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# Of the total student in a class, 55% of female and 35% of

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Manager
Joined: 24 Sep 2008
Posts: 189
Schools: MIT / INSEAD / IIM - ABC
Of the total student in a class, 55% of female and 35% of [#permalink]

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03 Nov 2008, 01:12
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Of the total student in a class, 55% of female and 35% of male passed an exam. Did more than half of the student in the class passed the exam?

A - More than half of students in class are female
B - The number of female 20 more than number of male students.
Manager
Joined: 24 Sep 2008
Posts: 189
Schools: MIT / INSEAD / IIM - ABC
Re: DS - %problem [#permalink]

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03 Nov 2008, 01:14
B - for me

3 equations:

Female=Male+20
Male+Male+20=Total students
0.35Male+0.55Female=students passed the exam

So, B is SUFF
SVP
Joined: 17 Jun 2008
Posts: 1547
Re: DS - %problem [#permalink]

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03 Nov 2008, 03:01
I think A.

From stmt1: f > m and m + f = 100%.

Assuming there are 100 students,
case 1: f = 51, m = 49
hence 0.55*49 + 0.35*51 = 44.8 < 50.

case 2: f = 99, m = 1
hence, 0.55*1 + 0.35*99 = 35.2 < 50.

Hence, in both extreme cases, the student that passed exam < 50%. Sufficient.

From stmt2: f = m+20 and hence [0.55m + 0.35(m+20)]/(2m+20) can be more than or less than 50%. Hence, insufficient.
Manager
Joined: 24 Sep 2008
Posts: 189
Schools: MIT / INSEAD / IIM - ABC
Re: DS - %problem [#permalink]

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03 Nov 2008, 03:42
scthakur wrote:
I think A.

From stmt1: f > m and m + f = 100%.

Assuming there are 100 students,
case 1: f = 51, m = 49
hence 0.55*49 + 0.35*51 = 44.8 < 50.

case 2: m = 99, f = 1
hence, 0.55*1 + 0.35*99 = 35.2 < 50.

Hence, in both extreme cases, the student that passed exam < 50%. Sufficient.

From stmt2: f = m+20 and hence [0.55m + 0.35(m+20)]/(2m+20) can be more than or less than 50%. Hence, insufficient.

I suppose case 2 u have taken is wrong...try out for female=99 so A becomes INSUFF
Current Student
Joined: 28 Dec 2004
Posts: 3357
Location: New York City
Schools: Wharton'11 HBS'12
Re: DS - %problem [#permalink]

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03 Nov 2008, 08:26
for argument sake we have 100 girls, 55 passed
we have 20 boys, so 7 passed

55+7=62/120 >50% of class..

so I think B is correct..

GODSPEED wrote:
scthakur wrote:
I think A.

From stmt1: f > m and m + f = 100%.

Assuming there are 100 students,
case 1: f = 51, m = 49
hence 0.55*49 + 0.35*51 = 44.8 < 50.

case 2: m = 99, f = 1
hence, 0.55*1 + 0.35*99 = 35.2 < 50.

Hence, in both extreme cases, the student that passed exam < 50%. Sufficient.

From stmt2: f = m+20 and hence [0.55m + 0.35(m+20)]/(2m+20) can be more than or less than 50%. Hence, insufficient.

I suppose case 2 u have taken is wrong...try out for female=99 so A becomes INSUFF
SVP
Joined: 17 Jun 2008
Posts: 1547
Re: DS - %problem [#permalink]

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03 Nov 2008, 10:41
GODSPEED wrote:
I suppose case 2 u have taken is wrong...try out for female=99 so A becomes INSUFF

Silly type in my post. I meant f = 99, but typed as m=99. I have corrected in my post. A will still be sufficient.
Manager
Joined: 12 Oct 2008
Posts: 104
Re: DS - %problem [#permalink]

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03 Nov 2008, 10:46
scthakur wrote:
GODSPEED wrote:
I suppose case 2 u have taken is wrong...try out for female=99 so A becomes INSUFF

Silly type in my post. I meant f = 99, but typed as m=99. I have corrected in my post. A will still be sufficient.

