If xy

Question

If xy < 3, is x < 3 ?

(1) |y|> 1
(2) |x| < 3

Bunuel · Answer

If xy < 3, is x < 3 ?

(1) |y|> 1. Probably the easiest way to deal with this statement would be to plug some numbers. Notice that \(|y|> 1\) means that \(y<-1\) or \(y>1\). Now, if \(y=2\) and \(x=-4\) then the answer is YES but if \(y=-2\) and \(x=4\) then the answer is NO. Not sufficient.

(2) |x| < 3 --> \(-3<x<3\): directly gives an YES answer to the question. Sufficient.

Answer: B.

Hope it's clear.

bschooladmit · Answer

Answer B.

From the question:
xy<3 => x,y can be both positive and negative or, opposite signs. x(-2)y(3)<3
1. |y| > 1 => y>1 y<-1 => y can take 2, 3, 4, 5 or -2, -3, -4, -5.. if y=-6 and x=6 xy is -36 <3. If y=-1, x=-2 xy<3.
here x = 6 in one case and -2 in another case.
Hence Insufficient.
2. |x|<3 => -3<x<3 . No matter what the values of x are, it will be <3. Sufficient.

Markusosv · Answer

I'm not quite sure that I've understood the question.

"Is xy < 3" This part I read as one question, "is x < 3?" This as another one.

Was the question "If xy<3, is x<3?"?

If I'm completely wrong please let me know why i might've misunderstood the semantics.

Thanks!

Bunuel · Answer

Yes, the question reads: " If  xy < 3, is x < 3 ?"

Hope it's clear.

Markusosv · Answer

Noticed it now. I must've misread earlier.

Thanks!

PerfectScores · Answer

Statement I is insufficient:

y = 0.1 then x < 30 it can be equal to 5 or -5.

Statement II is sufficient:

|x| < 3 means x is between -3 and 3 hence x will always be less than 3

Answer will be B.

stonecold · Answer

Here statement 2 is sufficient as if |x|<3 => x lies in the range of (-3,3)
hence x<3 is always true.
So B

ScottTargetTestPrep · Answer

We are given that the product of x and y is less than 3 and need to determine whether x is less than 3. Statement One Alone: |y| > 1 Since |y| > 1, either y > 1 or -y > 1, which means y < -1. We will pick a number for y in each interval to see what the value of x will be. First, if y > 1, say y = 2, and then we have: 2x < 3 x < 3/2 Here x < 3. However, if y < -1, say y = -3, and then we have: -3x < 3 x > -1 Since x is greater than -1, we see that x could be greater than 3. Statement one alone is not sufficient to answer the question. Statement Two Alone: |x| < 3 Since |x| < 3, either x < 3 or -x < 3, which means x > -3. So, we have: -3 < x < 3 Thus, we see that x will always be less than 3. Answer: B

Basshead · Answer

If xy < 3, is x < 3 ? (1) |y|> 1 y > 1 or y < -1 if y = 2 and x = 1; yes. if y = -3 and x = 4; no INSUFFICIENT. (2) |x| < 3 -3 < x < 3 Answers our question: x < 3 SUFFICIENT. Answer is B.

CEdward · Answer

If xy < 3, is x < 3 ?

xy < 3 implies one of the following cases:
a) x and y are both positive or negative
b) x and y have opposite signs

(1) |y|> 1
Insufficient. 
x = -3, y = 1 then YES x < 3
x = 3, y = -1 then NO x = 3

(2) |x| < 3
Sufficient. 
x = 2, y = 1 
x = -2, y = 1

In either case, x <3.

Answer is B.

If xy < 3, is x < 3 ?

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