GMAT Quantitative Reasoning Practice Test 6

Question : 70 of 100

Marks: +1, -0

Is there a point of intersection between the circle

(X^2+Y^2=4)

and the line

(Y=a X+b)

?
(1)

a=b^2

.
(2) The line intersects the

x

-axis at

(40,0)

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:

From statement (1) we learn that the equation of the line can be written as

Y=b^2 X+b

.
From statement (2) we learn that the line goes threw the point

(40,0)

, from that we can find the equation of the line by posting the coordinate in the equation:

0=b^2 40+b

. There is no need to solve it, both statements are sufficient to solve the problem.

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