At a one-day music workshop, some registered participants attended the

Question

At a one-day music workshop, some registered participants attended the morning session, and some attended the afternoon session. If 40% of the registered participants did not attend the morning session, what percent of the registered participants attended the afternoon session?

(1) Of the registered participants who attended the morning session, 1 out of every 4 attended the afternoon session.
(2) The number of registered participants who attended the morning session but did not attend the afternoon session was 3 times the number of registered participants who attended neither session.

Bunuel · Accepted Answer

GMAT Club Official Solution:

At a one-day music workshop, some registered participants attended the morning session, and some attended the afternoon session. If 40% of the registered participants did not attend the morning session, what percent of the registered participants attended the afternoon session?

Assume there are 100 registered participants. Since 40% did not attend the morning session, 40 participants did not attend the morning session and 60 participants attended the morning session. So, {Morning} = 60.

{Total} = {Morning} + {Afternoon} - {Both} + {Neither}

100 = 60 + {Afternoon} - {Both} + {Neither}

40 = {Afternoon} - {Both} + {Neither}

The question asks for {Afternoon}.

(1) Of the registered participants who attended the morning session, 1 out of every 4 attended the afternoon session.

Since 60 participants attended the morning session:

{Both} = 1/4 * 60 = 15

So:

40 = {Afternoon} - 15 + {Neither}

55 = {Afternoon} + {Neither}

This is not enough to determine {Afternoon}.

Not sufficient.

(2) The number of registered participants who attended the morning session but did not attend the afternoon session was 3 times the number of registered participants who attended neither session.

This tells us:

{Morning} - {Both} = 3 * {Neither}

60 - {Both} = 3 * {Neither}

This is not enough to determine {Afternoon}.

Not sufficient.

(1)+(2) From statement (1) {Both} = 15. So, from statement (2):

60 - {Both} = 3 * {Neither}

60 - 15 = 3 * {Neither}

{Neither} = 15

Now use the equation from statement (1):

55 = {Afternoon} + {Neither}

55 = {Afternoon} + 15

{Afternoon} = 40

So 40% of the registered participants attended the afternoon session.

Sufficient.

Answer: C.

AdarshSambare · Answer

Let total registered participants = 100.
Given:
40% did not attend morning session
So 60 attended morning.
We need % who attended afternoon.
(1) Of those who attended morning, 1/4 attended afternoon.
So afternoon attendees from morning group = 1/4 × 60 = 15.
But there may also be people who skipped morning and attended afternoon.
Cannot determine total afternoon attendance.
 Insufficient. 
(2) Morning but not afternoon = 3 × neither.
Let neither = x
Then morning only = 3x
Morning attendees = 60 = (morning only) + (both)
So:
60 = 3x + both
No information about afternoon total.
 Insufficient.

Now combine.
From (1):
Both = 15
From (2):
Morning only = 60 − 15 = 45
And morning only = 3 × neither
So neither = 15
Total:
Both = 15
Morning only = 45
Neither = 15
Therefore afternoon only =
100 − (15 + 45 + 15) = 25
Total afternoon attendees =
25 + 15 = 40%
Both together are sufficient.
 Answer: C

BongBideshini · Answer

Let:
 
 m = morning only 
 e = afternoon only 
 x = both sessions 
 n = neither  
Total registered = 100
Given:
40% did not attend the morning.
So:
e + n = 40, and 
m + x = 60
We need:
e + x 
 Statement (1):

Those attending morning = m + x = 60
So:
x = (1/4)(60) = 15
Then:
m = 45
But  e  is still unknown.
Cannot determine e + x.
  Insufficient

Statement (2): 
Morning only was 3 times neither.
m = 3n
Using:
m + x = 60
Still cannot determine x or e individually.
  Insufficient

Combine (1) and (2): 
From (1):
x = 15
m = 45
From (2):
45 = 3n
n = 15
Now:
e + n = 40
e + 15 = 40
e = 25
Therefore:
e + x = 25 + 15 = 40
So 40% attended the afternoon.
 Both together sufficient 
 Answer: C

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