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

Question

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

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

sanjitscorps18 · Answer

Considering the probabilities basis the information we get the below 
R △ , B △ , R ▢ , B ▢
Overall R △ + B △ + B ▢ + R ▢ = 1

(1) P(red and square-shaped) = 0.2
R ▢ = 0.2
However, everything else has to sum up the requirement of the question (either △ or Blue or both)
=> R △ + B △ + B ▢ = 0.8
Since we get a definite answer that R △ + B △ + B ▢ is not more than 0.8, this is sufficient

(2) P(blue) = 0.8
Now we'll write the probability as
R △ + R ▢ + 0.8 = 1
But we don't know what is R ▢ as it could be 0 too. Hence, we cannot be whether that R △ + 0.8 > 0.8

Option A

BrentGMATPrepNow · Answer

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: https://i.imgur.com/QoZQffL.png 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. https://i.imgur.com/K0qJD2s.png 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: https://i.imgur.com/rero5FT.png 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 There are several scenarios that satisfy statement 2. Here are two: Case a : https://i.imgur.com/IgM5SYS.png Here, the answer to the REPHRASED target question is NO, the some of the shaded boxes is NOT greater than 8 Case b : https://i.imgur.com/hfBdjxh.png 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 To learn more about the Double Matrix Method, watch this video: https://www.youtube.com/watch?v=jK-tiBrrf04 EXTRA PRACTICE QUESTION https://www.youtube.com/watch?v=DsbPUSH_Wu4 More questions to practice with: EASY: https://gmatclub.com/forum/of-the-120-p ... 15386.html MEDIUM: https://gmatclub.com/forum/in-a-certain ... 21716.html HARD: https://gmatclub.com/forum/a-group-of-2 ... 24888.html KILLER: https://gmatclub.com/forum/a-certain-hi ... 32899.html

egmat · Answer

This is a Yes/No question asking: Is P(blue OR triangle)  > 0.8 ?
  The Trick:  Use the complement rule!

The only objects that are NOT "blue or triangle-shaped or both" are objects that are  BOTH red AND square .

So:  P(blue OR triangle) = 1 - P(red AND square)

---
 Statement 1:  P(red and square) =  0.2

Using our formula:
P(blue OR triangle) = 1 - 0.2 =  0.8

Is 0.8 > 0.8?  NO

We get a definitive answer →   SUFFICIENT

---
 Statement 2:  P(blue) =  0.8

This tells us 8 objects are blue and 2 are red, but nothing about shapes.

Case 1:  2 red objects are squares
→ P(red AND square) = 0.2
→ P(blue OR triangle) = 0.8
→ Is 0.8 > 0.8?  NO

Case 2:  2 red objects are triangles
→ P(red AND square) = 0
→ P(blue OR triangle) = 1.0
→ Is 1.0 > 0.8?  YES

Different scenarios give different answers  →  NOT SUFFICIENT

---

Answer: A

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

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

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