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If lines k and j are in the xy coordinate plane, is the
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29 Sep 2009, 01:21
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If lines k and j are in the xy–coordinate plane, is the slope of line k greater than the slope of line j ? (1) The xintercept of line k is greater than the xintercept of line j (2) Lines k and j intersect at (7, 2)
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Re: xy–coordinate plane
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29 Sep 2009, 05:26
I get B but I am not sure. OA pls? Following is the reasoning: stmt 1: we just have two points on the xaxis. we can draw many lines via these two points and having different slopes. Insuff.
stmt2: we have the intersection point in the first quadrant. Now, draw a line perpendicular from (7,2) to the xaxis. This will be a vertical line. Now select two points on the axis just to right and left of (7,0) on xaxis. Let these points be the xintercepts of the lines. Now the slope of line with a greater xintercept say, (7.0001, 0 ) will always be ve [in order to intersect (7,2)] and the slope of the line with a smaller xintercept say (6.9999, 0 ) will always be +ve [in order to intersect (7,2)]
Suff.



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Re: xy–coordinate plane
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29 Sep 2009, 08:01
Approach of economist is nice. Lets do it more mathematically. 1)insuff. No need to explain. 2)insuff. No need to explain. together line k=> y=mx+n line j=> y=tx+y we know from 1 that n is greater than y. And we know from 2 that they are intersecting at point (7,2). That makes 2=7m+n 2=7t+y 7m+n=7t+y 7m+n<7t+n 7m<7t m<t SUFF. C.



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Re: xy–coordinate plane
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29 Sep 2009, 08:14
Maliyeci, I have two questions  In y = mx + b equation, m = slope and b is the Y intercept. From your represenation, how can we say that maliyeci wrote: we know from 1 that n is greater than y. when variables n and y are the Y intercepts. Not X intercepts. Can you please explain how you made this Inequality based on n > y(assuming y intercepts of L > y intercept of K). I am confused. maliyeci wrote: 7m+n<7t+n 7m<7t m<t



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Re: xy–coordinate plane
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29 Sep 2009, 08:36
mrsmarthi wrote: Maliyeci, I have two questions  In y = mx + b equation, m = slope and b is the Y intercept. From your represenation, how can we say that maliyeci wrote: we know from 1 that n is greater than y. when variables n and y are the Y intercepts. Not X intercepts. Can you please explain how you made this Inequality based on n > y(assuming y intercepts of L > y intercept of K). I am confused. maliyeci wrote: 7m+n<7t+n 7m<7t m<t I beg your pardon for the intercepts. Yes you are rigth. I gave the Y intercept. The x intercepts are respectively; n/m and y/t But they are sufficient to find an answer. That is the solution. 7m+n=2 n=27m n/m=2/m7 same as for the other y/t=2/t7 since n/m is greater than y/t; y/t is greater than n/m so 2/m7>2/t7 2/m>2/t so we can find the solution C is suff.



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Re: xy–coordinate plane
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29 Sep 2009, 09:16
Yes....this is correct. But with a small correction. maliyeci wrote: since n/m is greater than y/t; y/t is greater than n/m ==> n/m < y/t so 2/m7<2/t7 2/m<2/t so we can find the solution C is suff.



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Re: xy–coordinate plane
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03 Oct 2009, 13:27
Sorry to disappoint you guys, but seems that the answer should be E. First of all to solve this question think that the best way is graphic approach: We all agree that (1) and (2) alone are not sufficient. Lets combine > draw only Xaxis. k intercept is greater than j intercept > k intercept (k1) point right to j intercept point (j1) > Interception of lines is above Xaxis (point 7;2) > it will give us only three possible ways to draw the lines: A. j has negative slope, k has negative slope > slope of k>slope of j, (because j is closer to vertical line); B. j has positive slope, k has negative slope > slope of k<slope of j; C. j has positive slope, k has positive slope > slope of k>slope of j, (because k is closer to vertical line); So (1)+(2) not sufficient. Answer E. BUT the way you were solving also should get E: f(k)=mx+n f(j)=tx+p (1) The xintercept of line k is greater than the xintercept of line j > 0=mx+n; 0=tx+p > n/m>p/t or n/m<p/t > not sufficient; (2) Lines k and j intersect at (7, 2) 2=7m+n; 2=7t+p > 7m+n=7t+p >not sufficient; Combining the way you did: n=27m > n/m=2/m7 p=27t > p/t=2/t7 n/m<p/t > 2/m7<2/t7 > 1/m<1/t > (tm)/mt<0And here is the catch, from above statement you can not determine whether m>t or not. t=1<m=3 statement is true and t=1>m=3 statement is also true. Answer E.
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Re: xy–coordinate plane
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03 Oct 2009, 13:31
Bunuel wrote: Sorry to disappoint you guys, but seems that the answer should be E.
First of all to solve this question think that the best way is graphic approach:
We all agree that (1) and (2) alone are not sufficient.
Lets combine > draw only Xaxis. k intercept is greater than j intercept > k intercept (k1) point right to j intercept point (j1) > Interception of lines is above Xaxis (point 7;2) > it will give us only three possible ways to draw the lines: A. j has negative slope, k has negative slope > slope of k>slope of j, (because j is closer to vertical line); B. j has positive slope, k has negative slope > slope of k<slope of j; C. j has positive slope, k has positive slope > slope of k>slope of j, (because k is closer to vertical line);
So (1)+(2) not sufficient. Answer E.
BUT the way you were solving also should get E:
f(k)=mx+n f(j)=tx+p (1) The xintercept of line k is greater than the xintercept of line j > 0=mx+n; 0=tx+p > n/m>p/t or n/m<p/t > not sufficient; (2) Lines k and j intersect at (7, 2) 2=7m+n; 2=7t+p > 7m+n=7t+p >not sufficient;
Combining the way you did: n=27m > n/m=2/m7 p=27t > p/t=2/t7 n/m<p/t > 2/m7<2/t7 > 1/m<1/t > (tm)/mt<0 And here is the catch, from above statement you can not determine whether m>t or not. t=1<m=3 statement is true and t=1>m=3 statement is also true. Answer E. This exactly why I said IMO E . Thanks for explanation Bunuel!



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Re: xy–coordinate plane
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22 Nov 2012, 06:22
Bunuel wrote: Lets combine > draw only Xaxis. k intercept is greater than j intercept > k intercept (k1) point right to j intercept point (j1) > Interception of lines is above Xaxis (point 7;2) > it will give us only three possible ways to draw the lines: A. j has negative slope, k has negative slope > slope of k>slope of j, (because j is closer to vertical line); B. j has positive slope, k has negative slope > slope of k<slope of j; C. j has positive slope, k has positive slope > slope of k>slope of j, (because k is closer to vertical line);
Hi Bunuel, Request you to please look at the colored portion again and confirm if its correct. Isn't in Option A>Slope of j > Slope of K. If not, please provide your reasoning, may be I'm lacking some concept. thanks



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Re: xy–coordinate plane
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22 Nov 2012, 07:08
imhimanshu wrote: Bunuel wrote: Lets combine > draw only Xaxis. k intercept is greater than j intercept > k intercept (k1) point right to j intercept point (j1) > Interception of lines is above Xaxis (point 7;2) > it will give us only three possible ways to draw the lines: A. j has negative slope, k has negative slope > slope of k>slope of j, (because j is closer to vertical line); B. j has positive slope, k has negative slope > slope of k<slope of j; C. j has positive slope, k has positive slope > slope of k>slope of j, (because k is closer to vertical line);
Hi Bunuel, Request you to please look at the colored portion again and confirm if its correct. Isn't in Option A>Slope of j > Slope of K. If not, please provide your reasoning, may be I'm lacking some concept. thanks A steeper incline indicates a higher absolute value of the slope. So, if both lines have positive slope, then the line which is steeper has greater slope. If both lines have negative slope, then the line which is steeper has greater absolute value slope, its slope is "more negative", so less than the slope of another line. Similar questions to practice: iftheslopesofthelinel1andl2areofthesamesignis126759.htmlslopesofmandn124025.htmllinenandplieinthexyplaneistheslopeoftheline30553.htmllinesnandplieinthexyplaneistheslopeoflinen97007.htmlinthexyplaneistheslopeoflinelgreaterthanthe126941.htmlHope it helps.
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Re: If lines k and j are in the xy coordinate plane, is the
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27 Feb 2014, 09:13
I would solve algebraically.
Say line K is mx+b while like J is nx+c.
Question is is m>n?
Statement 1 tells us that b/m>c/n, but we know nothing about the signs of b and c hence insufficient.
Statement 2 says that 7m+b=7n+c, we could factorize to get mn=cb/7. Now question is is cb>0? We don't know this.
Now from both statements together we still don't know whether c>b, so E is the best answer choice here.
Hope this gives a hand Cheers! J



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If lines k and j are in the xy coordinate plane, is the
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28 Feb 2015, 04:11
tejal777 wrote: If lines k and j are in the xy–coordinate plane, is the slope of line k greater than the slope of line j ?
(1) The xintercept of line k is greater than the xintercept of line j (2) Lines k and j intersect at (7, 2) Answer: E refer to images attached.
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