Nirupam04 wrote:What is y-intercept of line L?
1) The slope of the line is 3 times its y-intercept
2) The x-intercept is -1/3
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Target question:
What is the y-intercept of line L?
IMPORTANT: If the x-intercept is -1/3 (as per statement 2), the slope of the line is guaranteed to be 3 times its y-intercept (as per statement 1).
Here's why.
From statement 2, we know that (-1/3, 0) is one point on the line. Let's let (0, k) be the coordinates of the y-intercept of the line. In other words, let's let the y-intercept equal k.
Using the slope formula, the slope = (k - 0)/(0 - (-1/3)) = k/(1/3) = 3k
So, if the y-intercept is k, the slope
must be 3k.
In other words, if we're given statement 2, then statement 1 provides no new information.
So, if statement 2 is sufficient, then statement 1 must also be sufficient (since it provides no new info). Likewise, if statement 2 is NOT sufficient, then statement 1 is NOT sufficient. At this point, we know that the answer must be either D (they're both sufficient) or E (neither is sufficient).
So, which is it?
Well, if we examine statement 2 on its own (the x-intercept is -1/3), we can see that we do not have enough information to determine
the y-intercept of line L.
Since we cannot answer the
target question with certainty, statement 2 is NOT SUFFICIENT
Moreover, since statement 1 provides no additional information, it too is NOT SUFFICIENT.
And the combined statements are NOT SUFFICIENT
Answer =
E
Cheers,
Brent
