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# In a class of 100 students, the percentage of boys in the class is

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In a class of 100 students, the percentage of boys in the class is  [#permalink]

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20 Sep 2018, 13:56
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65% (hard)

Question Stats:

27% (02:55) correct 73% (02:02) wrong based on 15 sessions

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In a class of 100 students, the percentage of boys in the class is equal to the percentage of students who pass in a test. If 2 out of every 3 girls in the class pass the test and the number of boys who do not pass the test is 10 less than the total number of girls in the class, which of the following is the closest to the percentage of boys who passed the test?

A. 40%
B. 50%
C. 60%
D. 70%
E. 80%

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In a class of 100 students, the percentage of boys in the class is  [#permalink]

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20 Sep 2018, 19:03
In a class of 100 students, the percentage of boys in the class is equal to the percentage of students who pass in a test. If 2 out of every 3 girls in the class pass the test and the number of boys who do not pass the test is 10 less than the total number of girls in the class, which of the following is the closest to the percentage of boys who passed the test?

A. 40%
B. 50%
C. 60%
D. 70%
E. 80%

Let boys =b, girls =g and those passed test =t with not passed as n
Since total is 100, % will actually mean the exact number..
So b=t and g=n
Girls passing test =2g/3 or girls not passing=g/3
boys not passing is = g-10
Therefore boys not passing+girls not passing=n=g=g-10+g/3.....g/3=10...g=30
So boys =100-30=70.., thus boys who passed = 70-(30-10)=50
%= 100*50/70=500/7=~70, so 70%

D

Or make a 2*2 matrix

................B................G............total
P................_............2G/3.........B
N............G-10............G/3.........G
T............P...................N...........100
So $$G-10+\frac{G}{3}$$=G.....G=30
Now B+G=100, so B=70
Boys who did not pass =G-10=30-10=20, so boys who passed=70-20=50
% of boys who passed = $$100*\frac{B_p}{B}$$=100*50/70=500/7=(490+10)/7=70+10/7~70%
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Re: In a class of 100 students, the percentage of boys in the class is  [#permalink]

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20 Sep 2018, 19:36
In a class of 100 students, the percentage of boys in the class is equal to the percentage of students who pass in a test. If 2 out of every 3 girls in the class pass the test and the number of boys who do not pass the test is 10 less than the total number of girls in the class, which of the following is the closest to the percentage of boys who passed the test?

A. 40%
B. 50%
C. 60%
D. 70%
E. 80%

Please follow the "grid" according to the colors presented in the question stem, to conclude:

$$? = \frac{{x - \left[ {\left( {100 - x} \right) - 10} \right]}}{x} = \frac{{2x - 90}}{x}$$

$$\left( {2x - 90} \right) + \frac{2}{3}\left( {100 - x} \right) = x\,\,\,\,\,\, \Rightarrow \,\,\,\,\,x = 70$$

$$? = \frac{{50}}{{70}} = \underleftrightarrow {\frac{5}{7} \cdot 100\% } = 5\left( {\frac{{98 + 2}}{7}} \right)\% = \underleftrightarrow {5\left( {14\frac{2}{7}} \right)\% } = 71\frac{3}{7}\% \,\,\,\,\,\,\mathop \Rightarrow \limits^{{\text{approx}}{\text{.}}} \,\,\,70\%$$

This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.
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Re: In a class of 100 students, the percentage of boys in the class is   [#permalink] 20 Sep 2018, 19:36
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