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# M31-30

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Math Expert
Joined: 02 Sep 2009
Posts: 52294

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14 Jun 2015, 13:10
00:00

Difficulty:

65% (hard)

Question Stats:

56% (01:10) correct 44% (01:36) wrong based on 55 sessions

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In the xy-plane, line $$m$$ is a line that does not pass through the origin. Is the slope of line $$m$$ is negative?

(1) The product of the x-intercept and the y-intercept of line $$m$$ is positive.

(2) Line $$m$$ passes through the points $$(a, \ b)$$ and $$(c, \ d)$$, where $$\frac{(b - d)}{(a-c)} < 0$$.

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Joined: 02 Sep 2009
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14 Jun 2015, 13:10
1
Official Solution:

In the xy-plane, line $$m$$ is a line that does not pass through the origin. Is the slope of line $$m$$ is negative?

(1) The product of the x-intercept and the y-intercept of line $$m$$ is positive. This means that either both $$x$$ and y-intercepts are negative or both $$x$$ and y-intercepts are positive. In either case the slope would be negative. Sufficient.

(2) Line $$m$$ passes through the points $$(a, \ b)$$ and $$(c, \ d)$$, where $$\frac{(b - d)}{(a-c)} < 0$$. This is basically the slope formula: rise over run and we are directly told that it's negative. Sufficient.

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Joined: 17 Sep 2015
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24 Oct 2015, 13:20
sorry, is statement (2) complete here? i don't understand what is meant by "...where (a-c)(b-d)"? Is the problem not showing properly on safari?
Math Expert
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25 Oct 2015, 05:14
iwantstanford wrote:
sorry, is statement (2) complete here? i don't understand what is meant by "...where (a-c)(b-d)"? Is the problem not showing properly on safari?

Edited. Does it look good now?
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Joined: 17 Sep 2015
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27 Oct 2015, 11:31
looks great. thank you sir!
Intern
Joined: 16 Mar 2015
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15 Apr 2016, 10:16
I think this is a poor-quality question. How is (a-c)(b-d)<0 the slope formula?
Math Expert
Joined: 02 Sep 2009
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15 Apr 2016, 10:18
Jak5189 wrote:
I think this is a poor-quality question. How is (a-c)(b-d)<0 the slope formula?

Check here: math-coordinate-geometry-87652.html
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06 Aug 2016, 07:35
I think this is a high-quality question and I agree with explanation.
Intern
Joined: 12 Oct 2016
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21 Nov 2016, 13:42
Bunuel wrote:
Jak5189 wrote:
I think this is a poor-quality question. How is (a-c)(b-d)<0 the slope formula?

Check here:

Hi Bunuel,

The expression is NOT the slope formula, but it has the same sign, meaning that the slope would be negative. Wouldn't that be more accurate?

PS: slope formula would be (b-d)/(a-c)
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Joined: 19 Jul 2016
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17 Jan 2017, 19:16
S1: whatever the sign of (X,Y),how do u draw the conclusion that in any case m will be negative??
S2: how this (a−c)(b−d)<0 expression become slope formula,please elaborate

Thnx
Intern
Joined: 07 Feb 2017
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10 Jul 2017, 05:47
request if anyone can elaborate further about point one , as the explanations states slope will be negative if both the x and y intercepts are negative or positive .
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Status: EAT SLEEP GMAT REPEAT!
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13 Jul 2017, 02:01
1
Bunuel wrote:
Official Solution:

In the xy-plane, line $$m$$ is a line that does not pass through the origin. Is the slope of line $$m$$ is negative?

(1) The product of the x-intercept and the y-intercept of line $$m$$ is positive. This means that either both $$x$$ and y-intercepts are negative or both $$x$$ and y-intercepts are positive. In either case the slope would be negative. Sufficient.

(2) Line $$m$$ passes through the points $$(a, \ b)$$ and $$(c, \ d)$$, where $$\frac{(b - d)}{(a-c)} < 0$$. This is basically the slope formula: rise over run and we are directly told that it's negative. Sufficient.

Hi Bunuel

In statement one what do you mean by the statement " In either case the slope would be negative." Can you please show which 2 cases.
Your help is much appreciated.

Thanks
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Math Expert
Joined: 02 Sep 2009
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13 Jul 2017, 02:10
1
gamerguy0074 wrote:
Bunuel wrote:
Official Solution:

In the xy-plane, line $$m$$ is a line that does not pass through the origin. Is the slope of line $$m$$ is negative?

(1) The product of the x-intercept and the y-intercept of line $$m$$ is positive. This means that either both $$x$$ and y-intercepts are negative or both $$x$$ and y-intercepts are positive. In either case the slope would be negative. Sufficient.

(2) Line $$m$$ passes through the points $$(a, \ b)$$ and $$(c, \ d)$$, where $$\frac{(b - d)}{(a-c)} < 0$$. This is basically the slope formula: rise over run and we are directly told that it's negative. Sufficient.

Hi Bunuel

In statement one what do you mean by the statement " In either case the slope would be negative." Can you please show which 2 cases.
Your help is much appreciated.

Thanks

x and y-intercepts of the red line below are negative --> slope is negative.

x and y-intercepts of the blue line below are positive --> slope is negative.
>> !!!

You do not have the required permissions to view the files attached to this post.

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27 Nov 2017, 07:37
The way I solved it:

Given: y=mx+c

A) The intercepts are: y= c and x= -c/m

The product of these two terms is positive.

c * (-c/m) > 0 is only possible when m is negative. Hence, negative slope.

B) is the basic formula for slope, which proves that the slope is negative.

Hence answer is D.
Re: M31-30 &nbs [#permalink] 27 Nov 2017, 07:37
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# M31-30

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