Payal Tandon
Co-founder, e-GMAT
Welcome to e-GMAT Support!
I am Payal, Co-Founder of e-GMAT.
Feel free to ask any Query.
Thank you for your query.
We will be contacting you soon on

If three straight lines intersect at a point as shown in the figure above, what is the value of x? – OGQR 2020 Question #215 with Solution

A 2 min read

OGQR 2020: Question No. 215

If three straight lines intersect at a point as shown in the figure above, what is the value of x?

  1. x = y = z
  2. z = 60
Source OGQR 2020
Type Data Sufficiency
Topic Geometry
Sub-Topic Lines and Angles
Difficulty Easy

Solution

Steps 1 & 2: Understand Question and Draw Inferences

We are given:

  • Three intersecting lines, as shown in the diagram.
  • And, the angles between these 3 lines.

We need to find:

  • The value of x.

Let us name all the three lines as L1, L2, and L3 as shown:

  • One angle between line L1 and L2 is x0.
  • Similarly, one angle between line L2 and L3 is z0.
  • And, one angle between line L1 and L3 is y0.
    • Hence, their vertically opposite angles will also be equal as shown in diagram below.

  • Therefore, by applying the property that sum of all the angles around a point is 3600, we can say that:
    • 2x + 2y + 2z = 3600
    • Or, x + y + z = 1800

To find value of x, we need the value of y and z.

With this understanding, let us now analyse the individual statements.

 

Step 3: Analyse Statement 1

“x = y = z”

  • x + x + x = 1800
    • 3x = 1800
    • From this equation, we can find the value of x.

Thus, statement 1 is sufficient to answer the question.

 

Step 4: Analyse Statement 2

“z = 60”

Since we do not know the value of y, we cannot find the value of x.

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

 

Step 5: Combine Both Statements Together (If Needed)

As we could determine the answer from statement 1 individually, this step is not required.

Hence, the correct answer is option A.

A high GMAT score can set you apart from the competition and help you get an admit at your dream business school. Start your GMAT Preparation with the most reviewed online GMAT prep company. Try out our FREE Trial Today!

About The Author