In a class, every student is either American or European. Every studen

Question

In a class, every student is either American or European. Every student is wearing a blazer or a sweater. If a student is selected randomly, is the probability of the student being a European wearing a sweater greater than that of his/her being an American wearing a blazer?

(1) The probability that a randomly selected student is either an American or wearing a blazer is  \frac{5}{6}

(2) The probability that a randomly selected student is either a European or wearing a sweater is  \frac{3}{5}

Namangupta1997 · Answer

chetan2u

A lot of unknowns even after taking both statements. How is C correct ?

chetan2u · Answer

There are 2 categories of people and within each of them, there are 2 sub categories. 
 In these questions, use 2 by 2 matrix.

Let the four categories be:  E_b, E_s,A_s,A_b  equal to w, y, z and x respectively as shown below.

2 by 2 matrix.

…………………E…………A………….Total 
 B ………….…w…………x……….w+x
 S ……….……..y…………z……..y+z
Total……....w+y………..x+z.….w+x+y+z
We are looking for whether  \frac{E_s}{t}>\frac{A_b}{t}  or  \frac{y}{t}>\frac{x}{t} ?

(1) The probability that a randomly selected student is either an American or wearing a blazer is  \frac{5}{6} 
This tells us that  \frac{w+x+z}{t}=\frac{5}{6} .
 1-\frac{w+x+z}{t}=1-\frac{5}{6} 
So,  P(E_s)=\frac{y}{t}=\frac{1}{6} 
Nothing about x/t

(2) The probability that a randomly selected student is either a European or wearing a sweater is  \frac{3}{5} 
This tells us that  \frac{w+y+z}{t}=\frac{3}{5} .
 1-\frac{w+y+z}{t}=1-\frac{3}{5} 
So,  P(A_b)=\frac{x}{t}=\frac{2}{5} 
Nothing about y/t

Combined 
We can clearly say 2/5>1/6 or x/t>y/t
Sufficient

IanStewart · Answer

No need for a matrix here - we just need to reverse the information in each statement. If, from Statement 1, 5/6 of students are American, wearing a blazer, or both, then the rest, or 1/6, are Europeans wearing sweaters. Similarly Statement 2 tells us that 2/5 of students are both American and wearing a blazer. So the answer is C.

chetan2u · Answer

Matrix may not be required in 50% cases. We can deduce the information without getting into matrix. 
But it is always better for students to get used to 2 by 2 matrix and make one wherever possible to avoid unnecessary mistakes or miss out on some information.

PyjamaScientist · Answer

chetan2u  Can you please your original answer, the matrix you have mentioned is slightly misaligned I suppose!

IanStewart · Answer

A matrix is never required, and I would never use one -- I'm replying only because I'm concerned some test takers who don't use matrices might think, reading this, that they need to learn them. There are better ways to do these kinds of problems.

chetan2u · Answer

I’ll too reply once and end it here as I too am worried for the students who are still trying to be at ease with such questions and may find a certain way suiting their needs. 
‘Best way to do a question’ would change with perspective of each. 
You may not find a method useful, while it may be helping thousands of students. Therefore, we should leave it to the judgement and skill of the members of the forum to understand what is best for them rather than imposing or negating a certain method.

IanStewart · Answer

I'll just point out that this discussion started because you said "it is always better for students to get used to 2 by 2 matrix and make one wherever possible," and now you seem to be saying more or less the opposite. What you're saying now is closer to something I'd agree with. I only replied at all because I post on gmatclub only to help test takers, and people who might be using a method they find faster and more flexible than matrices might read your post and think they need to learn a matrix, and they don't (and shouldn't). For test takers comfortable with them, there are alternatives that answer a greater variety of questions, and answer those questions more quickly.

chetan2u · Answer

Sorry, the discussion started because you wrote “matrix not required here”. I for one never wrote in the initial post that it is the best or the only way. I just solved it for a student. 
You too gave a solution through a para that can actually and comfortably be derived from the 2 by 2 matrix too. If you have an alternative, you should give it here so that the students are helped and can choose between the alternatives. 
Also, this discussion can continue until cows come home, so let’s end it here. We both have a common goal, that is to help students, and let us do it in our own ways.

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

In a class, every student is either American or European. Every studen

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Data Sufficiency (DS) Questions

In a class, every student is either American or European. Every studen

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards