GMAT Quantitative Reasoning Practice Test 6

Question : 69 of 100

Marks: +1, -0

Is there an intersection between the line

(Y=a X-b)

and the parabola

(Y=X^2+b)

?
(1)

a< 0

.
(2)

0>b

Statement (1) BY ITSELF is sufficient to answer the question, but statement (2) by itself is not.
Statement (2) BY ITSELF is sufficient to answer the question, but statement (1) by itself is not.
Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, even though NEITHER statement BY ITSELF is sufficient.
Either statement BY ITSELF is sufficient to answer the question.
Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the question, requiring more data pertaining to the problem.

Solution:

First, draw the parabola and the line.
We can see that the thing that determines if the two intersect is

b

and not

a

.
If

b>0

there is no intersection but if

b< 0

there is an intersection no matter what the value of

a

is.
Therefore, statement (2) is sufficient and (1) is not.

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