At a community center, 360 people enrolled in at least one of two week

Question

At a community center, 360 people enrolled in at least one of two weekend classes, pottery and photography. If 80 of these people did not enroll in photography, how many enrolled in both classes?

(1) Of the 360 people, 70 did not enroll in pottery.
(2) A total of 290 people enrolled in pottery.

M47-211

Bunuel · Accepted Answer

GMAT Club Official Solution:

At a community center, 360 people enrolled in at least one of two weekend classes, pottery and photography. If 80 of these people did not enroll in photography, how many enrolled in both classes?

Since all 360 people enrolled in pottery or photography or both, the 80 people who did not enroll in photography must have enrolled in  pottery only .

(1) Of the 360 people, 70 did not enroll in pottery.

If 70 people did not enroll in pottery, then those 70 people must have enrolled in  photography only . Thus, the number who enrolled in both classes is:

Total - Pottery only - Photography only = 360 - 80 - 70 = 210.

Sufficient.

(2) A total of 290 people enrolled in pottery.

Since 80 people enrolled in pottery only, the number who enrolled in both classes is:

Pottery - Pottery only = 290 - 80 = 210.

Sufficient.

Answer: D.

vasu1104 · Answer

total 360 people
two classes= pottery and photogrphy.
everyone enrolled in at least one of two classes. that means no one into neither of class. so they are in either of class or both.

80 = not in photography. that means total people enrolled in photography 280.

find = people in both class.

S-1
70 = not in pottery. so in pottery = 290
290+280-x = 360
x= 210
sufficient.

S-2
total pottery = 290
total photography we know= 280.

290+280-x= 360
x= 210
sufficient.

option D

SS990 · Answer

Given: (highlighted is deduced)

ph  
  nph  
  total  
 
   Po  
  ?  
  80

nPo  
  
 0

total  
   280   
  80  
  360

To find: Po-Ph?

(1) We can find Po-ph through below. Hence sufficient 
    
  ph  
  nph  
  tot  
 
   Po  
 ? 
 80 
   290   
 
   nPo  
  
 0 
   70   
 
   tot  
  280  
  80  
  360

(2) Same deduction and info as above. Hence sufficient

ph  
  nph  
  tot  
 
   Po  
 ? 
 80 
   290   
 
   nPo  
  
 0 
   70   
 
   tot  
  280  
  80  
  360

So the answer is D

HarishChaitanya · Answer

Total people = 360
80 people did not enroll in photography ⇒ these are only in pottery
Let number enrolled in both classes = x
Total in photography = 360 − 80 = 280
Only photography = 280 − x
Using statement (1):
70 people did not enroll in pottery ⇒ only photography = 70
So, 280 − x = 70
x = 210
Statement (1) is sufficient
Using statement (2):
Total in pottery = 290 ⇒ includes both + only pottery
So, x + 80 = 290
x = 210
Statement (2) is sufficient
Final answer: 210 and option (D) — each statement alone is sufficient.

KIYONGWE · Answer

I'm not seeing answers proposition to determine wich answer is correct

Bunuel · Answer

This is a data sufficiency question. Options for DS questions are always the same and usually omitted on the site.

The data sufficiency problem consists of a question and two statements, labeled (1) and (2), in which certain data are given. You have to decide whether the data given in the statements are sufficient for answering the question. Using the data given in the statements, plus your knowledge of mathematics and everyday facts (such as the number of days in July or the meaning of the word counterclockwise), you must indicate whether—

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
C. BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
D. EACH statement ALONE is sufficient to answer the question asked.
E. Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

Hope this helps.

At a community center, 360 people enrolled in at least one of two week

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GMAT Data Sufficiency (DS) Questions

At a community center, 360 people enrolled in at least one of two week

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