Data Sufficiency- 700 level

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Data Sufficiency- 700 level

by kinshuk97gupta » Thu Jul 02, 2020 5:46 am
If the graph of the function x=y^2–9 on the xy-coordinate plane intersects line l at points A and B, what is the greatest possible slope of line l?

(1) Point A has coordinates (0,a)
(2) Point B has coordinates (7,b)

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Re: Data Sufficiency- 700 level

by rvgmat12 » Fri Oct 01, 2021 11:34 pm
Each statement by itself is insufficient. Statement (1) tells us about the coordinates of Point A, but nothing about the coordinates of Point B. And Statement (2) tells us about the coordinates of Point B, but nothing about the coordinates of Point A. However, when the two statements are combined, we can determine the greatest possible slope of line l.

Where two lines intersect, their coordinates are identical, and their equations are equal to each other. So each of the two points given in Statements 1 and 2 must satisfy the function x=y^2–9. Plugging the coordinate values of Point A into the equation, we get 0=a^2–9. Solving for a, we get that a is equal to 3 or -3. Thus, the possible coordinates of Point A are (0, 3) and (0,-3). Plugging the coordinates of Point B into the equation, we get 7=b^2–9. Solving for b, we get that b is equal to 4 or -4. Thus, the possible coordinates of Point B are (7, 4) and (7, -4).

Given these coordinate options for points A and B, there are four possible forms line 1 could take. With this information, we can determine which of the four possible slopes yields the greatest value. However, there is no need to actually calculate which line has the greatest slope.