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An Example of a 750+ level GMAT Geometry Question

Getting a GMAT score that is above 700 is what most students who take the exam aspire for. Only 12% of those who take the GMAT test get a score that is above 700 and even fewer get a score above 750. A 750+ level question is generally considered to be difficult and can only be solved by a select few. However, this is not true. Even a 750+ level question can be solved if you have a good grasp of the basic concepts. Here is an example of a 750+ level GMAT geometry question that you can encounter in the GMAT question paper.


A right-angled triangle PQR exists on the xy-plane. The right angle is at the vertex P, and the side PR is parallel to the x-axis. The x and y coordinates of each of the vertices, P, Q, and R have to satisfy the following inequalities:

-3 <= x <= 6

5 <= y <= 15

How many different triangles can you construct that satisfy both of the aforementioned conditions?

(A) 1000
(B) 110
(C) 12,100
(D) 9,900
(E) 11,000


Option D: 9,900


As per the question, the total number of possibilities for the x and y coordinates of each vertex are:

Possibilities for x = 10

Possibilities for y = 11

There is a right angle at P and PR is parallel to the x-axis. This implies that the side PQ will be perpendicular to the x-axis, which in turn implies that PQ will be parallel to the y-axis.

Since PR is parallel to the x-axis, the value for y coordinate for both P and R will remain the same. Similarly, since PQ is parallel to the y-axis, the x coordinate for P and Q will remain the same.

Possibilities of x and y coordinates for P = (10 values for x)(11 values for y) = 10*11 = 110.

This is because it isn’t stated on where P should be apart from the range of x and y.

Once you select a coordinate for P, there are (10 – 1) = 9 possibilities for the x coordinate of R. The y coordinate of R will remain the same as that of P.

Once you select a coordinate for P, there are (11 – 1) = 10 possibilities for the y coordinate of Q. The x coordinate of Q will remain the same as that of P.

The total number of triangles which upon meeting the specified conditions that can be constructed are = (110)(9)(10) = 9900.

The problem uses both combinatorics and geometry.

How to Approach 750+ Level GMAT Questions

Scoring above 750 requires some serious planning and practice. It is suggested that you start your GMAT preparation with the quant section. Start by understanding the basic concepts and proceed on to solving practice questions. As seen from the above example, the question is pretty simple once you understand how to approach it. It only used the basic concepts but combined two topics. You can take GMAT mock tests to get a better idea of GMAT format and to develop strategies you can use in the actual test. This will definitely help you improve your GMAT score.

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