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m10 Q02

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Status: And the Prep starts again...
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m10 Q02 [#permalink]

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New post 22 Apr 2012, 23:57
If \(2X + 3Y = 12\) , what is \(X\) ?

1) \(X = 6 - (\frac{3}{2})Y\)
2) \(Y = 4 - (\frac{3}{2})X\)

Why is statement 1 not sufficient?

Can I not find the value of Y and substitute in \(2X + 3Y = 12\). I did this, please tell me what mistake I am making

\(2X = 12-3Y\)
From Statement 1 \(X = 6 - (\frac{3}{2})Y\)
Which can be simplified to \(X = (\frac{9}{2})Y\)
Therefore, \(Y = (\frac{2}{9})X\)

Now if i can substitute this Y in \(2X = 12-3Y\)
\(2X = 12-\frac{6}{9}X\)
\(2X = 12-\frac{2}{3}X\)
\(2X+\frac{2}{3}X = 12\)
\(\frac{8X}{3} = 12\)
\(8X = 36\)
\(X = \frac{36}{8}\)
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Re: m10 Q02 [#permalink]

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New post 23 Apr 2012, 00:35
ENAFEX wrote:
If \(2X + 3Y = 12\) , what is \(X\) ?

1) \(X = 6 - (\frac{3}{2})Y\)
2) \(Y = 4 - (\frac{3}{2})X\)

Why is statement 1 not sufficient?

Can I not find the value of Y and substitute in \(2X + 3Y = 12\). I did this, please tell me what mistake I am making

\(2X = 12-3Y\)
From Statement 1 \(X = 6 - (\frac{3}{2})Y\)
Which can be simplified to \(X = (\frac{9}{2})Y\)
Therefore, \(Y = (\frac{2}{9})X\)

Now if i can substitute this Y in \(2X = 12-3Y\)
\(2X = 12-\frac{6}{9}X\)
\(2X = 12-\frac{2}{3}X\)
\(2X+\frac{2}{3}X = 12\)
\(\frac{8X}{3} = 12\)
\(8X = 36\)
\(X = \frac{36}{8}\)


The red part is not correct: \(x = 6 - \frac{3}{2}y\) --> \(x=\frac{12-3y}{2}\), not \(x=\frac{9}{2}y\)

If \(2x + 3y = 12\), what is \(x\) ?

(1) \(x = 6 - (\frac{3}{2})y\) --> multiply both parts by 2: \(2x=12-3y\) --> rearrange: \(2x + 3y = 12\), so we have the same equation as in the stem. Not sufficient.

(2) \(y = 4 - (\frac{3}{2})x\) --> \(2y=8-3x\) --> \(3x+2y=8\). We have two distinct linear equations, hence we can get the single numerical value of \(x\). Sufficient.

Answer: B.
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Kudos [?]: 133134 [0], given: 12415

Manager
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Status: And the Prep starts again...
Joined: 03 Aug 2010
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Re: m10 Q02 [#permalink]

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New post 23 Apr 2012, 03:22
That was silly!!

Sorry to waste your time. :D GGRRR
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My First Blog on my GMAT Journey

Arise, Awake and Stop not till the goal is reached

Kudos [?]: 61 [0], given: 20

Re: m10 Q02   [#permalink] 23 Apr 2012, 03:22
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