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# Each of the students in a certain class received a single

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Director
Joined: 03 Sep 2006
Posts: 777
Each of the students in a certain class received a single  [#permalink]

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03 Jun 2007, 02:08
2
18
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Difficulty:

25% (medium)

Question Stats:

74% (01:15) correct 26% (01:19) wrong based on 810 sessions

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Each of the students in a certain class received a single grade of P, F,or I.What percent of the students in the class were females?

(1) Of those who received a P, 40 percent were females.
(1) Of those who received either an F or I, 80 percent were males.
Math Expert
Joined: 02 Sep 2009
Posts: 53067
Re: Each of the students in a certain class received a single  [#permalink]

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08 Jun 2013, 03:42
8
7
Nwsmith11 wrote:
Each of the students in a certain class received a single grade of P, F,or I.What percent of the students in the class were females?

(1) Of those who received a P, 40 percent were females.
(1) Of those who received either an F or I, 80 percent were males.

So taking 1&2 together we know 80% of those with a fail/incomplete were male so 20% with F&I were female correct? If 40% of those who passed were female, then we can determine that 30% of the students were female.

This was my rationale towards an answer of C. Can anyone explain where I went wrong?

No, the correct answer is E. Consider the following examples:

P=50 and F+I=50, then the # of females = 0.4*50 + 0.2*50 = 30.
P=10 and F+I=90, then the # of females = 0.4*10 + 0.2*90 = 22.

Hope it's clear.
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Manager
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04 Jun 2007, 07:58
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1
Sometimes making a table is easier than getting into Venn diagrams.

I found it easy to get to E after I filled in the empty boxes and still couldnt say I had sufficient information.
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Manager
Joined: 04 May 2007
Posts: 110

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03 Jun 2007, 15:55
1
LM

I started to use Venn but there was no point IMHO.

We don't know what P or F or I represent. no proportion of the total class was given.

does 40% of P represent 10% of the entire class? 90% of the class?

what does 20% of F or I represent of the total percentage of the class? we dont know. maybe my reasoning is wrong, but that is how I came up with my answer: E
Director
Joined: 03 Sep 2006
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04 Jun 2007, 17:13
1
vikramjit_01 wrote:
Sometimes making a table is easier than getting into Venn diagrams.

I found it easy to get to E after I filled in the empty boxes and still couldnt say I had sufficient information.

Thanks! This is what I was looking for in form of either table or venn diagram!
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Re: Each of the students in a certain class received a single  [#permalink]

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07 Jun 2013, 19:34
So taking 1&2 together we know 80% of those with a fail/incomplete were male so 20% with F&I were female correct? If 40% of those who passed were female, then we can determine that 30% of the students were female.

This was my rationale towards an answer of C. Can anyone explain where I went wrong?
Senior Manager
Joined: 21 Jan 2010
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08 Jun 2013, 17:24
vikramjit_01 wrote:
Sometimes making a table is easier than getting into Venn diagrams.

I found it easy to get to E after I filled in the empty boxes and still couldnt say I had sufficient information.

SVP
Joined: 06 Sep 2013
Posts: 1693
Concentration: Finance
Re: Each of the students in a certain class received a single  [#permalink]

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17 Oct 2013, 05:49
1
LM wrote:
Each of the students in a certain class received a single grade of P, F,or I.What percent of the students in the class were females?

(1) Of those who received a P, 40 percent were females.
(1) Of those who received either an F or I, 80 percent were males.

Yup, its E. We can't assume that P,F or I are equally weighted.
Intern
Joined: 20 Dec 2014
Posts: 19
Re: Each of the students in a certain class received a single  [#permalink]

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17 Mar 2015, 09:47
2
1
Takeaways: This one was a bit tricky because I approached the problem as a double matrix set but it had 3 variables in the columns and 2 variables(male/female) in the rows. I also attempted to do percentages that lead up to a total but it was getting more complex than I would like. What has helped was recognizing this as a weighted average problem. Therefore an easy method could be:
T (total) = F + P +I
Since we have male and female : T=(M)F+(F)F+(M)P+(F)P+(M)I+(F)I or organize like this T=(M)F+(M)P+(M)I+(F)F+(F)P+(F)I
Translating the statement word by word I got (W/100)T= F? which is the main question we are looking to answer but made it easier on myself by just writing (F/T)*100%=?
1. Of those who received a P, 40% were females
This is clearly insufficient because (F)(P)= .4P and (M)(P)= .6P does not give us any actual numbers to plug in and we still need the other weighted averages.

2. Of those who received either an F or I , 80% were males.
T=.8F+.2F+ (M)P+(F)P+(.8)I+(.2)I
Insufficient because we need actual numbers because weighted averages depend on quantities

(1) and (2)
Insufficient because although we have several percentages we still need quantities because we can have 80/100 total students in f and I be males but then have 4/10 students in P be women.

Bunuel - thoughts?
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Re: Each of the students in a certain class received a single  [#permalink]

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18 Mar 2015, 19:10
1
3
Hi GMAT01,

You ARE correct. When dealing with these type of broad percent-based questions, it's important to be a bit cynical. You do NOT know how many students are in each subgroup, so it would take a LOT of information to answer this question.

As an example, when Fact 1 tells us "Of those who received a P, 40 percent were females", we don't know if 5 people got a P (in which 2 of them were female) or 500 people got a P (in which 200 of them were female). Making the individual group numbers relatively big or relatively small will impact the overall calculation. This can save you some time and effort.

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Re: Each of the students in a certain class received a single  [#permalink]

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20 Sep 2015, 20:02
Bunuel wrote:
Nwsmith11 wrote:
Each of the students in a certain class received a single grade of P, F,or I.What percent of the students in the class were females?

