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Overlapping Sets

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Overlapping Sets

by piyush2694 » Fri Dec 21, 2018 12:19 am

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Of the people who attended a workshop, 60 percent were teachers and some of the teachers were teachers of language arts. What percent of the people who attended the workshop were teachers of language arts?

(1) 200 people attended the workshop.
(2) 72 of the teachers who attended the workshop were not teachers of language arts.
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by Manasa3190 » Sat Dec 29, 2018 9:58 pm

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Given,
Teachers = 60%
Non_teachers = 40%

1) 200 people attended the workshop.
Teachers = 120
But no other info is given to deduce teachers of language arts
Insufficient

2) 72 of the teachers who attended the workshop were not teachers of language arts.
We only know the percentage, but not the number of people attended the workshop
Insufficient

From (1) and (2),
Total teachers = Art language + non art language
Art Language = total teachers - non art language
= 120 - 76
= 48
Sufficient
option C is correct

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edited

by deloitte247 » Sun Dec 30, 2018 8:04 am

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What % of people who attended the workshop were teachers of language art.?

Statement 1
200 people attended the workshop
If 200 people attend the workshop, then 120 were teachers
x of 120 = Language art teachers
$$require\ \%=\frac{x}{200}\cdot100\ $$
but we don't know the value of x, hence statement 1 is INSUFFICIENT.

Statement 2
72 of the teachers who attended the workshop were not teachers of language arts.
Let no of people in attendance = y
If y people attended the workshop, then
$$\left(60\%of\ y\right)-72\ were\ teachers\ of\ language\ arts.$$
$$0.6y-72\ were\ teachers\ of\ language\ arts$$
$$required\ \%=\frac{\left(0.6y-72\right)}{y}\cdot100$$
But we don't know the value of y,
Hence, statement 2 is INSUFFICIENT.

combining statement 1 and 2 together
From statement 1, we know that y = 200
$$hence\ \frac{\left(0.6y-72\right)}{y}\cdot100$$
$$hence\ \frac{\left(\left(0.6\cdot200\right)-72\right)}{200}\cdot100$$
$$hence\ \frac{\left(120-72\right)}{200}\cdot100$$
$$\frac{\left(48\right)}{200}\cdot100=24\%$$
Both statements together are SUFFICIENT.

$$Answer\ is\ Option\ C$$
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by Brent@GMATPrepNow » Sun Dec 30, 2018 9:21 am

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I thought I'd point out that Manasa3190's approach is known as the Double Matrix Method. This technique can be used for most questions featuring a population in which each member has two characteristics associated with it.
Here, we have a population of people, and the two characteristics are:
- teacher or not teacher
- teach language arts or doesn't teach language arts

This question type is VERY COMMON on the GMAT, so be sure to master the technique.

To learn more about the Double Matrix Method, watch this video: https://www.gmatprepnow.com/module/gmat- ... ems?id=919

Once you're familiar with this technique, you can attempt these additional practice questions:

Easy Problem Solving questions
- https://www.beatthegmat.com/finance-majo ... 67425.html

Medium Problem Solving questions
- https://www.gmatprepnow.com/module/gmat- ... /video/920
- https://www.beatthegmat.com/posted-speed ... 72374.html
- https://www.beatthegmat.com/motel-t271938.html
- https://www.beatthegmat.com/of-the-appli ... 70255.html
- https://www.beatthegmat.com/opening-nigh ... 64869.html
- https://www.beatthegmat.com/at-least-100 ... 74669.html
- https://www.beatthegmat.com/prblem-solving-t279424.html

Difficult Problem Solving questions
- https://www.gmatprepnow.com/module/gmat- ... /video/946
- https://www.beatthegmat.com/ratio-problem-t268339.html
- https://www.beatthegmat.com/overlapping- ... 65223.html
- https://www.beatthegmat.com/fractions-t264254.html
- https://www.beatthegmat.com/overlapping- ... 64092.html
- https://www.beatthegmat.com/mba/2011/05/ ... question-2

Easy Data Sufficiency questions
- https://www.gmatprepnow.com/module/gmat- ... /video/943
- https://www.beatthegmat.com/for-what-per ... 70596.html
- https://www.beatthegmat.com/ds-quest-t187706.html

Medium Data Sufficiency questions
- https://www.beatthegmat.com/sets-matrix-ds-t271914.html
- https://www.beatthegmat.com/each-of-peop ... 71375.html
- https://www.beatthegmat.com/a-manufacturer-t270331.html
- https://www.beatthegmat.com/in-costume-f ... 69355.html
- https://www.beatthegmat.com/mba/2011/05/ ... question-1

Difficult Data Sufficiency questions
- https://youtu.be/dsCeqF9Kbk8
- https://www.beatthegmat.com/double-set-m ... 71423.html
- https://youtu.be/dOZ9KM1m5Hs
- https://www.beatthegmat.com/sets-t269449.html
- https://www.beatthegmat.com/mba/2011/05/ ... question-3

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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