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# M14-24

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Math Expert
Joined: 02 Sep 2009
Posts: 49298

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16 Sep 2014, 00:53
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Difficulty:

35% (medium)

Question Stats:

80% (00:46) correct 20% (04:24) wrong based on 51 sessions

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If $$A$$, $$B$$, $$C$$, $$D$$ and $$E$$ are non-zero numbers, do lines $$Ax + By = C$$ and $$Dx + Ey = F$$ have the same slope?

(1) $$\frac{A}{B} = \frac{D}{E}$$

(2) $$\frac{E}{B} = \frac{D}{A}$$

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Joined: 02 Sep 2009
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16 Sep 2014, 00:53
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Official Solution:

$$Ax + By = C$$. So, $$y=-\frac{A}{B}x+\frac{C}{B}$$, so the slope of this line is $$-\frac{A}{B}$$;

$$Dx + Ey = F$$. So, $$y=-\frac{D}{E}x+\frac{F}{E}$$, so the slope of this line is $$-\frac{D}{E}$$;

The question asks whether $$-\frac{A}{B}=-\frac{D}{E}$$, or whether $$\frac{A}{B}=\frac{D}{E}$$.

(1) $$\frac{A}{B}=\frac{D}{E}$$. Directly answers the question. Sufficient.

(2) $$\frac{E}{B}=\frac{D}{A}$$. We can rewrite this as $$\frac{A}{B}=\frac{D}{E}$$. Sufficient.

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Joined: 27 May 2014
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27 Nov 2017, 10:38
Answer cannot be D, Because they gave non-zero integer..we dont know the value of A,B,C,D (this might be positive or neg).My Answer will be E.
Math Expert
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27 Nov 2017, 11:06
rakeshdba05 wrote:
Answer cannot be D, Because they gave non-zero integer..we dont know the value of A,B,C,D (this might be positive or neg).My Answer will be E.

You are wrong. The question asks whether $$\frac{A}{B}=\frac{D}{E}$$ and each statement gives a definite YES answer to this question. To justify E you should give examples, which give an YES and a NO answer to the question.
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Re: M14-24 &nbs [#permalink] 27 Nov 2017, 11:06
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# M14-24

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