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Of the students in a certain class, 55% of the female and [#permalink]

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29 Mar 2009, 09:59

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56% (03:58) wrong based on 127 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.

Re: Of the students in a certain class, 55% of the female and [#permalink]

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19 Apr 2009, 10:09

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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 show your calculations

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.

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.

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. The answer is ALWAYS NO. Fact 2 is SUFFICIENT

Re: Of the students in a certain class, 55% of the female and [#permalink]

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29 Mar 2009, 10:38

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 show your calculations

I'll venture a B.

stmnt1 is clearly not sufic. stmnt2 - plugging in numbers, we can find the answer.

Re: Of the students in a certain class, 55% of the female and [#permalink]

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29 Mar 2009, 10:57

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

Re: Of the students in a certain class, 55% of the female and [#permalink]

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19 Apr 2009, 22:40

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.

Re: Of the students in a certain class, 55% of the female and [#permalink]

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10 Jun 2009, 03:38

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.

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.
_________________

Re: Of the students in a certain class, 55% of the female and [#permalink]

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10 Jun 2009, 22:12

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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