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

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## A box contains 10 objects. Each object is either blue or red,

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[email protected] wrote: ↑Fri Aug 05, 2022 6:09 amA 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**