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Director  Joined: 04 Jan 2008
Posts: 608
Of the students in a certain class, 55% of the female and  [#permalink]

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1
7 00:00

Difficulty:   95% (hard)

Question Stats: 36% (02:45) correct 64% (02:34) wrong based on 162 sessions

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Of the students in a certain class, 55% of the female and 35% of the male passed an exam. Did more than half of the students in the class pass the exam?

(1) More than half of the students in the class are female.
(2) The number of the female students is 20 more than the number of the male students.
Manager  Joined: 22 Feb 2009
Posts: 114
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Re: Of the students in a certain class, 55% of the female and  [#permalink]

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5
1
nitya34 wrote:
Of the students in a certain class, 55% of the female and 35% of the male passed an exam. Did more than half of the students in the class pass the exam?

(1) More than half of the students in the class are female.
(2) The number of the female students is 20 more than the number of the male students.

Good Q

Lets say total students=100, Female x,then Male=100-x.

As per question
0.55x+0.35(100-x) > 0.5 * 100
solving we get is x>75 ?

St 1. not sufficient as we need to prove number of female > 75
St 2 : if x+y=100 and x-y=20 then solving we get x=60 (number of female). therefore we can say Number of female < 75 and therefore SUFFICIENT.

hence IMO B
##### General Discussion
Manager  Joined: 19 Aug 2006
Posts: 157
Re: Of the students in a certain class, 55% of the female and  [#permalink]

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nitya34 wrote:
Of the students in a certain class, 55% of the female and 35% of the male passed an exam. Did more than half of the students in the class pass the exam?

(1) More than half of the students in the class are female.
(2) The number of the female students is 20 more than the number of the male students.

Good Q

I'll venture a B.

stmnt1 is clearly not sufic.
stmnt2 - plugging in numbers, we can find the answer.
GMAT Instructor B
Joined: 04 Jul 2006
Posts: 1126
Re: Of the students in a certain class, 55% of the female and  [#permalink]

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Suppose there are f% of the students are female: 55f/100 + 35(100-f)/100 = 35 + 20f/100 percent of the students passed. Thus we need to know whether f/5 > 15, i.e. whether f > 75

(1) f > 50 not suff
(2) only tells us that f > 50 not suff
(t) not suff

easier drawing a number line:

(male)35-----15-----50--5--55 (female)

we need to know whether 15m 3m
Intern  Joined: 29 Dec 2006
Posts: 30
Re: Of the students in a certain class, 55% of the female and  [#permalink]

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i got B. after picking several numbers, i got the answer that more than 1/2 of the class did not pass.
Manager  Joined: 02 Mar 2009
Posts: 98
Re: Of the students in a certain class, 55% of the female and  [#permalink]

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1
Ok I got B as well but did it in a different way. I like Bandit's way better though. None the less, here goes:

1 not sufficient..we all agree.

2: The minimum number of males must be 20 and this is because we need a whole number that can split into the proportions 35% and 65%. I arrived at this by computing the prime factorizing 35, 65 and 100. 35= 5*7; 65= 5*13 and 100 = 2*2*5*5. Thus the 5 of 100 will cancel but the 2*2*5 will not. Thus the number of males must be multiples of 20.

Now I used M=20 and F=40 (because females is simply 20 more)

At this the numbers passed = 29 < 30
We can stop here..we need not calculate for M=40, 60,etc because as the proportion of males increase, since the passing rate is low for males, we are all the more sure that less than half of the students have passed.

Thus Ans B
Director  Joined: 29 Aug 2005
Posts: 591
Re: Of the students in a certain class, 55% of the female and  [#permalink]

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E for me.

When statements involve absolute relationship (i.e Stmt2 F-20=M) vs. relative (e.g. F/M=2/5) , you cannot say "lets assume F+M=100".

Let's look at the stem:
0.55F+0.35M>0.5(F+M)?

Simplify: 0.05F>0.15M? or F>3M or
F/M>3?

Stmt1: F>M or F/M>1
This is not sufficient to answer the question.

Stmt2: F-20=M
This statement does not give a relative value of F to M. It does not matter whether F-1=M or F-100000=M. We need total number of students to be able to use this statement. Hence, it is not sufficient.

