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Re: In the xy-plane, is the slope of line L greater than the [#permalink]
02 Feb 2012, 11:53

3

This post received KUDOS

Expert's post

Smita04 wrote:

In the xy-plane, is the slope of line L greater than the slope of line K? (1) L passes through (5, 0) and K passes through (-5, 0). (2) L and K intersect with each other in the 2nd quadrant.

Answer is E, not C as everyone stated above.

Note that: a steeper incline indicates a higher absolute value of the slope.

Obviously each statement alone is not sufficient. When taken together, we can have 2 cases:

Attachment:

The slope of K is greater than that of L.png [ 8.41 KiB | Viewed 3690 times ]

You can see that the slope of K (blue) is greater than that of L (red): 2>-1;

Attachment:

The slope of K is less than that of L.png [ 8.09 KiB | Viewed 3687 times ]

In this case the slope of K (blue) is less than that of L (red): -8<-1/2. Here, both lines have negative slopes. Line K is steeper than line L, which indicates that the absolute value of its slope is greater than that of line L, since slopes are negative, then slope of K is "more negative" (so less) than slope of L.

I believe drawing this out will make the scenario's clearer. However, 3 scenarios here - slope of L > | = | < m considered. a. meaning L can be = M or > | < M too. not sufficient.

b. no clue about the lines and slopes here. insufficient.

a+b means, Line L has negative slope hence it enters 2nd quad Line M has positive slope hence it enters 2nd quad from 3rd quad(possibly).

In the xy-plane, is the slope of line L greater than the slope of line K? (1) L passes through (5, 0) and K passes through (-5, 0). (2) L and K intersect with each other in the 2nd quadrant.

From statement 1 alone we dont have any information regarding the slopes of the two lines . statement 2 alone we cannot predict anything about the slope. Now combine both the statements. L passes from 1 st quadrant to the 2 nd quadrant.Implies slope is negative.

K is already in the second quadrant( -5,0) .For it to interect with the line L it has to have a positive slope or even if its negative ,its magnitude is higher than that of line L.

Hence 2 statements together are requried . Sorry you need to imagine the figure ,I would have helped better with a diagram !! _________________

Re: In the xy-plane, is the slope of line L greater than the [#permalink]
21 Oct 2012, 08:24

Bunuel wrote:

Smita04 wrote:

In the xy-plane, is the slope of line L greater than the slope of line K? (1) L passes through (5, 0) and K passes through (-5, 0). (2) L and K intersect with each other in the 2nd quadrant.

Answer is E, not C as everyone stated above.

Note that: a steeper incline indicates a higher absolute value of the slope.

Obviously each statement alone is not sufficient. When taken together, we can have 2 cases:

Attachment:

The slope of K is greater than that of L.png

You can see that the slope of K (blue) is greater than that of L (red): 2>-1;

Attachment:

The slope of K is less than that of L.png

In this case the slope of K (blue) is less than that of L (red): -8<-1/2. Here, both lines have negative slopes. Line K is steeper than line L, which indicates that the absolute value of its slope is greater than that of line L, since slopes are negative, then slope of K is "more negative" (so less) than slope of L.

Re: In the xy-plane, is the slope of line L greater than the [#permalink]
23 Oct 2012, 07:18

Expert's post

mydreammba wrote:

Bunuel wrote:

Smita04 wrote:

In the xy-plane, is the slope of line L greater than the slope of line K? (1) L passes through (5, 0) and K passes through (-5, 0). (2) L and K intersect with each other in the 2nd quadrant.

Answer is E, not C as everyone stated above.

Note that: a steeper incline indicates a higher absolute value of the slope.

Obviously each statement alone is not sufficient. When taken together, we can have 2 cases:

Attachment:

The slope of K is greater than that of L.png

You can see that the slope of K (blue) is greater than that of L (red): 2>-1;

Attachment:

The slope of K is less than that of L.png

In this case the slope of K (blue) is less than that of L (red): -8<-1/2. Here, both lines have negative slopes. Line K is steeper than line L, which indicates that the absolute value of its slope is greater than that of line L, since slopes are negative, then slope of K is "more negative" (so less) than slope of L.

I think when we follow graphs we might miss some of the cases, i think it is better to solve by algebra? am i correct?

