killer inequality!

[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

[marcusking]

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

The lowest value |x + y| could ever be is 0, and according to our rules this is allowable examine

|-1 + 1| which is 0 so we can eliminate a,b,d

now we have to see if |x+y| can ever exceed 4 the most x or y can ever be is 1.999... so |1.9999+1.9999| is always less than 4

the answer is C.

[x2suresh]

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

agree with C..

e.g when x=1 Y=-1
|x+y| =0


This is D trap Question.

[cjb]

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

Well, |x + y| >= 0, always.

But, if x + y = 0 (e.g. x = 1.5, y=-1.5), then it is not the case that:

|x + y| > 0

so A is false. B and D are false because |x + y| does not have to be greater than one, as we just determined.

In fact, 0 <= lx+yl < 4, but that is not among the answers here
C is true, since there is any x or y values that satisfy 0 <= lx+yl < 4 will also satisfy C.

In a real test, I think I'd get careless about the possibility of x + y = 0, and mis the differenxe between < and <=...

[maihuna]

I have not understood the trap here, how D is wrong:

Most importatnlly how u going to consider |x+y| negative?

[Uri]

I have not understood the trap here, how D is wrong:

Most importatnlly how u going to consider |x+y| negative?

when x=-1 and y=1, we can have zero as the least value. (d) restricts the range from taking the value of zero.

(c) does not say that |x+y| is negative. it only says that |x+y| will be greater than -1. So, it includes zero as well.

hope this clears your doubt.

[ManuGMAT]

The Answer is E (let us not forget that this also an option for answers)

We already established earlier in the thread the X>=0.

X>=0 is not same as X>-1

Since none of the options has X>=0 so anser is E

[Uri]

The Answer is E (let us not forget that this also an option for answers)

We already established earlier in the thread the X>=0.

X>=0 is not same as X>-1

Since none of the options has X>=0 so anser is E

choosing (E) would perhaps be a hasty decision. problem no. 129 (page- 169) in GMAT OG 11 is an example which would support my statement.
"X>=0 is not same as X>-1 ". but any number that satisfies the inequality X>-1 will also satisfy X>=0.

ashish1354, can we have the OA and the source please?

[roger_michael]

My vote goes to C.

[billzhao]

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

The answer should be (C).

First, we know the ranges of x and y as below:

1<=x<2 or -2<x<=-1 and -2<y<2

So x+y<4 and x+y could be 0 if x=-0.5 and y=0.5

So 0<=|x+y|<4

Now we analyze the answer choices:

(A) and (B) must be out first as |x+y| will not reach 4.

Left with (C) and (D): we can eliminate (D) because if x+y=0, (D) gives a wrong range.

So the answer should be (C). The question is asking: "which of the following will be true?". (C) satisfies the range and the argument.

[lunarpower]

yeah, it's (c).

the question asks only for a statement that MUST BE TRUE. it does NOT ask for the ACTUAL SET OF VALUES.

this is a huge difference.

real life equivalent:

in the u.s. you can buy cigarettes at age 18 and alcohol at age 21.

let's say person X can buy cigarettes but not alcohol.

if i ask "what is the actual range of possibilities for the age of person X?", then the answer is 18 < X < 21. that is THE answer, and there is no other correct answer.

however, if i ask "which of the following is true?", then the correct answer could be something like 6 < X < 35. because, after all, the person X in the above example (who is at least 18, but younger than 21) must, indeed, be between 6 and 35 years old.

same thing in this example: the absolute value obviously must be > 0, but those values still fall well within the range of choice (c).

--

you can also think of the question in the same way in which you'd think about a data sufficiency question:

Is -1 < |x + y| < 4?

(1) 1 < x < 2 and 0 < y < 2
--> SUFFICIENT

just as ...
Is X between 6 and 35 years old?
(1) X can buy cigarettes, but not alcohol, in the united states
--> SUFFICIENT

the same reason those answers are "sufficient" is the reason that (c) is the correct answer to this problem.

--

the one fault of this question, though, is that, in my opinion, it's too "gotcha" to show up on the gmat. if the gmat were to give a problem like this one, then there would NOT be a choice (e) like the one here, whose sole purpose is to trip up students whose understanding is otherwise solid.