Together, still we cannot answer the question. Hence, E.
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GMAT 1: 750 Q50 V40 Re: Of the students in a certain class, 55% of the female and  [#permalink]

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seofah wrote:
Stmt2: F-20=M
This statement does not give a relative value of F to M. It does not matter whether F-1=M or F-100000=M. We need total number of students to be able to use this statement. Hence, it is not sufficient.

We cannot get 55% and 35% for any F and M. This is a trap here. In other words, M cannot be 1 or any number up to 19, because 35% * M will not be an integer value. So, M can be 20 and more. But for M>=20, the total number of students who passed exam will be always less than a half.
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Manager  Joined: 08 Feb 2009
Posts: 118
Schools: Anderson
Re: Of the students in a certain class, 55% of the female and  [#permalink]

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3
Let F = number of females,
M = number of males
$$\Rightarrow$$ (F+M) = number of people in class.

Question is whether $$\frac{(0.55) F + (0.35) M}{(F+M)} \hspace{20}\geq \hspace{20} \frac{1}{2}$$

Simplifying, we get:

$$F \hspace{10}> \hspace{10}3M$$

(1)
It is NOT SUFFICIENT because the statement only says that $$F \hspace{10}> \hspace{10}M$$

(2)
$$F \hspace{5}= \hspace{5}M + 20$$

Substituting statement-2 in $$F \hspace{10}> \hspace{10}3M$$

$$\Rightarrow$$ $$M + 20 \hspace{10}> \hspace{10}3M$$

$$\Rightarrow$$ $$10 \hspace{10}> \hspace{10}M$$

Clearly, the above statement can be disproved using the fact that $$35% \hspace{5}of\hspace{5} M \geq\hspace{5} 20$$, in order for it to be an integer.

Thus, statement-2 is SUFFICIENT.

Manager  Joined: 28 Jan 2004
Posts: 156
Location: India
Re: Of the students in a certain class, 55% of the female and  [#permalink]

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B.
Stmt 1 - We agree that it is insuff.
Stmt 2 -
No. of Boys = X
No. of girls = X + 20
So total students = X + X + 20 = (2X + 20)
We can assume that the number of students be 100 (it will not make a diff. as X will change accordingly)

So Boys = 40
Girls = 60

%Boys passed = 35% of 40 = 14
%Girls passed = 55% of 60 = 33
Total passed = 47 which is less then 50.
Hence suff.
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GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: Of the students in a certain class, 55% of the female and  [#permalink]

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2
Hi All,

This question can be solved by TESTing VALUES.

The prompt comes with an interesting 'restriction' though. You CANNOT have a fraction of a person (e.g. 2/3 of girl, 1/8 of a boy, etc.), so we have to TEST VALUES that "fit" with the percentages that are given...

We're told that 55% of the females and 35% of the males in a class passed an exam. We're asked if MORE than half passed the exam. This is a YES/NO question.

Since we're dealing with 55% of females and 35% of males, there must be a MULTIPLE of 20 females AND a MULTIPLE of 20 males in the class. NO other possible numbers exist that will "fit" with this data. As an example, you could NOT have 2 females and 3 males, since the percents would then give us "fractions of a person."

Since 55% of 20 = 11 and 35% of 20 = 7, we now also have a "math shortcut" (we can use those multiples to save some time) that we can take advantage of. Knowing that, we can now deal with the two Facts in a more efficient way...

Fact 1: More than half of the students are FEMALE.

This is important; it tells us that we do NOT have an equal number of females and males.

IF....we have...
40 females and 20 males
22 females passed and 7 males passed
29/60 is LESS than half and the answer to the question is NO

IF....we have....
60 females and 20 males
33 females passed and 7 males passed
40/80 is EXACTLY HALF and the answer to the question is NO

IF....we have....
80 females and 20 males
44 females passed and 7 males passed
51/100 is MORE than half and the answer to the question is YES.
Fact 1 is INSUFFICIENT

Fact 2: The number of females is 20 more than the number of males... The first TEST that we ran in Fact 1 will ALSO "fit" here:

IF....we have...
40 females and 20 males
22 females passed and 7 males passed
29/60 is LESS than half and the answer to the question is NO

IF....we have...
60 females and 40 males
33 females passed and 14 males passed
47/100 is LESS than half and the answer to the question is NO

IF....we have...
80 females and 60 males
44 females passed and 21 males passed
65/140 is LESS than half and the answer to the question is NO

From this work, you might notice how the numerator gets further and further "away" from exactly half. This is a pattern.
Fact 2 is SUFFICIENT

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