You should choose approach which suits you best. For me personally, it wasn't too hard to find two examples satisfying both statements and giving different answers to the question _________________

Re: In the xy-plane, is the slope of line L greater than the [#permalink]
27 Oct 2012, 03:45

Bunuel wrote:

Smita04 wrote:

In the xy-plane, is the slope of line L greater than the slope of line K? (1) L passes through (5, 0) and K passes through (-5, 0). (2) L and K intersect with each other in the 2nd quadrant.

Answer is E, not C as everyone stated above.

Note that: a steeper incline indicates a higher absolute value of the slope.

Obviously each statement alone is not sufficient. When taken together, we can have 2 cases:

Attachment:

The slope of K is greater than that of L.png

You can see that the slope of K (blue) is greater than that of L (red): 2>-1;

Attachment:

The slope of K is less than that of L.png

In this case the slope of K (blue) is less than that of L (red): -8<-1/2. Here, both lines have negative slopes. Line K is steeper than line L, which indicates that the absolute value of its slope is greater than that of line L, since slopes are negative, then slope of K is "more negative" (so less) than slope of L.

Re: In the xy-plane, is the slope of line L greater than the [#permalink]
08 May 2013, 22:23

Hi bunuel... I must say excellent solution but one thing that i did not understand is how did u form equation for the two different lines when we do not have any point of intersection ....... Can u pls elaborate on that point.

Re: In the xy-plane, is the slope of line L greater than the [#permalink]
09 May 2013, 01:39

Expert's post

Archit143 wrote:

Hi bunuel... I must say excellent solution but one thing that i did not understand is how did u form equation for the two different lines when we do not have any point of intersection ....... Can u pls elaborate on that point.

Archit

We know that the lines intersect in 2nd quadrant, so the lines drawn are just examples. _________________

Re: In the xy-plane, is the slope of line L greater than the [#permalink]
09 May 2013, 01:52

Bunuel wrote:

Smita04 wrote:

In the xy-plane, is the slope of line L greater than the slope of line K? (1) L passes through (5, 0) and K passes through (-5, 0). (2) L and K intersect with each other in the 2nd quadrant.

Answer is E, not C as everyone stated above.

Note that: a steeper incline indicates a higher absolute value of the slope.

Obviously each statement alone is not sufficient. When taken together, we can have 2 cases:

Attachment:

The slope of K is greater than that of L.png

You can see that the slope of K (blue) is greater than that of L (red): 2>-1;

Attachment:

The slope of K is less than that of L.png

In this case the slope of K (blue) is less than that of L (red): -8<-1/2. Here, both lines have negative slopes. Line K is steeper than line L, which indicates that the absolute value of its slope is greater than that of line L, since slopes are negative, then slope of K is "more negative" (so less) than slope of L.

Bunnel, I too answered E, but just want you to confirm once if my approach is correct. Even after combining both statements, i realized that, since L passes through 2nd quadrant, it can as well pass through point K, if say, it passes through K, then the answer depends on slope of K. If it passes above point K in 2nd quadrant, then also, it depends on slope of K. Hence, data is insufficient. Is my interpretation correct?

Re: In the xy-plane, is the slope of line L greater than the [#permalink]
09 May 2013, 01:58

Expert's post

mamathak wrote:

Bunuel wrote:

Smita04 wrote:

In the xy-plane, is the slope of line L greater than the slope of line K? (1) L passes through (5, 0) and K passes through (-5, 0). (2) L and K intersect with each other in the 2nd quadrant.

Answer is E, not C as everyone stated above.

Note that: a steeper incline indicates a higher absolute value of the slope.

Obviously each statement alone is not sufficient. When taken together, we can have 2 cases:

Attachment:

The slope of K is greater than that of L.png

You can see that the slope of K (blue) is greater than that of L (red): 2>-1;

Attachment:

The slope of K is less than that of L.png

In this case the slope of K (blue) is less than that of L (red): -8<-1/2. Here, both lines have negative slopes. Line K is steeper than line L, which indicates that the absolute value of its slope is greater than that of line L, since slopes are negative, then slope of K is "more negative" (so less) than slope of L.

Bunnel, I too answered E, but just want you to confirm once if my approach is correct. Even after combining both statements, i realized that, since L passes through 2nd quadrant, it can as well pass through point K, if say, it passes through K, then the answer depends on slope of K. If it passes above point K in 2nd quadrant, then also, it depends on slope of K. Hence, data is insufficient. Is my interpretation correct?

Do you mean line K? Point has no slope... _________________