I thought so at first too. But if you plugged in let's say 100 for boys and 200 for girls, and then tried plugging in 100 for girls and 20 boys, you'd see that A is insuff.
Therefore B is always sufficient, doesn't matter what no's you plug in
Current Student
Joined: 28 Dec 2004
Posts: 3357
Location: New York City
Schools: Wharton'11 HBS'12
Re: DS - %problem [#permalink]

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03 Nov 2008, 10:49
scthakur wrote:
GODSPEED wrote:
I suppose case 2 u have taken is wrong...try out for female=99 so A becomes INSUFF

Silly type in my post. I meant f = 99, but typed as m=99. I have corrected in my post. A will still be sufficient.

you need to look at extreme cases in these type of questions, say if the number of girls approaches infinity, then the number of boys is insignificant..which means that over all avg will approach 55%
SVP
Joined: 17 Jun 2008
Posts: 1547
Re: DS - %problem [#permalink]

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03 Nov 2008, 11:11
linau1982 wrote:
I thought so at first too. But if you plugged in let's say 100 for boys and 200 for girls, and then tried plugging in 100 for girls and 20 boys, you'd see that A is insuff.
Therefore B is always sufficient, doesn't matter what no's you plug in

Now, I have a hard time trying to analyze it.

For stmt2: say f = 21, m = 1 and total = 22. In this case, percentage will be less than 50.
And if, f = 200 and m = 180 and total = 380 then in this case, percentage will be > 50. HEnce, I feel B is insufficient.

Where am I going wrong?
Intern
Joined: 24 Aug 2008
Posts: 10
Re: DS - %problem [#permalink]

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03 Nov 2008, 11:24
And I get it now. Scratch off my answer of E, looks like i was wrong

Last edited by csboard23 on 03 Nov 2008, 11:41, edited 1 time in total.
Current Student
Joined: 28 Dec 2004
Posts: 3357
Location: New York City
Schools: Wharton'11 HBS'12
Re: DS - %problem [#permalink]

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03 Nov 2008, 11:29
scthakur wrote:
linau1982 wrote:
I thought so at first too. But if you plugged in let's say 100 for boys and 200 for girls, and then tried plugging in 100 for girls and 20 boys, you'd see that A is insuff.
Therefore B is always sufficient, doesn't matter what no's you plug in

Now, I have a hard time trying to analyze it.

For stmt2: say f = 21, m = 1 and total = 22. In this case, percentage will be less than 50.
And if, f = 200 and m = 180 and total = 380 then in this case, percentage will be > 50. HEnce, I feel B is insufficient.

Where am I going wrong?

55% of 200=110 35%of180=63.. 173/380 <50%
SVP
Joined: 17 Jun 2008
Posts: 1547
Re: DS - %problem [#permalink]

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03 Nov 2008, 11:54
fresinha12 wrote:
55% of 200=110 35%of180=63.. 173/380 <50%

Thanks. I was somehow reading 55% for male and 35% for female.
Intern
Joined: 22 Nov 2007
Posts: 11
Re: DS - %problem [#permalink]

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03 Nov 2008, 20:36
How is:

For stmt2: say f = 21, m = 1 and total = 22. < 50%??

For females: (55/100)*21=11.55 which by itself is greater than the 50% of 22 which is 11.

Adding the .35 for males makes it even greater.
Manager
Joined: 23 Aug 2008
Posts: 63
Re: DS - %problem [#permalink]

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03 Nov 2008, 21:20
GODSPEED wrote:
Of the total student in a class, 55% of female and 35% of male passed an exam. Did more than half of the student in the class passed the exam?

A - More than half of students in class are female
B - The number of female 20 more than number of male students.

