Inequality(GPREP)

[aj5105]

Is |x -y| > |x| + |y|?

(1) y < x

(2) xy < 0

[doclkk]

I would guess D.

Statement 1. Y<X

Regardless what numbers you choose, the answer is always no.

5-2=3 > 5+2 NOT TRUE

5-(-2) = 7 > 5+2 NOT TRUE

-2-(-4) = 2 >2 + 4 NOT TRUE

AD cross out BCE

Statement 2

XY<0

X = -1
Y = 1

-1-1 = -2 > 1+1 2 - Not true.

I can't think of a single instance of when |X-Y| > |X| + |Y|

Which leads me to believe that you wrote the question wrong because i didn't need the statements at all for this question ...

Or am i missing something?

[matanga]

Are you sure the question asks if abs(x-y) > abs(x) + abs(y) ? Shouldn't it be abs(x) - abs(y) ??

[sreak1089]

Answer is B in my opinion.

is |x-y| > |x| + |y|

stmt 1 says y < x => if say x = 5, y=4 then |x-y| < |x| + |y|
however, if x=5, y=-4, then |x-y| == |x| + |y|

Hence stmt 1 NOT SUFFICIENT

stm2 says xy < 0 ==> x -ve, y +ve or x +ve, y -ve

Lets take example, -6,3 or 6, -3 |x-y| == |-6 -3| == 9 or |6 - (-3)| == 9
which will be same as |x| + |y| == |-6| + |3| == 9 or |6| + |-3| == 9

Hence stmt 2 SUFFICIENT

Ans: B

[shibal]

agree with sreak1089
IMO [spoiler]B[spoiler][/spoiler][/spoiler]

[mike22629]

People: using the number lines makes problems like this so easy.....

lx - yl > lxl + lyl

A.) y < x

Remember lx - yl means the distance between x and y so....

----------------0--------y=1--------x=2
so lx-yl = 1
but lxl + lyl = 3

However....

-------y=-1---0--------x=1
lx-yl = 2
lxl + lyl = 2

so from this information in the first problem what do you realize?
It is really a question asking about whether x and y are positive or negative

B.) xy < 0

this tells you that x and y have the same sign. Hence...
lxl + lyl Will ALWAYS be greater than lx-yl

This question is tricky because lx - yl can NEVER be greater than lxl + lyl but it can be equal to it.

IMO B.

[El Cucu]

Is |x -y| > |x| + |y|?

(1) y < x

(2) xy < 0

Hi Aj
May the question has an error as never the value |x -y| could be greater than |x| + |y|, could you pls. re check? Tks in advance.

[sreak1089]

Hi Elcucu, the question is whether will you be able to answer with a definite YES or NO from the given data for the question. You will be able to say that answer to the question is NO based on the data given in (2).