Interesting GMATFix Problem-17

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arora007: Community Manager; Posts: 1048; Joined: Mon Aug 17, 2009 3:26 amFollowed by: 27 members; Location: India; Thanked: 51 times; GMAT Score:670

by arora007 » Tue Sep 21, 2010 12:55 pm

If x and y are distinct non-zero integers, is |x+y| = |x| - |y| ?
1) xy<2
2) x-y >0

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Source: Beat The GMAT — Data Sufficiency | Tue Sep 21, 2010 12:55 pm

clock60: Legendary Member; Posts: 759; Joined: Mon Apr 26, 2010 10:15 amFollowed by: 3 members; Thanked: 85 times

by clock60 » Tue Sep 21, 2010 2:40 pm

hope the reduced question asks is xy<0
(1)xy<2 sufficent, as x,y are distinct integers, and neither is equal to 0, they must have opposite signs to be less than 2
if they are both -ve the product will be +ve. they can`t be -1*-2=2 as we need xy<2, and they can`t be 1*2=2 as again xy<2,so one of them must be +ve and one -ve
suff
(2) many options are possible if x>y
x=2,y=1 xy>0 the answer is no
x=1,y=-2 xy<0 the answer is yes

my pick for A

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arora007: Community Manager; Posts: 1048; Joined: Mon Aug 17, 2009 3:26 amFollowed by: 27 members; Location: India; Thanked: 51 times; GMAT Score:670

by arora007 » Tue Sep 21, 2010 3:39 pm

A is wrong

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clock60: Legendary Member; Posts: 759; Joined: Mon Apr 26, 2010 10:15 amFollowed by: 3 members; Thanked: 85 times

by clock60 » Tue Sep 21, 2010 9:47 pm

honestly, i checked solution one more time but didn`t spot mistake,
waiting for the reply from others,
only one question arora
may be st 1 is written
x*y<=2? in this case i see that st 1 insufficient

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gmatmachoman: Legendary Member; Posts: 2326; Joined: Mon Jul 28, 2008 3:54 amFollowed by: 2 members; Thanked: 173 times; GMAT Score:710

by gmatmachoman » Wed Sep 22, 2010 12:14 am

1) xy<2

@ clock

case 1:

x= 3 y = -1

xy <2

|x+y| = |x| - |y|
YES

case 2:

x= -3, Y = 1

|x+y| = |x| - |y|

|-3+1| NOT EQUAL to |x| - |y|

St 1 is insufficient

Combining St1 & st2 (x>Y)

use the example of case 1

Pick C

R&D on GMAT algorithm:

https://www.beatthegmat.com/r-d-on-gmat- ... tml#305739

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clock60: Legendary Member; Posts: 759; Joined: Mon Apr 26, 2010 10:15 amFollowed by: 3 members; Thanked: 85 times

by clock60 » Wed Sep 22, 2010 1:01 am

dear gmatmachoman
i almost agree with your reasoning, but one thing is confusing, with your examples

x=3, y=-1
|x+y|=|3-1|=|2|=2
|x|-|y|=|3|-|-1|=3-1=2, completely agree

x=-3, y=1
|x+y|=|-3+1|=|-2|=2
|x|-|y|=|-3|-|1|=3-1=2 with my calculations

but in your solving you came that if with x=-3.y=1 |x+y| is not equal |x|+|y|????
can you elaborate a little bit more?

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gmatmachoman: Legendary Member; Posts: 2326; Joined: Mon Jul 28, 2008 3:54 amFollowed by: 2 members; Thanked: 173 times; GMAT Score:710

by gmatmachoman » Wed Sep 22, 2010 1:41 am

clock60 wrote:dear gmatmachoman
i almost agree with your reasoning, but one thing is confusing, with your examples

x=3, y=-1
|x+y|=|3-1|=|2|=2
|x|-|y|=|3|-|-1|=3-1=2, completely agree

x=-3, y=1
|x+y|=|-3+1|=|-2|=2
|x|-|y|=|-3|-|1|=3-1=2 with my calculations

but in your solving you came that if with x=-3.y=1 |x+y| is not equal |x|+|y|????

LHS |-3+1| = |-2| = 2

RHS : |-3| + |1| = 3 +1 = 4

LHS is NOT EQUAL to RHS

can you elaborate a little bit more?

R&D on GMAT algorithm:

https://www.beatthegmat.com/r-d-on-gmat- ... tml#305739

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clock60: Legendary Member; Posts: 759; Joined: Mon Apr 26, 2010 10:15 amFollowed by: 3 members; Thanked: 85 times

by clock60 » Wed Sep 22, 2010 2:07 am

LHS |-3+1| = |-2| = 2

RHS : |-3| + |1| = 3 +1 = 4

LHS is NOT EQUAL to RHS
why do you add? in the problem we must substract
|x+y| = |x| - |y| ?

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arora007: Community Manager; Posts: 1048; Joined: Mon Aug 17, 2009 3:26 amFollowed by: 27 members; Location: India; Thanked: 51 times; GMAT Score:670

by arora007 » Wed Sep 22, 2010 2:36 am

plugin values, find E as the answer.

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CrazyGmatter: Senior | Next Rank: 100 Posts; Posts: 38; Joined: Fri Dec 14, 2007 11:58 pm; Thanked: 3 times

by CrazyGmatter » Wed Sep 22, 2010 9:52 pm

can you post the official explanation pls...

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