If xy < 3, is x < 3 ?

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!

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

Hope it's clear.

Noticed it now. I must've misread earlier.

Thanks!

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.

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

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

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.

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.