EgmatQuantExpert BunuelEgmatQuantExpert wrote:

Solution

Given:

• PQ is a straight line.

• Coordinate of point P is (a, b).

• a > 0.

To find:• In which quadrant Q lies.

Let us assume the coordinate of point Q is (x, y)

To find the quadrant of point Q, we need to find the exact value of the coordinate of point Q.

Analysing statement 1: The origin bisects PQ in 1: 1 ratio.

Hence, 0 = \(\frac{a + x}{2}\)and 0= \(\frac{b + y}{2}\)

• Therefore. x= -a and y= -b

• However, we still don’t know the exact value of x and y.

Hence, statement 1 is not sufficient to answer the question.

Analysing statement 2:The slope m of the line PQ is non-negative.

Slope m of a line is \(\frac{y2 – y1}{x2-x1}\).

Hence, m= \(\frac{y-b}{x-a}\)

However, we still don’t have any information about the values of x and y.

Hence, statement 2 is not sufficient to answer the question.

Combining both the statements together:From statement 1:

• x= -a and y= -b

From statement 2:

• m= \(\frac{y-b}{x-a}\)

We cannot find the value of x and y even after combining both the statements together.

Hence, option E is the correct answer.

Correct answer: option E. Can you let me know where I have gone wrong in my reasoning.

I thought C is the answer and my reasoning is given below.

Given a straight line PQ, with co-ordinates of P as (a,b) where a > 0

=> P is either on the 1st quadrant or on x axis or on the 4rth quadrant. Any pattern of line with positive, negative, infinite or zero slope can be drawn using points in these quadrants.

STATEMENT 1 : Origin bisects the line in the ratio 1 : 1

From the set of lines that could possibly be the answer we can eliminate all lines that doesnt pass through the origin.

As line passes through origin and a >0, line y axis and all lines with slope infinity (|| to y axis) can be eliminated.

If point P is in quadrant 1 it has to pass though quadrant 3 to satisfy this condition. This implies that the line will have a positive slope

If b is 0, then PQ is part of the x axis itself, and the point Q will be (-a,0) => Slope is 0 here

If the point P lies in 4rth quadrant, then Q must lie in the 2nd quadrant so that the origin bisects PQ. Here PQ will have negative slope.

HENCE STATEMENT 1 is not enough to answer the question

STATEMENT 2 : slope is non negative.

0 is neither positive nor negative. So I believe this statement essentially means slope is positive. We cannot narrow down the options here. The point Q could be in first quadrant itself

However, combining the 2 we can conclude that Q should pass through origin and should be in third quadrant. Hence both together can answer the question