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

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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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[email protected] 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:
Image

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

Case b:
Image
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
Brent Hanneson - Creator of GMATPrepNow.com
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