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All of the students in a certain class are either 7 or 8 yea

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All of the students in a certain class are either 7 or 8 yea [#permalink] New post 18 Mar 2018, 06:37
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80% (01:43) correct 20% (00:00) wrong based on 5 sessions
All of the students in a certain class are either 7 or 8 years old. 80 percent of the students are boys and 25 percent of the girls are 8 years old. If there are an equal number of 7-year-olds and 8-year-olds, what percent of the students in the class are boys who are 7 years old?

Drill 2
Question: 13
Page: 499


[Reveal] Spoiler: OA
35

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Re: All of the students in a certain class are either 7 or 8 yea [#permalink] New post 20 Mar 2018, 09:16
From the question stem draw out a double matrix. It is easier to solve with a double matrix rather than forming a equation.
Put two columns B for Boys and G for Girls
Put two rows 7 yrs for 7 yrs students and 8 yrs for 8 yrs students

Now take a nice number so that it is easier to work for Eg. 100 for total students.
Fill up the information:

Boys \((B) =\frac{80}{100} * 100 = 80\)
Hence Girls\((G) = 20\)

Now find the number of 8 yrs old girl \(= 20 * \frac{25}{100} = 5\)
From this find the number of girls who are 7 yrs old = \(20-5 = 15\)

Let x = number of boys that are 7 yrs old
and Y = number of boys that are 8 yrs old

Given,
\(x + 15 = y + 5\)
also we can deduce \(x + y = 80\)
solve the two pair of equation to find the value for x and y
\(x = 35 and Y = 45\)

Therefore, % of boys that are 7 yrs old is 35
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GMAT Club Legend
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Re: All of the students in a certain class are either 7 or 8 yea [#permalink] New post 21 Mar 2018, 14:04
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Explanation

Wouldn’t this be a lot easier if you knew how many students there are?

The question doesn’t say, so plug in your own number.

The question deals in percentages, so let’s say there are 100 students in the class. That means that there are 80 boys and 20 girls, and 50 students who are 7 and 50 students who are 8. 25 percent of 20 is 5, which leaves 15 girls who are 7.

Subtract 15 from 50 and you are left with 35 boys who are 7. You can also employ the group grid.

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Re: All of the students in a certain class are either 7 or 8 yea   [#permalink] 21 Mar 2018, 14:04
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