A class in a certain school consists of boys and girls in the ratio of

Question

A class in a certain school consists of boys and girls in the ratio of 2:1. In a mathematics test, 60% of the class passed the test. If 40% of the boys failed the test, what percentage of the class are girls who passed the test?

A. 10%
B. 20%
C. 30%
D. 40%
E. 60%

A. 10%
B. 20%
C. 30%
D. 40%
E. 60%

Lampard42 · Answer

Assume 30 students in class. So boys 20 and girls 10.

60%passed so 18 students passed.
40% of boys failed. So 60% of boys = .6*20=12 passed the test.
Remaining 6 students who passed must be girls; so % is 6/30*100=20% IMO B.

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pushpitkc · Answer

The easiest way to solving this problem is by assuming a random number for the total
number of students in the class.  Arvind42  has already demonstrated this.

If there are 3x students in the class and 40% of the boys failed the test, 60% or 0.6*2x = 1.2x pass.

We are told that 60% of the class passes the test -> 0.6*3x or 1.8x of the class passes the test. The
remaining 0.6x(1.8x - 1.2x) are girls who pass the test.

Therefore, the percentage of girls in the class who pass the test are  \frac{0.6x}{3x}  =  20%(Option B)

GMATWhizTeam · Answer

Solution 
 • Let us assume that there are total 30 student in the class.
• Now, based on the information given in the question, let us make the following tree-structure:
  https://www.dropbox.com/s/q685cltkxux8zfz/20_07_tree.jpg?dl=1 
• From the above tree structure, the percent of girls who passed the mathematics test out of the total class  = \frac{6}{30}*100 = 20 % 
Thus, the correct answer is  Option B.

Sabby · Answer

Hi,
We have 2/3 boys, or let's say 20/30 boys and 10/30 girls

2/3*4/10= 8/30 boys who failed
which means we have 4/10 or 12/30-8/30= 4/30 girls who failed 
Therefore we have 6/30 girls who passed : 2/10 or 20/100

Answer B)

CEdward · Answer

I assumed the total # in the class was 120. I got 7/30 in the end. Can someone see the attachment and let me know where I went wrong? Should be 6/30 = 20%.

Sabby · Answer

Hi  CEdward

Actually, you wrote 36 boys failed the test whereas 40/100 of 80 boys is 32. This changed your overall result.
You get 32 boys who failed, 48 who passed and 16 girls who failed and 24 girls who passed.
24/120 = 4/20 = 20/100

Hope this helps

glagad · Answer

I assumed the total number of B & G in the classroom quite late while solving the problem. While I got the correct answer, I got it after a long time.

My question -
a) Can we solve this question without assuming numbers? If yes, how?
b) How do we differentiate which questions can be easily solved using substitution (of values) over the algebraic methods/brute force approaches? Also, which questions should we not use the method of substitution?

Thanks

Ikemen · Answer

Let total class size = B + G =3.

40% B failed means 60% B passed. We have 2 B, so 2 * 0.6 = 1.2 B passed. 
60% of the class passed, this means 60% * 3 = 1.8 passed.
1.8 - 1.2 = 0.6 G passed.

0.6/3 = 1/5 =20%

A class in a certain school consists of boys and girls in the ratio of

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A class in a certain school consists of boys and girls in the ratio of

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