At a company training workshop, the attendees are divided into two

Question

At a company training workshop, the attendees are divided into two groups: trainees and supervisors. At the end of the workshop, attendees were asked to complete the feedback survey to receive a completion certificate. Do more than half of all attendees complete the survey?

(1) No more than 2/5 of the supervisors complete the survey.
(2) The percentage of trainees who complete the survey is 5/4 of the percentage of supervisors who complete the survey.

Bunuel · Accepted Answer

GMAT Club Official Solution:

At a company training workshop, the attendees are divided into two groups: trainees and supervisors. At the end of the workshop, attendees were asked to complete the feedback survey to receive a completion certificate. Do more than half of all attendees complete the survey?

(1) No more than 2/5 of the supervisors complete the survey.

This limits only the supervisors’ completion rate. We know neither the trainees’ completion rate nor the ratio of supervisors to trainees. Not sufficient.

(2) The percentage of trainees who complete the survey is 5/4 of the percentage of supervisors who complete the survey.

This gives only a relationship between the two completion rates, not their actual values. The overall completion rate could be above half or not above half depending on the supervisors’ completion rate and on how many trainees versus supervisors there are. Not sufficient.

(1)+(2) From (1), the supervisors’ completion rate is at most 2/5. By (2), the trainees’ completion rate is at most (5/4) * (2/5) = 1/2. Since the weighted average of two groups must be between the individual average rates, and since the individual averages are at most 2/5 and at most 1/2, the overall rate cannot possibly be more than 1/2. Sufficient.

Answer: C.

harjas2222 · Answer

Correct me if i am wrong

Statement 1) 2/5 supervisors completed the survey but no info about the trainees Insufficient
 
but from this statement we understand the percent of supervisors who completed the survey is less than 40%

Statement 2)

Percent Trainees who completed the survey = 5/4 of percent of supervisors who completed the survey
 x = 1.25 x

combine (C)

x is lower than 40%
1.25 *40 = 50% maximum

Both groups seem to be below 50% thus sufficent when combined

Adit_ · Answer

Both statements alone is clearly insufficient.
As statement 1 talks of 40% supervisors complete survey but how many of trainees?
Statement 2: percentage relation one is 5/4x the other. Hmm but what is x?

Combining the two:
This is a case of weighted averages of alligation.
Take 40% critical point.
Then the other is 50%

40 50
 \ /
 50
 / \
0 10

As we see we get 0 parts of 40% which is not possible as 40% ppl do give survey. And these two values will be smaller than 40,50 as what we chose is the highest critical value.

Thus the answer is NO.

Answer:  Option C

Adit_ · Answer

I am sure you got the concept right but both groups arent below 50, one is 50% like you mentioned yourself but the average is still less than 50 because we cant have 0 supervisors that vote.

harjas2222 · Answer

Thank you so much, I needed the explanation and yours is crystal clear.

Adit_ · Answer

Of course, happy to help

At a company training workshop, the attendees are divided into two

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