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Out of total 36 students in a class, what percent of students passed

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Out of total 36 students in a class, what percent of students passed  [#permalink]

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New post 20 May 2018, 11:24
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Out of total 36 students in a class, what percent of students passed the talent hunt exam, if each of the 36 students appeared for the exam?

(1) 70% of boys and 12.5% of girls passed the talent hunt exam.

(2) There are more than 12 boys in the class.
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Re: Out of total 36 students in a class, what percent of students passed  [#permalink]

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New post 03 Jun 2018, 03:22
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As you said, number of boys passed should be integer so based on the same logic number of girl passed should be integer.

let number of boys are B and number of girls are G

B+G = 36

1) 70% of boys passed the exam. So 0.7B should be integer. B should be multiple of 10
12.5 % of girls passed. 0.125G should be integer. G should be multiple of 8.
only one such value exist for B and G for which B+G = 36. B = 20 and G = 16

So Ans A
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Re: Out of total 36 students in a class, what percent of students passed  [#permalink]

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New post 03 Jun 2018, 06:03
1
let b: Total number of boys
g: Total number of girls.
As per the question, b+g =36.
statement 1:
70% of boys passed the exam. so b has to be a multiple of 10 (for it to be an integer) so b could be 10/20/30.
similarly, only 12.5% girls passed the exam. so, g has to be a multiple of 8(12.5/100=1/8).

now try with different b+g combinations.
case1 :
when b =10, g =26 ---doesn't satisfy as b is not multiple of 8.
case 2 :
when b=20 ,g=16 --- satisfies
case 3:
when b =30,g=6 ---doesn't satisfy as b is not multiple of 8.

hence a is sufficient.
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Out of total 36 students in a class, what percent of students passed  [#permalink]

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New post 08 Jun 2018, 18:04
To find: The percent of students that passed the exam. Or we can find the number of students that passed the exam, which will also give us the answer.

Statement 1
\(\frac{7}{10}\) of boys passed. So number of boys has to be a multiple of 10.
Possible number of boys: 10,20,30. Those are all the possibilities. Next multiples of 10 will exceed the total number, 36.

12.5% of girls passed. You should know by heart that this is \(\frac{1}{8}\). So number of girls has to be a multiple of 8.
Possible number of girls: 8,16,24,32. Those are all the possibilities. Next multiples of 8 will exceed the total number, 36.

To summarize,
Possible number of boys: 10,20,30.
Possible number of girls: 8,16,24,32.
You can quickly scan these 2 sets to see which number of boys and which number of girls will sum to 36. Only boys=20 and girls=16 works. We found the number of boys in the class and the number of girls in the class, thus can find how many passed.

Sufficient

Statement 2
No info about how many passed.
Not sufficient

Answer: A
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Out of total 36 students in a class, what percent of students passed  [#permalink]

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New post 16 Sep 2018, 09:03
Out of total 36 students in a class, what percent of students passed the talent hunt exam, if each of the 36 students appeared for the exam?

(1) 70% of boys and 12.5% of girls passed the talent hunt exam.

(2) There are more than 12 boys in the class.

Boys + girls = 36

(1)

means that 0,7*boys and 0,25*girls must be an integer.
there could be X girls and Y boys:
X must be a multiplier of 0,25: 4,8,12,16,20,24,28,32
Now, Y must be a multiplier of 0,7, and the number must be 36-X. We have only one option - 20. There were 36-20= 16 girls and 20 boys. 4 girls and 14 boys passed the exam. (28/36)*100= 2800/36 [%] passed the exam.

(2)

clearly not sufficient.
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Out of total 36 students in a class, what percent of students passed   [#permalink] 16 Sep 2018, 09:03
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Out of total 36 students in a class, what percent of students passed

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