Of the people who attended a workshop, 60 percent were teachers and so

Question

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.

Kurtosis · Answer

St1: 60 percent of 200 = 120 teachers
Can't distinguish between language art teachers and non language teachers in this group of 120 teachers. Hence not sufficient

St2: 72 teachers are non language arts teachers. Value of language art teachers cannot be determined. Not sufficient

Combining 1 and 2, 
Total number of teachers = 120
Non Language arts teachers =72
Language arts teachers = 48

Percentage = (48/200)*100

Answer: C

chetan2u · Answer

Hi,
we are given that teachers are 60% of total people who... some of these teachers are teachers of language arts. 
we hav eto find ..percent of the people who attended the workshop were teachers of language arts?

what is required for this..
% of teachers who are in language..
total who attended workshop or total number of teacher..

lets see the statements..
(1) 200 people attended the workshop. 
now we know total.. and thus the number of teachers attending workshop is known.. but % of language teachers not known,... insuff

(2) 72 of the teachers who attended the workshop were not teachers of language arts.
we do not know total teachers so insuff..

combined..
we know number of teachers and number of these who are not language teachers.. their diff wil give us our ans.. suff

C

MathRevolution · Answer

Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

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.

Modify the original condition and the question. Suppose people attending a workshop 100p and then teachers are 60p. Then, suppose teachers of language arts np, there are 2 varibles(n,p), which should match with the number of equations. So you need 2 equations. For 1) 1 equation, for 2) 1 equation, which is likely to make C the answer. When 1) & 2), it becomes 100p=200 and then (60-n)p=72. You can get a value of n in a unique way, which is sufficient. Therefore, the answer is C.

 For cases where we need 2 more equations, such as original conditions with “2 variables”, or “3 variables and 1 equation”, or “4 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 70% chance that C is the answer, while E has 25% chance. These two are the majority. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since C is most likely to be the answer using 1) and 2) separately according to DS definition (It saves us time). Obviously there may be cases where the answer is A, B, D or E.

anairamitch1804 · Answer

(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 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   X 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   X 100 can be answered. Not to mention, you’ll get it equal to 24 percent. Sufficient

Take C

Of the people who attended a workshop, 60 percent were teachers and so

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Data Sufficiency (DS) Questions

Of the people who attended a workshop, 60 percent were teachers and so

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards