If lines k and j are in the xy coordinate plane, is the : Data Sufficiency (DS)

maliyeci

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Re: xy–coordinate plane [#permalink]

29 Sep 2009, 08:01

1

Kudos

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.

maliyeci

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Re: xy–coordinate plane [#permalink]

29 Sep 2009, 08:36

1

Kudos

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. :roll:

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=2-7m
n/m=2/m-7
same as for the other
y/t=2/t-7
since -n/m is greater than -y/t; y/t is greater than n/m
so
2/m-7>2/t-7
2/m>2/t
so we can find the solution
C is suff.

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Re: xy–coordinate plane [#permalink]

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 x-axis. 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 x-axis. This will be a vertical line. Now select two points on the axis just to right and left of (7,0) on x-axis. Let these points be the x-intercepts of the lines. Now the slope of line with a greater x-intercept say, (7.0001, 0 ) will always be -ve [in order to intersect (7,2)] and the slope of the line with a smaller x-intercept say (6.9999, 0 ) will always be +ve [in order to intersect (7,2)]

Suff.

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Re: xy–coordinate plane [#permalink]

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. :roll:

maliyeci wrote:

7m+n<7t+n
7m<7t
m<t

mrsmarthi

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Re: xy–coordinate plane [#permalink]

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/m-7<2/t-7
2/m<2/t
so we can find the solution
C is suff.

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Re: xy–coordinate plane [#permalink]

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 X-axis. k intercept is greater than j intercept --> k intercept (k1) point right to j intercept point (j1) --> Interception of lines is above X-axis (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 x-intercept of line k is greater than the x-intercept 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=2-7m --> n/m=2/m-7
p=2-7t --> p/t=2/t-7
n/m<p/t --> 2/m-7<2/t-7 --> 1/m<1/t --> (t-m)/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! :beer

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Re: xy–coordinate plane [#permalink]

22 Nov 2012, 06:22

Bunuel wrote:

Lets combine --> draw only X-axis. k intercept is greater than j intercept --> k intercept (k1) point right to j intercept point (j1) --> Interception of lines is above X-axis (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: If lines k and j are in the xy coordinate plane, is the [#permalink]

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 m-n=c-b/7. Now question is is c-b>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 [#permalink]

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 x-intercept of line k is greater than the x-intercept of line j
(2) Lines k and j intersect at (7, 2)

Answer: E

refer to images attached.

Attachments

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B

arnkaprx

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Re: If lines k and j are in the xy coordinate plane, is the [#permalink]

04 Jul 2023, 04:15

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 X-axis. k intercept is greater than j intercept --> k intercept (k1) point right to j intercept point (j1) --> Interception of lines is above X-axis (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 x-intercept of line k is greater than the x-intercept 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=2-7m --> n/m=2/m-7
p=2-7t --> p/t=2/t-7
n/m<p/t --> 2/m-7<2/t-7 --> 1/m<1/t --> (t-m)/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.

Can't we also use the formula - m = y2-y1/x2-x1 here? By that we get slope for line k = 2-0/7-x1 and slope for line j is = 2-0/7-x2. And since (1) says that x2 > x1, we can say that m(j) < m(k)? And thus C.

B

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Re: If lines k and j are in the xy coordinate plane, is the [#permalink]

09 Sep 2023, 16:09

This question is best approached by visually thinking about slope as if it's the physical steepness of a road, lines (roads) can fulfill both conditions with either one of them steeper than the other.

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Re: If lines k and j are in the xy coordinate plane, is the [#permalink]

09 Sep 2023, 16:09

GMAT Data Sufficiency (DS) Questions

If lines k and j are in the xy coordinate plane, is the