Is |x-y||x| - |y| A. y is less than x B. xy0

Question

Is |x-y|>|x| - |y|

A. y is less than x
B. xy>0

Dek · Answer

not sure mate. Got this during GmatPrep. Need to know the logic behind this solution

bsd_lover · Answer

Disclaimer: I am only just coming to grips wit DS

|x+y| > |x|-|y| ? Stmt 1 x > y Lets see , if x and y are positive then this works well but if x = -1 and y = -3 then |x+y|=4 and |x|-|y| = -2 so Insufficient Stmt 2 is obviously insufficient by itself but it implies that either x and y are both positive or they are both negative. But the case that I described for stmt 1 already has 2 negatives, hence Stmt 1 and Stmt 2 BOTH are insufficient Ans E I would be interested to hear other people's solutions...

subhen · Answer

Answer should be E.

Check out the attachment

Fig · Answer

(E) for me too

Is |x-y|>|x| - |y| ? From 1 y < x <=> x - y > 0 So, |x-y| = x - y Then, I will try to find all cases to eliminate the absolute values from the right side of the inequality. If 0 < y < x then, o |x| - |y| = x - y = |x-y| If y < 0 < x then, o |x| - |y| = x - (-y) = x + y and o x + y < x - y as y < 0 So, o |x| - |y| = x + y < x - y = |x-y| If y < x < 0 then, o |x| - |y| = -x - (-y) = y - x and o y-x < 0 < x-y (Condition of stat 1) Thus, |x| - |y| < |x-y| Finally, o If 0 < y < x, then |x| - |y| = |x-y| o If y < 0 and y < x, then |x| - |y| < |x-y| INSUFF. From 2 x*y > 0 Implies: o x > 0 and y > 0 or o x < 0 and y < 0 the cases analysed from 1 are still existing here: o If 0 < y < x, then |x| - |y| = |x-y| o If y < 0 and y < x, then |x| - |y| < |x-y| INSUFF. From (1) and (2): We remain with the same cases. INSUFF.

Dek · Answer

Wow! Thats a lot for 2 mins. Maybe I'll request GMAT to let me do this during my essay time. :idea:

Fig · Answer

I have detailed all here

... Probabbly the best approach is to pick numbers : but u have to be sure to know what u do... In other words, to cover all relevant interval or conditions

bsd_lover · Answer

Hi Dek,

 To be honest this is one of the lesser time consuming problems that I have seen on this forum. Look at my previous post, I didnt really need to check for too much to be able to prove that both the statements are insufficient.

Fig's reply is outstanding and his comprehensive method will work for pretty much all modulus / inequality type DS questions that most people have trouble with. 

cheers,

Is |x-y|>|x| - |y| A. y is less than x B. xy>0

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