* Killer inequality question

[ashish1354]

If 1<= lxl < 2 and 0<=lyl<2, which of the following will be true?

A) 0 < lx+yl <=4
b) 1 < lx+yl <=4
c) -1 < lx+yl < 4
d) 1 <= lx+yl <4
e)none of these

[boiarski]

I believe the answer is E, for the following reasons:

1<= lxl < 2, implies that if x were positive then 1<=x<2, and if x were negative then -2<X<=-1

0<=lyl<2, implies that -2<y<2

Evaluating lx+yl then becomes rather simple, firstly you can immediately knock out option c, as no absolute value can be less than 0. For this question we now simply have to establish the limits of x+y. If y were -1 and x were 1 then x+y would be 0, which means that we only have to evaluate now whether option a is right or wrong. The largest value of lx+yl would be x being less than 2 and y being less than 2, or x being greater than -2 and y being greater than -2, either absolute value sum would lead to less than 4, or a complete formula of 0<=lx+yl<4. None of the equations match this, so the answer is E.

[JonathanSchneider]

Can you please cite the source of this question? We cannot answer posts that do not cite the source.