Do at least 60 percent of the students in Pats class walk to school?

1. We don't have information of the composition of the class i.e what percentage of males and females.
Not sufficient

2.
Let x= number of students who don't walk to school
=> 2x= number of students who walk to school
% of students who walk to school = 2x/3x*100 %
= (2/3)*100%
=66.67 %

Sufficient

Answer B
_________________

Let there be 100 students. The questions asks if at least 60 of those walk to school.

1) Clearly insufficient, since we have no information about Male/Female Ratio or whatsoever.
2) Tells us that the ratio is 2:1. So from every 3, 2 walk to school which is >66% --> Sufficient.

Answer B

We need to determine whether at least 60 percent of the students in Pat’s class walk to school.

Statement One Alone:

At least 60 percent of the female students in Pat’s class walk to school.

We do not know how many male and female students are in Pat’s class, nor do we know the percentage of male students who walk to school. Thus, statement one is not sufficient to answer the question.

Statement Two Alone:

The number of students in Pat’s class who walk to school is twice the number of students who do not walk to school.

If we let n = the number of students who do not walk to school, then the number of students who do walk to school is 2n. Furthermore, the total number of students can be represented by n + 2n = 3n. Thus, the percentage of students who walk to school is:

(2n)/(3n) x 100% = 2/3 x 100% = 66.7%

Statement two is sufficient to answer the question.

Answer: B
_________________

(1)
Is unsufficient, we don´t know the percent of how many male students in Pat´s class walk to school.
(2)
x: number of students in Pat´s class that don´t walk to school.
2x: number of students in Pat´s class that walk to school
3x: The total number of students in Pat´s class (x+2x=3x)

I took this approach based on the probability of an event formula:

% of students who walk to school: \(\frac{2x(desired outcome)}{3x(possible outcomes)}\)\((100)\)%

I couldn´t understand well at first why we had \(\frac{2x}{3x}\), relating it to that formula was my way of understanding it, please let me know if its misleading or if there´s a better way to represent the idea.

Thanks

Hope the illustration makes sense

Bunuel niks18 chetan2u niks18 amanvermagmat gmatbusters



Would st 1 be suff if I would have known NUMBER OF females students who walk to school?

Q stem asks: No of students who walk to school / total number of students >= 0.6

Usually in a percentage problem in question stem , I look out for %tages in answer options and
not absolute values. Is this approach a sound one?
_________________

Yes, then the statement I would be sufficient, and you would find such official questions.
_________________

Answer: Option B

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Your Question : Would st 1 be suff if I would have known NUMBER OF females students who walk to school?

Answer is NO

you need relative number of female and male to answer that.
you can answer if: you have ratio/ percentage of male and female students or exact number of male and female students.



_________________

2 of 3 students are coming to school, thus 66.66%
Answer B.

Dear Experts,

I have a small doubt, how are we so sure that only 2 categories(People who walk to school & People who don't walk to school) exist in the school) exist. In my mind I thought there could be other categories as students who come by car etc, hence I marked E.

@Bunnel

Please advice.

Que : WTS = 60% of total = 60 ( If Total = 100)

1. 60% F WTS - Insufficient
2.WTS = 2 NWTS ,
WTS + NWTS = 100
3 NWTS = 100
NWTS = 100/3 = 33.33
WTS = 100 - 33.33 = 66.66

B SUFFICIENT

Hi, the second statement says student's in pat's class who walk to school= 2* number of students who do not walk to school. How can we infer that these students belong to pat's class??? i marked E hence.

statement 2 alone is sufficient as we will always get more than 60% students.
_________________

chetan2u Bunuel if the statement (1) had 60 percent of females walk to school and 60 percent of males walk to school, that would mean 60/100(F) + 60/100(M) ie 60/100(M+F), then this statement (1) would have been sufficient right?

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Hi BrentGMATPrepNow, Given is W <=60%?
In St 2, W = 2N . Threfore I mark it as E. How's it possible to put both walk and not walk under one variable here (total 3W) and how to overcome this type of error? Thanks Brent

Whenever you use a variable, you should make sure you have a clear understanding of what that variable represents.
In your equation W = 2N, you are saying that:
W = the number of students in Pat’s class who walk to school
N = the number of students in Pat’s class who don't walk to school

So, the total number of students in Pat's class = (number of students who walk to school) + (number of students who don't walk to school)
= W + N
= 2N + N [after we substitute 2N for W]
= 3N

If 3N = the total number of students in Pat's class, and W students walk to school, then the FRACTION of students who walk to school = W/3N
Substitute 2N for W to get: the FRACTION of students who walk to school = 2N/3N
From here, all we need to recognize is that 2N/3N = 2/3 = 66.6666...%
So the answer to the target question is "YES, at least 60 percent of the students in Pat’s class walk to school"
So statement 2 is sufficient

Great explanation always thanks BrentGMATPrepNow. So the focus here is the "number" of students therefore we are able to add it up as 3N rather than walk/not walk. Thanks Brent