Ankit04041987 wrote:
If xy < 3, is x < 3 ?
(1) |y|> 1
(2) |x| < 3
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
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