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If x and y are negative numbers, is x<y?

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If x and y are negative numbers, is x<y? [#permalink] New post 13 Aug 2013, 10:44
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If x and y are negative numbers, is x<y?

(1) 3x+4<2y+3

(2) 2x−3<3y−4

Bunuel, can you please explain the graphical method to solve this question?

Thanks
[Reveal] Spoiler: OA

Last edited by Bunuel on 13 Aug 2013, 10:55, edited 1 time in total.
RENAMED THE TOPIC.
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Re: If x and y are negative numbers, is x<y? [#permalink] New post 13 Aug 2013, 11:09
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nitin6305 wrote:
If x and y are negative numbers, is x<y?

(1) 3x+4<2y+3

(2) 2x−3<3y−4

Bunuel, can you please explain the graphical method to solve this question?

Thanks

Dear nitin6305,
I'm happy to help with this. :-)

Idea #1: to graph an inequality, solve for slope-intercept form (i.e. y = mx + b form). When we do that
Graph (1) becomes: y > 3x/2 + 1/2
Graph (2) becomes: y > 2x/3 + 1/3
We plot the exact lines (y = 3x/2 + 1/2 and y = 2x/3 + 1/3) to determine the boundaries of the regions. If the inequality is y > mx + b, then the region representing the inequality is above the line; if the inequality is y < mx + b, then the region representing the inequality is below the line.

Idea #2: any question about whether x is > or = or < y is question about the line y = x. Read this post about the magical properties of the line y = x.
http://magoosh.com/gmat/2012/gmat-math- ... -line-y-x/

Here's the image:
Attachment:
inequalities with y = x.JPG
inequalities with y = x.JPG [ 82.84 KiB | Viewed 1385 times ]

The darker green region, above the line y > 3x/2 + 1/23, is the region representing the first inequality. The yellow region, above the line y = 2x/3 + 1/3, is the region representing the second inequality. The bright spring green region is their overlap, the region satisfied by both inequalities. Notice that everything in that bright spring green region is above the solid green line, which is y = x. Points above the line y = x always have y > x.

Does all this make sense?
Mike :-)
_________________

Mike McGarry
Magoosh Test Prep

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Re: If x and y are negative numbers, is x<y? [#permalink] New post 13 Aug 2013, 11:18
mikemcgarry wrote:
nitin6305 wrote:
If x and y are negative numbers, is x<y?

(1) 3x+4<2y+3

(2) 2x−3<3y−4

Bunuel, can you please explain the graphical method to solve this question?

Thanks

Dear nitin6305,
I'm happy to help with this. :-)

Idea #1: to graph an inequality, solve for slope-intercept form (i.e. y = mx + b form). When we do that
Graph (1) becomes: y > 3x/2 + 1/2
Graph (2) becomes: y > 2x/3 + 1/3
We plot the exact lines (y = 3x/2 + 1/2 and y = 2x/3 + 1/3) to determine the boundaries of the regions. If the inequality is y > mx + b, then the region representing the inequality is above the line; if the inequality is y < mx + b, then the region representing the inequality is below the line.

Idea #2: any question about whether x is > or = or < y is question about the line y = x. Read this post about the magical properties of the line y = x.
http://magoosh.com/gmat/2012/gmat-math- ... -line-y-x/

Here's the image:
Attachment:
inequalities with y = x.JPG

The darker green region, above the line y > 3x/2 + 1/23, is the region representing the first inequality. The yellow region, above the line y = 2x/3 + 1/3, is the region representing the second inequality. The bright spring green region is their overlap, the region satisfied by both inequalities. Notice that everything in that bright spring green region is above the solid green line, which is y = x. Points above the line y = x always have y > x.

Does all this make sense?
Mike :-)


Dear Mike

Thanks a lot for the prompt response.

All of the above makes sense. :-D

Nitin
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Re: If x and y are negative numbers, is x<y? [#permalink] New post 31 Aug 2013, 11:20
Is there a quicker way to solve?
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Re: If x and y are negative numbers, is x<y? [#permalink] New post 31 Aug 2013, 11:24
Expert's post
Re: If x and y are negative numbers, is x<y?   [#permalink] 31 Aug 2013, 11:24
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