Events & Promotions
|
|
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
May 0808:00 AM PDT
-08:30 AM PDT
Join the special YouTube live-stream for selecting the winners of GMAT Club MBA Scholarships sponsored by Juno live. Watch who gets these coveted MBA scholarships offered by GMAT Club and Juno.
24 Jul 2008, 07:07
Kudos
Bookmarks
line L and k intersect at (4,3). does the product of slopes of L and K = negative number ?
1. product of x intercepts L and K is +ve
2. product of Y intercepts L and K is -ve
1. product of x intercepts L and K is +ve
2. product of Y intercepts L and K is -ve
Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Quantitative Questions Forum
Still interested in this question? Check out the "Best Topics" block below for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
Updated on: 24 Jul 2008, 08:10
Originally posted by jallenmorris on 24 Jul 2008, 07:14.
Last edited by jallenmorris on 24 Jul 2008, 08:10, edited 2 times in total.
Last edited by jallenmorris on 24 Jul 2008, 08:10, edited 2 times in total.
Kudos
Bookmarks
C. - sorry this is so long!!!
#1) If the product of each x-intercept is + that meas both are negative or both are positive. L could have x intercept of -1 and K could have x-intercept of -2..product would be positive and product of slope would be positive. L could have x-intercept of 1 and K could have intercept of 5. product of both is positive, but K could have a negative slope, so the product of the slope would be negative. We've established 2 scenarios for the slope, each with a different +ve or -ve answer.
#2) here the Y intercepts must be different signs. L could have Y-intercept of 1 and K could have y-intercept of -1...product would be -ve but both slopes are +ve so we have +ve product of both slopes. now L could have y-intercept of 4 (negative slope) and K could have y-intercept of -1...+ve slope. Product of slopes is negative. We've established one +ve and one -ve for this one too. Insufficient.
#1 & #2 Together)
The x-intercept products must be positive and the y-intercepts must be negative.
Select a set of points that make this true and try to see if every set allows you to answer the question definitively whether the product of the slopes is negative.
Line L | Line K
{x-intercept,y-intercept} | {x-intercept,y-intercept}
First set:
Line L x-intercept=7 y-intercept = 7, slope = -1
Line K x-intercept=1 y-intercept = -1 slope = 1
product of x = +7; product of y = -7; product of slope = -1 => Answers stem question with "Yes"
In order to have the product of y-intercepts = negative, the y-intercepts must be on opposite sides of the x-axis. In order for the product of the x-intercepts to be positive, they must be on the same side of the x-axis.
As you can see from the First Set, the product of the slopes is negative when this occurs. What is the rule behind this?
If we keep line L the same, but we try to change line K to make it where the product of the slopes will be positive we run into a problem. If we have the x-intercept of x be L, then the x intercept of K needs to be positive too or the products will not be positive. If we make the x intercept greater than 4 (in order to make L have a negative slope) this makes the Y value positive, which gives us a negative product of the y-intercepts. This fits. What about the other way around? Is it possible to make the product of the slopes positive? This would mean each has a negative slope or a positive slope, but not one of each.
Positive Slope for L & K
Lets keep L the same for now. Change K. If L is the same, it has a negative y-intercept, so K needs to have a positive intercept. This is where the problem lies. When you make the slope positive and the y-intercept +ve, the x-intercept will ALWAYS be negative. So we have some rules we've discovered.
Positive Slope WITH Positive Y-Intercept = Negative X-intercept.
Positive Slope with Positive X-intercept = Negative Y-intercept
What the question is asking us is to have 2 lines that have different slopes. Lets look at the possibilities:
Positive Slope => + X, -Y OR -X with + Y (or 0, but that would not fit in this question so we leave it out)
Negative Slope => +X, + Y or -X with -Y (or 0, but same reason)
What do we need to satisfy the question (product of x-intercept = +, product of y-intercept= -)?