(1) Of those who received a P, 40 percent were females.
(1) Of those who received either an F or I, 80 percent were males.

So taking 1&2 together we know 80% of those with a fail/incomplete were male so 20% with F&I were female correct? If 40% of those who passed were female, then we can determine that 30% of the students were female.

This was my rationale towards an answer of C. Can anyone explain where I went wrong?

No, the correct answer is E. Consider the following examples:

P=50 and F+I=50, then the # of females = 0.4*50 + 0.2*50 = 30.
P=10 and F+I=90, then the # of females = 0.4*10 + 0.2*90 = 22.

Hope it's clear.

@Bunnel - Is it safe to say that in these type of questions until we get the entire class strength in either of the statements, we would always choose E. As stated in your example, we are plugging different set of values and getting different set of answers.

Thanks.
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Re: Each of the students in a certain class received a single  [#permalink]

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26 Jan 2017, 07:14
1
1
This is a weighted average question.

(1) Females make up 40% of group 1 (P)
(2) Females make up 20% of group 2 (F or I)

Together, Female will make up somewhere between 20% and 40% of the whole population. The exact percentage depends on the ratio of group sizes. If there are twice as many people in group 1, then the percentage will be twice as close to group 1 datapoint (40%) as it is to group 2. On the other hand if there are three times as many people in group 2, then the percentage will be three times as close to group 2 datapoint (20%) as it is to group 1. Consider below scenario :-

Let T = total number of students in the class

Each received a single grade so T = F + P +I

? % of T = Females

1. of those who received a P, 40% were females

it doesnt give us the the exact number

2. of those who received either an I or I(I or I ??..may be one of the other two) , 80% were males.

Still it doesnt give us the number of females

so E
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Re: Each of the students in a certain class received a single  [#permalink]

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30 Jan 2017, 16:55
4
2
LM wrote:
Each of the students in a certain class received a single grade of P, F,or I.What percent of the students in the class were females?

(1) Of those who received a P, 40 percent were females.
(1) Of those who received either an F or I, 80 percent were males.

We are given that each of the students in a certain class received a single grade of P, F, or I. We can let p = the number of students who received P, f = the number of students who received F, and i = the number of students who received I. Thus, the total number of students in the class is p + f + i. We need to determine the percentage of students who were females.

Statement One Alone:

Of those who received a P, 40 percent were females.

This means 0.4p students are females. However, since we know neither the values of p, f, and i nor the percentage of students who received an F or I, statement one alone is not sufficient to answer the question.

Statement Two Alone:

Of those who received either an F or I, 80 percent were males.

This means 20 percent of the students who received either an F or I were females. In other words, 0.2(f + i) students are females. However, since we know neither the values of p, f, and i nor the percentage of students who received a P, statement two alone is not sufficient to answer the question.

Statements One and Two Together:

From the two statements, we can say that the percentage of students in the class who were females is:

(0.4p + 0.2(f + i))/(p + f + i) x 100

However, since we don’t know the values of p, f, and i, we can’t determine the numerical value of the expression above. Statements one and two together are still not sufficient.

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Re: Each of the students in a certain class received a single  [#permalink]

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15 Nov 2018, 22:03
Is this approch fine?
P = .4 F so .6 M
F+L = .8M so .2F

.4F+.2F\ (.6M+.4F)+(.2F+.8M)

Even after cancelling F we dont know M so not sufficiant.
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Re: Each of the students in a certain class received a single  [#permalink]

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21 Jan 2019, 10:04
LM wrote:
Each of the students in a certain class received a single grade of P, F,or I.What percent of the students in the class were females?

(1) Of those who received a P, 40 percent were females.
(2) Of those who received either an F or I, 80 percent were males.

Making a chart:

Even if we assume T=100 (which we could do since we're not given any concrete numbers and the problem asks for a %), we can't determine the breakdown of 100 between P, F, I or between Male+Fem without more information.
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Re: Each of the students in a certain class received a single  [#permalink]

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30 Jan 2019, 13:20
Top Contributor
LM wrote:
Each of the students in a certain class received a single grade of P, F,or I.What percent of the students in the class were females?

(1) Of those who received a P, 40 percent were females.
(2) Of those who received either an F or I, 80 percent were males.

Target question: What percent of the students in the class were females?

Let's 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 students, and the two characteristics are:
- male or female

Since the target question asks for a PERCENT, let's say there are 100 students in total.
So, in order to answer the target question, we need to determine the number of females in the group.

We can set up our matrix as follows:

At this point, we should recognize that statement 1 does not provide any information about the male/female split of students who received an F or an I.
So, statement 1 cannot be sufficient.

Likewise, statement 2 does not provide any information about the male/female split of students who received a P.
So, statement 2 cannot be sufficient.

Statements 1 and 2 combined
Even when we combine the two statements, we realize that we're not told the number of students who received a P and the number of students who received an F or an I
So, there are many possible scenarios that satisfy BOTH statements. Here are two:

Case a: It COULD be the case that 50 students got a P, and 50 students got an F or an I.

In this case, the answer to the target question is 30 percent of the students are female

Case b: It COULD be the case that 90 students got a P, and 10 students got an F or an I.

In this case, the answer to the target question is 38 percent of the students are female

Since we cannot answer the target question certainty, the combined statements are SUFFICIENT

This question type is VERY COMMON on the GMAT, so be sure to master the technique.

Here's a practice question too!

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Re: Each of the students in a certain class received a single   [#permalink] 30 Jan 2019, 13:20
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