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Inequality and absolute values

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Inequality and absolute values

by papgust » Sun Feb 28, 2010 6:30 am
If xy ≠ 0, is x > y?

(1) 4x = 3y
(2) |y - x| = x - y

OA: D
Source: Magoosh.com


For these kinds of problems, I've always found plugging in method quite tedious although it's solvable by plugging in. Any easy approach to this problem.
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by ajith » Sun Feb 28, 2010 6:49 am
papgust wrote:If xy ≠ 0, is x > y?

(1) 4x = 3y
(2) |y - x| = x - y

OA: D
Source: Magoosh.com


For these kinds of problems, I've always found plugging in method quite tedious although it's solvable by plugging in. Any easy approach to this problem.
1) 4x = 3y

True for both of these sets of x and y
x= -3 y =-4 ; x>y
x=3 y =4 ; x<y

Insufficient

2) |y - x| = x - y

y-x is -ve or zero

y-x <=0

x>= y

Insufficient (x can be equal to y)

Combining

sufficient to conclude that x>y

C, Please check OA
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by papgust » Sun Feb 28, 2010 11:17 pm
I'm sorry. It's a typo.

OA is C
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by girish3131 » Mon Mar 08, 2010 5:35 am
@Ajith

i didn't get this point when u say

|y - x| = x - y

y-x is -ve or zero


acc to me eq 2 is sufficient.... ans is B

b'coz

y-x = x-y i.e. x=y

or

y-x = -(x-y) i.e. y-x = y-x # wat to conclude from this point , am not 100% sure...

still i prefer B , on the basis of above info...

Plz correct me if wrong...

TA...
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by Testluv » Wed Mar 10, 2010 4:05 pm
girish3131 wrote:@Ajith

i didn't get this point when u say

|y - x| = x - y

y-x is -ve or zero


acc to me eq 2 is sufficient.... ans is B

b'coz

y-x = x-y i.e. x=y

or

y-x = -(x-y) i.e. y-x = y-x # wat to conclude from this point , am not 100% sure...

still i prefer B , on the basis of above info...

Plz correct me if wrong...

TA...
Let's look at the second statement:

|y - x| = x - y

Absolute value is always positive or zero. Therefore, the left hand side must be positive or zero. The two sides of the equation must be equal. Therefore, the right hand side also must be positive or zero:

x - y >= 0

x >= y

So, as Ajith points out, either x is bigger than y, or else x is equal to y. Because we don't know for sure whether x is bigger than y, this statement is insufficient by itself.
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