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

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

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New post 26 Oct 2018, 00:55
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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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New post 26 Oct 2018, 01:02
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

Answer: Option 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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New post 26 Oct 2018, 03:02
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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New post 26 Oct 2018, 03:27
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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New post 26 Oct 2018, 05:13
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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New post 26 Oct 2018, 05:48
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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New post 26 Oct 2018, 23:57
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
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Re: x and y are non-negative integers. If xy+2x+3y=0, then y=?  [#permalink]

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New post 28 Oct 2018, 19:19
=>
\(xy+2x+3y=0\)
\(=> xy+2x+3y+6=6\)
\(=> (x+3)(y+2)=6\)
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.
Answer: 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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New post 08 Nov 2018, 19:38
y(x+3) + 2x=0
y=-2x/(x+3)

only way y can be non-negative is if y=0
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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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