GMAT Data Sufficiency Practice Question 25

Geometry | Coordinate Geometry | Data Sufficiency

The given question is a challenging GMAT 650+ level quant data sufficiency question testing concepts in Geometry. Concepts covered: Coordinate Geometry - Properties of Straight Lines - x-intercept and y-intercept - quadrants in x-y plane.

Question 25: Does the line L whose equation is y = mx + c cut the x-axis in the positive direction of x-axis?

Statement 1: The intercepts of Line K, perpendicular to L, are of the opposite signs.
Statement 2: Line L passes through the 4th quadrant.


Get to Q51 in GMAT Quant


Online GMAT Course
@ INR 3500


Video Explanation


GMAT Live Online Classes


Start Tue, Oct 12, 2021


Explanatory Answer | GMAT Geometry DS Practice Question

Step 1: Evaluate Statement 1 ALONE

Statement 1: The intercepts of Line K, perpendicular to L, are of the opposite signs.
Inference 1: If the intercepts of line K are of opposite signs, line K is a positive sloping line.
Inference 2: So, we can infer that line L is a negative sloping line.

Possibility 1: Negative sloping Line L with a positive x-intercept

line with positive x intercept

In this possibility, answer to the question is YES

Possibility 2: Negative sloping Line L with a negative x-intercept

line with negative x intercept

In this possibility, answer to the question is NO

Because both possibilities exist, we are not able to answer the question using statement 1.

Statement 1 alone is NOT sufficient.
Eliminate answer options A and D.


Step 2: Evaluate Statement 2 ALONE

Statement 2: Line L passes through the 4th quadrant.

Possibility 1: Line L passes through IV quadrant. Has a positive x-intercept.

line with positive x intercept

In this possibility, answer to the question is YES

Possibility 2: Line L passes through IV quadrant. Has a negative x-intercept

line with negative x intercept

In this possibility, answer to the question is NO

Because both possibilities exist, we are not able to answer the question using statement 2.

Statement 2 alone is NOT sufficient.
Eliminate answer option B.


Step 3: Evaluate Statements TOGETHER

Statement 1: The intercepts of Line K, perpendicular to L, are of the opposite signs.
Statement 2: Line L passes through the 4th quadrant.

Key Inference from Statement 1: Line L is a negative sloping line.

Possibility 1: Negative Sloping Line L passes through IV quadrant. Has a positive x-intercept.

line with positive x intercept

In this possibility, answer to the question is YES

Possibility 2: Negative Sloping Line L passes through IV quadrant. Has a negative x-intercept

line with negative x intercept

In this possibility, answer to the question is NO

Because both possibilities exist, we are not able to answer the question despite combining the statements.

Statement TOGETHER are NOT sufficient.
Eliminate answer option C.

Choice E is the correct answer.



GMAT Online Course
Try it free!

Register in 2 easy steps and
Start learning in 5 minutes!

★ Sign up

Already have an Account?

★ Login

GMAT Live Online Classes

Next Batch Oct 12, 2021

★ GMAT Live Info

GMAT Coaching in Chennai

Next Batch
after Lockdown

★ GMAT Class Info

GMAT Coaching in Chennai

Sign up for a Free Demo of our GMAT Classes in Chennai

★ Schedule Demo

GMAT Hard Math Videos On YouTube


GMAT Sample Questions | Topicwise GMAT Questions


Where is Wizako located?

Wizako - GMAT, GRE, SAT Prep
An Ascent Education Initiative
14B/1 Dr Thirumurthy Nagar 1st Street
Nungambakkam
Chennai 600 034. India

How to reach Wizako?

Phone: (91) 44 4500 8484
Mobile: (91) 95000 48484
WhatsApp: WhatsApp Now
Email: learn@wizako.com
Leave A Message