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alms: Newbie | Next Rank: 10 Posts; Posts: 2; Joined: Sat Jul 30, 2011 4:05 am

by alms » Sat Jul 30, 2011 5:08 am

Is|x-y| > |x| - |y| ?
(1) y<x
(2) xy < 0

I struggle with this type of problems can someone please share some tips on how to approach this? and how to solve this particular one?

Many thanks

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Source: Beat The GMAT — Data Sufficiency | Sat Jul 30, 2011 5:08 am

Ozlemg: Master | Next Rank: 500 Posts; Posts: 407; Joined: Tue Jan 25, 2011 9:19 amFollowed by: 7 members; Thanked: 25 times

by Ozlemg » Sat Jul 30, 2011 9:46 am

i thinkk it it B
search on net, there ar elots of info about inequalities

The more you suffer before the test, the less you will do so in the test!

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edge: Senior | Next Rank: 100 Posts; Posts: 49; Joined: Sun Jun 26, 2011 5:45 pm; Thanked: 2 times

by edge » Sat Jul 30, 2011 5:08 pm

My answer is D.

St1 is sufficient. The expression evaluates to true for both (x, y) = (2, 1) and (2, -3).
St2 is sufficient. xy < 0, therefore (x > 0 AND y < 0) OR (x < 0 AND y > 0). Trying (2, -3) and (-2, 3), the expression evaluates to true.

EDIT: Since you asked for tips, I think the best way is to just pick numbers intelligently which satisfy the statements when evaluating them.

EDIT: The correct answer is B. When evaluating St1, I failed to account for y = 0 for which the inequality evaluates to false. I need to take my own advice. Make sure you don't assume anything that is not explicitly given.

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sl750: Master | Next Rank: 500 Posts; Posts: 496; Joined: Tue Jun 07, 2011 5:34 amFollowed by: 1 member; Thanked: 38 times

by sl750 » Sun Jul 31, 2011 4:42 am

You can use numbers to test such cases. Just test two cases where you get a No and a Yes and you are good to eliminate that statement

In this case. For statement 1, consider
x=2, y=1, substituting these values into the equation, we get
Is 1>1, No
x=2 y=-1
Is 3>-1, Yes. We can eliminate answers A and D

For statement 2, either x>0 and y<0 or x<0 and y>0. Let's try some cases
x=2, y=-2
Is 4>0, Yes
x=-2,y=1, Yes. You will see that the equation on the left will always be the absolute sum of x and y.
So answer is B

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