If one line has +x and - y (slope will be +), the other must have +x, + y (slope will be -)
Reverse is true
If one line has +x and + y (slope will be -), the other must have +x, - y (slope will be +)
If one line has -x and +y (slope will be +), the other must have -x, -y (slope will be -)
Reverse is true
If one line has -x and -y (slope will be -), the other must have -x, +y (slope will be +)
Can we ever get it where the lines both have negative or both have positive slopes? No. Why? Because when of the options stated above, the options above list out the combinations and each one has a different slope sign.
I was never able to come up with situations where I could get a slope of each sign as well as a slope of both + or both -.
#1) If the product of each x-intercept is + that meas both are negative or both are positive. L could have x intercept of -1 and K could have x-intercept of -2..product would be positive and product of slope would be positive. L could have x-intercept of 1 and K could have intercept of 5. product of both is positive, but K could have a negative slope, so the product of the slope would be negative. We've established 2 scenarios for the slope, each with a different +ve or -ve answer.
#2) here the Y intercepts must be different signs. L could have Y-intercept of 1 and K could have y-intercept of -1...product would be -ve but both slopes are +ve so we have +ve product of both slopes. now L could have y-intercept of 4 (negative slope) and K could have y-intercept of -1...+ve slope. Product of slopes is negative. We've established one +ve and one -ve for this one too. Insufficient.
#1 & #2 Together)
The x-intercept products must be positive and the y-intercepts must be negative.
Select a set of points that make this true and try to see if every set allows you to answer the question definitively whether the product of the slopes is negative.
Line L | Line K
{x-intercept,y-intercept} | {x-intercept,y-intercept}
First set:
Line L x-intercept=7 y-intercept = 7, slope = -1
Line K x-intercept=1 y-intercept = -1 slope = 1
product of x = +7; product of y = -7; product of slope = -1 => Answers stem question with "Yes"
In order to have the product of y-intercepts = negative, the y-intercepts must be on opposite sides of the x-axis. In order for the product of the x-intercepts to be positive, they must be on the same side of the x-axis.
As you can see from the First Set, the product of the slopes is negative when this occurs. What is the rule behind this?
If we keep line L the same, but we try to change line K to make it where the product of the slopes will be positive we run into a problem. If we have the x-intercept of x be L, then the x intercept of K needs to be positive too or the products will not be positive. If we make the x intercept greater than 4 (in order to make L have a negative slope) this makes the Y value positive, which gives us a negative product of the y-intercepts. This fits. What about the other way around? Is it possible to make the product of the slopes positive? This would mean each has a negative slope or a positive slope, but not one of each.
Positive Slope for L & K
Lets keep L the same for now. Change K. If L is the same, it has a negative y-intercept, so K needs to have a positive intercept. This is where the problem lies. When you make the slope positive and the y-intercept +ve, the x-intercept will ALWAYS be negative. So we have some rules we've discovered.
Positive Slope WITH Positive Y-Intercept = Negative X-intercept.
Positive Slope with Positive X-intercept = Negative Y-intercept
What the question is asking us is to have 2 lines that have different slopes. Lets look at the possibilities:
Positive Slope => + X, -Y OR -X with + Y (or 0, but that would not fit in this question so we leave it out)
Negative Slope => +X, + Y or -X with -Y (or 0, but same reason)
What do we need to satisfy the question (product of x-intercept = +, product of y-intercept= -)?
If one line has +x and - y (slope will be +), the other must have +x, + y (slope will be -)
Reverse is true
If one line has +x and + y (slope will be -), the other must have +x, - y (slope will be +)
If one line has -x and +y (slope will be +), the other must have -x, -y (slope will be -)
Reverse is true
If one line has -x and -y (slope will be -), the other must have -x, +y (slope will be +)
Can we ever get it where the lines both have negative or both have positive slopes? No. Why? Because when of the options stated above, the options above list out the combinations and each one has a different slope sign.
I was never able to come up with situations where I could get a slope of each sign as well as a slope of both + or both -.
gmatcraze