I think it's B;
Although the extreme example F=21, M=1 would prove B invalid, I think this example is invalid because the class must have at least 20 males (since 35% of males pass the exam, we can't have 0.35 of 1 male passing an exam)

Statement 1:
If F=1000, M=20, then more than half passed (557/1020 TRUE)
If F=60, M=40, then fewer than half passed (47/100, FALSE)
insufficient

Statement 2:
If F=10020, M=10000, then fewer then half passed (5511+3500/20020 FALSE)
If F=40, M=20, then fewer than half passed ((22+7)/60, still FALSE at best possible case)
Sufficient
Manager
Joined: 16 Oct 2008
Posts: 54
Re: DS - %problem [#permalink]

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04 Nov 2008, 04:30
Of the total student in a class, 55% of female and 35% of male passed an exam. Did more than half of the student in the class passed the exam?

A - More than half of students in class are female
B - The number of female 20 more than number of male students.
-----------
I got B,

stmt 1) try to forced # to be 100 then if F=60 and M=40 then only 47 students pass exam --> No
but if F=80, M=20, then student pass is 51 ---> yes
so stmt 1) insuff

stmt 2) F=M+20
then
0.35M+0.55F > 0.5(F+M)
0.05F > 0.15M
F > 3M
M+20 > 3M
10>M
then if M < 10, more than half of student will pass the exam
Manager
Joined: 24 Sep 2008
Posts: 189
Schools: MIT / INSEAD / IIM - ABC
Re: DS - %problem [#permalink]

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04 Nov 2008, 09:59
Time to post OA guys....it's E

Official explanation:

A - INSUFF, as we all got this one
B - number female Y then number of male Y-20

%student who pass the exam: [0.55Y+0.35(Y-20)]/(2Y-20)=(0.9Y-7)/(2Y-20) if (0.9Y-7)/(2Y-20)>0.5 then Y should be >130, so Y can be any value so INSUFF

Didn't get the explanation of B - please pitch in!
SVP
Joined: 05 Jul 2006
Posts: 1747
Re: DS - %problem [#permalink]

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04 Nov 2008, 15:54
Of the total student in a class, 55% of female and 35% of male passed an exam. Did more than half of the student in the class passed the exam?

A - More than half of students in class are female
B - The number of female 20 more than number of male students.[/quote]

1000 IN CLASS , M = M AND FEMALES = 1000-M

55/100(1000-M) + 35/100M > 50/100 *1000

55(1000-M)+35M >500

11(1000-M)+7M> 500

11,000-4M> 500

is m< 2625?

from 1

1000-m>500

ie: m>500........insuff

from 2

100-m = m+20

2m = 80 ie: m = 40.......suff

B
SVP
Joined: 17 Jun 2008
Posts: 1547
Re: DS - %problem [#permalink]

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04 Nov 2008, 22:27
GODSPEED wrote:
Time to post OA guys....it's E

Official explanation:

A - INSUFF, as we all got this one
B - number female Y then number of male Y-20

%student who pass the exam: [0.55Y+0.35(Y-20)]/(2Y-20)=(0.9Y-7)/(2Y-20) if (0.9Y-7)/(2Y-20)>0.5 then Y should be >130, so Y can be any value so INSUFF

Didn't get the explanation of B - please pitch in!

Look at it the other way. The question does not say anywhere that y > 130. Thus, y can be 50, 100 or even 200. If y is less than or equal to 130, (0.9Y-7)/(2Y-20)>0.5 will not be true.
Manager
Joined: 30 Sep 2008
Posts: 111
Re: DS - %problem [#permalink]

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05 Nov 2008, 03:43
GODSPEED wrote:
Of the total student in a class, 55% of female and 35% of male passed an exam. Did more than half of the student in the class passed the exam?

A - More than half of students in class are female
B - The number of female 20 more than number of male students.

Y is the number of female students, X is the number of male students

The question <=> Is 0.55Y + 0.35X >= 0.5 (X + Y)

<=> 0.5Y >= 0.15X
<=> Y >= 0.03X

A <=> Y>X (insuff)
B <=> Y = X + 20 (insuff)

A + B <=> B (insuff)

My answer is E
Re: DS - %problem   [#permalink] 05 Nov 2008, 03:43
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