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A school is comprised of 400 people both teachers and...

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by BTGmoderatorLU » Sat Feb 03, 2018 1:09 pm
A school is comprised of 400 people both teachers and students. If 10 percent of the people are teachers and 100 new people enter the school in the following year, how many of those people must be teachers to increase the percentage of teachers to 20 percent?

A. 10
B. 15
C. 25
D. 50
E. 60

The OA is E.

If total people is 400 (teachers and students), T + S = 400, if 10% of the 400 are teachers, 40 are teachers, right? Then,

The next year will be a total of 500, T + S =500, 20% of 500 is 100, then the correct answer will be 60 teachers, right?

I'm confused with this PS question. Experts, any suggestion? Thanks in advance.
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by EconomistGMATTutor » Sat Feb 03, 2018 1:46 pm
LUANDATO wrote:A school is comprised of 400 people both teachers and students. If 10 percent of the people are teachers and 100 new people enter the school in the following year, how many of those people must be teachers to increase the percentage of teachers to 20 percent?

A. 10
B. 15
C. 25
D. 50
E. 60

The OA is E.

If total people is 400 (teachers and students), T + S = 400, if 10% of the 400 are teachers, 40 are teachers, right? Then,

The next year will be a total of 500, T + S =500, 20% of 500 is 100, then the correct answer will be 60 teachers, right?

I'm confused with this PS question. Experts, any suggestion? Thanks in advance.
Hi LUANDATO,

You have used the correct approach.
The right answer is 60.

I am available if you'd like any follow up.
GMAT Prep From The Economist
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by Jeff@TargetTestPrep » Fri Feb 09, 2018 10:15 am
LUANDATO wrote:A school is comprised of 400 people both teachers and students. If 10 percent of the people are teachers and 100 new people enter the school in the following year, how many of those people must be teachers to increase the percentage of teachers to 20 percent?

A. 10
B. 15
C. 25
D. 50
E. 60
The school originally has 40 teachers and 360 students.

We can let the number of teachers who enter the school = n and create the equation:

(40 + n)/(400 + 100) = 1/5

5(40 + n) = 400 + 100

200 + 5n = 500

5n = 300

n = 60

Answer: E

Jeffrey Miller
Head of GMAT Instruction
[email protected]

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by [email protected] » Fri Feb 09, 2018 4:26 pm
Hi LUANDATO,

We're told that a school is comprised of 400 people (teachers and students) and that 10 percent of the people are teachers. 100 new people will enter the school in the following year. We're asked for the number of those people who must be teachers to increase the percentage of teachers to 20 percent. This question can be solved by TESTing THE ANSWERS.

Since 10% of the initial 400 people are teachers, there are (.1)(400) = 40 teachers. We're only adding 100 new people to the School, so it's likely that a LOT of them would have to be teachers to DOUBLE the percent of teachers in the School (from 10% to 20%).

Let's TEST Answer D: 50

IF.... we increase the number of teachers by 50....
Total Teachers = 40+50 = 90
Total People = 400 + 100 = 500
90/500 = 9/50 = 18% would be teachers. This is TOO LOW though (it's supposed to be 20%), so we clearly need MORE teachers. There's only one answer that fits...

Final Answer: E

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