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Inequalities

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Inequalities

by jsasipriya » Mon Jul 19, 2010 2:58 pm
Is X>Y?

1) X>Z+1
2) Y>Z


From the above two equations, can we simplify them as below?

X - 1 > Z ........... from equation (1)


X - 1 > Y ............ combining the above & equation (2)

Is the above simplification mathematically correct?
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by Patrick_GMATFix » Mon Jul 19, 2010 6:00 pm
the equations you tried to combine are:

X-1 > Z and...
Y > Z

The conclusion you came to is... X-1 > Y. This is not a valid conclusion. Think of X-1 as one number. Let's call it K. The equations become.

K > Z and Y > Z. Your conclusion is that K > Y. We have no way to prove this mathematically. All we know is that K and Y are both greater than Z. we cannot determine whether K > Y, K = Y or K < Y.
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