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This table lists enrollment in an afterschool program by act

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kuttingchai
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This table lists enrollment in an afterschool program by act [#permalink] New post   29 May 2013, 00:56
2
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20
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A
B
C
D
E

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95% (hard)

Question Stats:

38% (02:41) correct 62% (02:24) wrong based on 167 sessions
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Basketball - 19
Math - 12
Wrestling - 11

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.
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A
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Bunuel
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Re: This table lists enrollment in an afterschool program by act [#permalink] New post   29 May 2013, 05:36
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Basketball - 19
Math - 12
Wrestling - 11

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?


Given:
a+d+e+g=19 (Set A = Basketball);
b+d+f+g=12 (Set B = Math);
c+e+f+g=11 (Set C = Wrestling).

g=?

(1) 21 students only participate in one activity.

This implies that a+b+c=21.

Next, since 30 students are enrolled in at least one program and 21 students are enrolled in only one program, then 30-21=9 students are enrolled in 2 or 3 programs: d+e+f+g=9.

Now, add 3 equations which are given in the stem: (a+b+c)+2d+2e+2f+3g=42 -->(a+b+c)+2(d+e+f+g)+g=42 --> 21+2*9+g=42 --> g=3.

Sufficient.

(2) 6 students participate in both basketball and math --> d+g=6. Not sufficient to get g.

Answer: A.

Hope it's clear.
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hapless12
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Re: This table lists enrollment in an afterschool program by act [#permalink] New post   12 Jun 2014, 07:23
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Hi Bunuel,

What if I use:
30 = A+B+C - 2 (sum of two group overlaps) + all 3 + neither.

How will this formula of urs applicable here.
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Re: This table lists enrollment in an afterschool program by act [#permalink] New post   12 Jun 2014, 07:26
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hapless12 wrote:
Hi Bunuel,

What if I use:
30 = A+B+C - 2 (sum of two group overlaps) + all 3 + neither.

How will this formula of urs applicable here.


We are not given neither two group overlaps nor all 3. So, we cannot apply this formula directly.
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clipea12
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Re: This table lists enrollment in an afterschool program by act [#permalink] New post   13 Jun 2014, 11:25
Bunuel wrote:
hapless12 wrote:
Hi Bunuel,

What if I use:
30 = A+B+C - 2 (sum of two group overlaps) + all 3 + neither.

How will this formula of urs applicable here.


We are not given neither two group overlaps nor all 3. So, we cannot apply this formula directly.


why can't we apply it?

a, b and c are given
30 -A-B-C= - 2 (sum of two group overlaps) + all 3 + neither (first equation )

in (1) 21 students only participate in one activity
sum of two group overlaps + all 3 = 9 which constitute a second equation;
therefore we can solve for 'all 3'
correct me if im wrong :roll:
thx
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Re: This table lists enrollment in an afterschool program by act [#permalink] New post   06 Jun 2021, 14:30
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: This table lists enrollment in an afterschool program by act [#permalink]
06 Jun 2021, 14:30
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