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 [ 82.84 KiB | Viewed 2241 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