therefore, the answer is A.
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Re: x and y are non-negative integers. If xy+2x+3y=0, then y=?  [#permalink]

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y(x+3) + 2x=0
y=-2x/(x+3)

only way y can be non-negative is if y=0 Re: x and y are non-negative integers. If xy+2x+3y=0, then y=?   [#permalink] 08 Nov 2018, 19:38
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