Graphical solution to OG DS #109

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Graphical solution to OG DS #109

by xyz21 » Sun Feb 22, 2009 8:13 pm
Are positive integers p and q both greater than n?

1) p - q > n
2) q > p


If I solve using analytical method in OG then I get the correct answer. But I also like to solve all inequality problems graphically. If I assume q = x and p = y and plot the two inequalities as below..

Please see the attached file for plot

(1) y - x > n {line with 45 degree slope in first quadrant passing (0,n) and feasible region above the line}
(2) x > y {line with 45 degree slope in first quadrant passing (0,0) and feasible below the line}

.. then I get infeasible solution since there is no intersection between the "shaded" regions of two inequalities (the lines are parallel). How to resolve this?


Thanks very much.
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by Alara533 » Thu Mar 12, 2009 3:20 pm
Hi...

Here you have assumed n to be positive and the graph (y-x > n) is drawn as if y is always greater than x. It can also happen that x is greater than y and n is a -ve value. In that case the feasible regions of the two graphs will have common points and that is happening here.

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Re: Graphical solution to OG DS #109

by logitech » Thu Mar 12, 2009 9:00 pm
xyz21 wrote:Are positive integers p and q both greater than n?

1) p - q > n
2) q > p


If I solve using analytical method in OG then I get the correct answer. But I also like to solve all inequality problems graphically. If I assume q = x and p = y and plot the two inequalities as below..

Please see the attached file for plot

(1) y - x > n {line with 45 degree slope in first quadrant passing (0,n) and feasible region above the line}
(2) x > y {line with 45 degree slope in first quadrant passing (0,0) and feasible below the line}

.. then I get infeasible solution since there is no intersection between the "shaded" regions of two inequalities (the lines are parallel). How to resolve this?


Thanks very much.
I understand the value of solving a question using different methods, but I always look for a GMAT solution - short & sweet

p - q > n
q - p > 0

+
-----------------------

0 > n ( Negative )

Question stem gives us: p and q are both positive! ( I don't know how many times I forgot to use the information given in the question stem )
LGTCH
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by bondguy » Sat Feb 13, 2010 10:25 pm
logitech provided simple elegant solution /

yet i m interested how can we use graph to solve such probes /

xyz21 started to solve this problem graphically / yet i can't see how to extract the solution this way