From statement 1)
|y|<1 & |x|<2|y|<1: This means two things: y<1 or -y<1.
-y<1 can be rewritten as y>-1 (when multiplied by -ve, the sign changes. In this case lesser than becomes greater than)
We can summarize as: -1<y<1
Similarly, we can summarize -2<x<2
This is all we know from statement 1. If you draw a number line, x and y could lie anywhere as long as they satisfy respective conditions.
For ex: Y=0 and X=1; In this case Y is less than X.
or Y=1 and X = -1; In this case Y is greater than X.
Hence statement 1 is insufficient.
AD BCEFrom statement 2)
y>0 and x is not 0
Again, we know nothing about the number except that y is positive and x can be positive or negative. Using simple numbers for X= -1 and Y =1, we can see that Y is indeed greater than X.
But if X= 100 and Y = 1, Y is less than X.
Hence statement 1 is insufficient.
BCENow your chance of getting this question right is 50%. Taking 1 and 2 together:
We know Y > 0 and range of Y is -1<Y<1, combining these two we can write 0<Y<1; i.e Y is a positive fraction.
Similarly -2<x<2 but x cannot be 0.
Again, take X=-1/2 and Y=1/2; Y is greater than X.
X=1/2 and Y=1/4; Y is less than X.
Hence answer is E.
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Kudosity killed the cat but your kudos can save it.