experts plz help

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runzun: Senior | Next Rank: 100 Posts; Posts: 31; Joined: Wed Dec 29, 2010 11:22 pm

experts plz help

by runzun » Sun Aug 21, 2011 5:37 pm

This table lists enrollment in an afterschool program by activity. There are 30 total students enrolled in the entire program. Students may participate in one, two, or three activities. How many students participate in all three activities?

(1) 21 students only participate in one activity.

(2) 6 students participate in both basketball and math.

OA is A.. but i am not able to understand the logic..
plz help
Activity enrollment

basketball 19
math 12
wrestling 11

sorry for the confusion

Last edited by runzun on Mon Aug 22, 2011 5:13 pm, edited 1 time in total.

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Source: Beat The GMAT — Data Sufficiency | Sun Aug 21, 2011 5:37 pm

GmatKiss: Legendary Member; Posts: 2789; Joined: Tue Jul 26, 2011 12:19 am; Location: Chennai, India; Thanked: 206 times; Followed by:43 members; GMAT Score:640

by GmatKiss » Mon Aug 22, 2011 1:51 am

runzun wrote:This table lists enrollment in an afterschool program by activity. There are 30 total students enrolled in the entire program. Students may participate in one, two, or three activities. How many students participate in all three activities?

(1) 21 students only participate in one activity.

(2) 6 students participate in both basketball and math.

OA is A.. but i am not able to understand the logic..
plz help

"This table lists" is this attached! am unable to view this attachment!

Quote

GMAT/MBA Expert

Whitney Garner: GMAT Instructor; Posts: 273; Joined: Tue Sep 21, 2010 5:37 am; Location: Durham, NC; Thanked: 154 times; Followed by:74 members; GMAT Score:770

by Whitney Garner » Mon Aug 22, 2011 8:39 am

runzun wrote:This table lists enrollment in an afterschool program by activity. There are 30 total students enrolled in the entire program. Students may participate in one, two, or three activities. How many students participate in all three activities?

(1) 21 students only participate in one activity.

(2) 6 students participate in both basketball and math.

OA is A.. but i am not able to understand the logic..
plz help

runzun:

Please include the entire question. With only the information given in the quote above, the answer would be E. (either the OA is wrong or something is missing).

Whit

Whitney Garner
GMAT/GRE/EA Instructor & Anxiety/Accommodations Coach
www.whitneygarner.com

Contributor to Beat The GMAT!

Math is a lot like love - a simple idea that can easily get complicated

Quote

runzun: Senior | Next Rank: 100 Posts; Posts: 31; Joined: Wed Dec 29, 2010 11:22 pm

by runzun » Mon Aug 22, 2011 9:35 am

If we add up the participants in each activity, we have a total of 42 students. This discrepancy is accounted for by the fact that some students may participate in multiple activities.Since only 30 are enrolled, this means 12 places must be accounted for.

(1) If 21 students only participate in one activity, then 9 participate in multiple activities. However, we must account for 12 spaces. This means that 3 students are triple counted (12 - 9), and 6 are double counted. Therefore, 3 students participate in all three activities. To solve this using algebra, set D = the number of students in 2 activities and T = the number of students in all 3:

D + T = 9

21 + 2D + 3T = 42 {This accounts for the double and triple counting of students in multiple activities}
2D + 3T = 21

Combining the two equations, we get:
2(9 - T) + 3T = 21
18 - 2T+ 3T = 21
T = 3
SUFFICIENT

(2) The limitation of this statement is that it does not tell us how many of those 6 students, if any, also wrestle. It is possible that all 6 students participate in all activities. This would account for the table. Alternately, perhaps these 6 students only participate in these two activities, and another 6 students participate in a different pair of activities. We cannot reach a definitive conclusion.
INSUFFICIENT.

The credited response is (A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

this is the explanation but I am unable to understand..
plz help