GMAT PREP DS problem

[alex.gellatly]

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.

Thanks

[sanju09]

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.

Thanks

(1) If 200 people attended the workshop, then 120 were teachers and x of the 120 teachers were teachers of language arts, where x < 120. The required percent is [x/200] × 100. We don't know x, hence we cannot answer the required percent. Insufficient


(2) If y people attended the workshop, then 0.6 y were teachers and 0.6 y - 72 were teachers of language arts. The required percent is [(0.6 y - 72)/y] × 100. We don't know y, hence we cannot answer the required percent. Insufficient

Taking together, we know y = 200, and hence the required percent is [(0.6 y - 72)/y] × 100 [spoiler]can be answered. Not to mention, you'll get it equal to 24 percent. Sufficient

Take C[/spoiler]

[buoyant]

Could experts please explain how to solve this in matrix method?

[GMATGuruNY]

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.

This is an EITHER/OR group problem.
Every attendee EITHER is a teacher OR is not..
Every attendee EITHER works in language arts OR does not.
For an EITHER/OR group problem, use a GROUP GRID (also known as a double-matrix) to organize the data.

Let T = teacher, NT = not a teacher, L = language arts, NL = not language arts.
In the grids below, the entries in any given row or column must add up to the TOTAL of that row or column.

60 percent were teachers.
The following grid is yielded:

Question stem:
What percent of the people who attended the workshop were teachers of language arts?
Rephrased:
In the grid above, what is the value of x/T?

Statement 1: 200 people attended the workshop.
The following grid is yielded:

No way to determine x/T.
INSUFFICIENT.

Statement 2: 72 of the teachers who attended the workshop were not teachers of language arts.
The following grid is yielded:

No way to determine x/T.
INSUFFICIENT.

Statements combined:
The following grid is yielded:

Thus, x/T = 48/200 = 24/100 = 24%.
SUFFICIENT.

The correct answer is C.

[Mathsbuddy]

Hi there,

I get a different answer, based on the following:

T = Teachers
TL = Teachers of language arts
A = Total number of attendees

Lets look at the ratios
T:(TL):A
0.6: (0.6*f):1

We need to know the fraction f of teachers who taught language arts

Statement 1 makes no reference to f, so INSUFFICIENT
Statement 2 gives us f = 1 - 0.72 = 0.28, so SUFFICIENT

[GMATGuruNY]

=

Hi there,

I get a different answer, based on the following:

Statement 2 gives us f = 1 - 0.72 = 0.28, so SUFFICIENT

The value in red does not reflect the information given in Statement 2.
Statement 2 states that 72 teachers -- not 72% of the attendees -- did not teach language arts.

[Brent@GMATPrepNow]

I'd like to point out that Mitch's "group grid" (aka Double Matrix Method) 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 workshop attendees, and the two characteristics are:
- teacher or not a teacher
- works in language arts or does NOT work in 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 our free 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/the-aam-aadm ... 72242.html
- https://www.beatthegmat.com/finance-majo ... 67425.html

Medium Problem Solving questions
- https://www.beatthegmat.com/probability- ... 73360.html
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- 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/ds-french-ja ... 22297.html
- https://www.beatthegmat.com/prblem-solving-t279424.html

Difficult Problem Solving questions
- 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.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://www.beatthegmat.com/double-set-m ... 71423.html
- https://www.beatthegmat.com/sets-t269449.html
- https://www.beatthegmat.com/mba/2011/05/ ... question-3

Cheers,
Brent

[Mathsbuddy]

I think this is a good lesson to READ THE QUESTION PROPERLY!
Thanks!

=

Hi there,

I get a different answer, based on the following:

Statement 2 gives us f = 1 - 0.72 = 0.28, so SUFFICIENT

The value in red does not reflect the information given in Statement 2.
Statement 2 states that 72 teachers -- not 72% of the attendees -- did not teach language arts.

[Mathsbuddy]

Here;'s a correction to my earlier entry (where IO had not read the question properly):

T = Teachers
TL = Teachers of language arts
A = Total number of attendees

Lets look at the ratios
T:(TL):A
0.6: (0.6*f):1

We need to know the fraction f of teachers who taught language arts

Statement 1 makes no reference to f, so INSUFFICIENT
Statement 2 gives us f = 1 - 72/TL, so still INSUFFICIENT
Combined, we get everything we need, so SUFFICIENT