Brent@GMATPrepNow wrote: ↑

Fri Aug 05, 2022 6:09 am

A box contains 10 objects. Each object is either blue or red, and each object is either triangle-shaped or square-shaped. If an object is randomly selected from the box, is the probability greater than 0.8 that it’s blue, triangle-shaped, or both?

(1) P(red and square-shaped) = 0.2
(2) P(blue) = 0.8

Answer: A
Source: www.gmatprepnow.com

Given: A box contains 10 objects. Each object is either blue or red, and each object is either triangle-shaped or square-shaped.
One approach is to use the Double Matrix Method. This technique can be used for most questions featuring a population in which each member has two characteristics associated with it (aka overlapping sets questions).
Here, we have a population of 10 objects, and the two characteristics are:
- blue or red
- triangle-shaped or square-shaped

So, we can set up our matrix as follows:


Target question: Is the probability greater than 0.8 that it’s blue, triangle-shaped, or both?
In the diagram below, the three shaded boxes represent objects that are blue, triangle-shaped, or both.

So, we can REPHRASE the target question as: "Is the sum of the three shaded boxes greater than 8?", since this would mean the probability is greater than 0.8 that the selected object is blue, triangle-shaped, or both.

Statement 1: P(red and square-shaped) = 0.2
When we add this information to our diagram we get:

This means the sum of the shaded boxes is 8.
So, the answer to the REPHRASED target question is NO, the some of the shaded boxes is NOT greater than 8
Since we can answer the REPHRASED target question with certainty, statement 1 is SUFFICIENT

Statement 2: P(blue) = 0.8[/quote]
There are several scenarios that satisfy statement 2. Here are two:

Case a:

Here, the answer to the REPHRASED target question is NO, the some of the shaded boxes is NOT greater than 8

Case b:

Here, the answer to the REPHRASED target question is YES, the some of the shaded boxes is greater than 8
Since we can’t answer the REPHRASED target question with certainty, statement 2 is NOT SUFFICIENT

Answer: A