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M31-30

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M31-30 [#permalink]

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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 \(\frac{(b - d)}{(a-c)} < 0\).
[Reveal] Spoiler: OA

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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.


Answer: D
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Re: M31-30 [#permalink]

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New post 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?

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New post 27 Oct 2015, 11:31
looks great. thank you sir!

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New post 15 Apr 2016, 10:16
I think this is a poor-quality question. How is (a-c)(b-d)<0 the slope formula?

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Re: M31-30 [#permalink]

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New post 06 Aug 2016, 07:35
I think this is a high-quality question and I agree with explanation.

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New post 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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Re: M31-30 [#permalink]

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New post 17 Jan 2017, 19:16
expert please help me to understand:
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

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New post 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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Re: M31-30 [#permalink]

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New post 13 Jul 2017, 02:01
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.


Answer: D


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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Re: M31-30 [#permalink]

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New post 13 Jul 2017, 02:10
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.


Answer: D


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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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: M31-30 [#permalink]

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New post 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.

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Re: M31-30   [#permalink] 27 Nov 2017, 07:37
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