adityagogia9899 wrote:

VeritasPrepKarishma wrote:

bsjames2 wrote:

In the xy-coordinate plane, line l and line k intersect at the point (4,3). Is the product of their slopes negative?

1) The product of the x-intercepts of lines l and k is positive.

2) The product of the y-intercepts of lines l and k is negative.

Please explain your answer

This question has a great takeaway - something I am sure you know intuitively but you may not think of it while doing this question because it is seldom written out:

The slope of a line is -(y intercept)/(x intercept)

Above, sreehari uses this concept to solve the question very efficiently.

If you are wondering why it is so, think what 'intercept' represents...

The point of x intercept is (x, 0) (where y co-ordinate is 0)

The point of y intercept is (0, y) (where x co-ordinate is 0)

So slope = (y - 0)/(0 - x) = -y/x

Hi karishma

Slope of line 1 is -y1/x1

slope of line 2 is -y2/x2

if we multiply both the slopes

wont the product be positive??

Kindly help

The best approach to tackle statement questions in DS is as follows:

Step 1: Convert all the alphabetical statements in algebraic statements

Step 2: Reduce the number of variable to minimum

Step 3: Check how many variables are left. You may probably need that many statements to solve the questions but you might need lesser number of statements to answer the question.

Caution: Don't waste your time in solving the question. You have to analyse the data sufficiency and not solve the question.

Step 1: Introduce as many variable as required. In this case we require 4 variables: x1, y1, x2, y2

Reducing the alphabetical statement to algebraic one:

Product of slopes will be: (-y2/x2)*(-y1/x1) = y2y1/x2x1

We have to see if y2y1/x2x1<0?

Step 2: Reduce number of variables. In this case, we took 4 variables. But to determine the sign of slope we need to find out only two variable i.e. y2y1 and x2x1 and that two their signs and not their values. Thus, to answer the constraint we need to know 2 things and not 4.

Step 3: Check statements:

1) The product of the x-intercepts of lines l and k is positive.

This gives us the sign of x2x1 as positive. But we don't know whether y2y1 is positive or negative. Thus, this is not sufficient.

2) The product of the y-intercepts of lines l and k is negative.

This gives us the sign of y2y1 as positive. But we don't know whether x2x1 is positive or negative. Thus, this is not sufficient.

Now combining both these statements, we can know the sign of y2y1 as well as x2x1 which is coming out to be negative.

Thus, C becomes our solution.

Hope it is useful to you!!!

Kudos if you like it!!!!