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Each year, all employees for a particular company complete an annual self-evaluation during the month of September, and all employees, including those who left the company after completing their annual self-evaluation, are subsequently evaluated by their supervisors. An employee hired after the month of September completes his or her first self-evaluation the following September. Each self-evaluation includes information about career goals, job responsibilities, and an overall rating of job performance, and approximately 70% rated job performance as being satisfactory or better. Approximately 40% of the self-evaluation ratings differed from the ratings given by the employee's supervisor.

Select for Must be true the statement that must be true given the information provided and select for Must be false the statement that must be false given the information provided. Make only two selections, one in each column.­


All employees working at the company in March have completed at least one self-evaluation.

Not necessary. It is possible that someone was hired in Feb and left in April. No self evaluation.


Fewer than half of all employees had a job performance rating of satisfactory or better from their supervisor.

Not necessary.
Given: Approximately 70% rated job performance as being satisfactory or better. Approximately 40% of the self-evaluation ratings differed from the ratings given by the employee's supervisor.

Say of 100 people, 70 rate themselves satisfactory and 30 unsatisfactory. 40 of the ratings were different when given by supervisor. It is possible that:
- 60 satisfactory ratings were maintained while 10 satisfactory and 30 unsatisfactory were flipped. So 90 were satisfactory as per supervisors and 10 not satisfactory.
- 30 satisfactory ratings were maintained while 40 satisfactory were flipped. So overall 30 satisfactory and 70 not satisfactory.



No employee who completed a self-evaluation in a given calendar year was hired by the company for the first time in December of that calendar year.

Correct. If an employee completed his self eval in 2024, it means he was working in the company in Sept 20204. He could not have joined the company for the first time in December.

Select for "Must be True"


More than half of all employees had an unsatisfactory job performance.


No indication of "as per whom?" What is the parameter to decide overall "unsatisfactory job performance"? Own rating/supervisor rating/combination thereof - no idea


At least one employee who rated his or her performance as satisfactory in a given year did not receive an evaluation by his or her supervisor that year.

False.
Given: all employees, including those who left the company after completing their annual self-evaluation, are subsequently evaluated by their supervisors.

Select for "Must be False"
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I come up with this way to evaluate Statement 2:

S = SS = USUM
E = S(70 - a)a70
E = Ub(30 - b)30
SUM70 - (a-b)30 + (a-b)100

Assume there are 100 employees --> there are 100 self-evaluations and 100 supervisor evaluations.

Let's denote:
  • E = S: Employees evaluating job performance as Satisfactory or better (70)
  • E = U: Employees evaluating job performance as Unsatisfactory (30)
  • S = S: Supervisors evaluating job performance as Satisfactory or better
  • S = U: Supervisors evaluating job performance as Unsatisfactory

There are a total of 70 for E = S and 30 for E = U.

Let a = # of evaluations where E = S but S = U. b = # of evaluations where E = U but S = S

We have: a + b = 40

S2 says that fewer than half has S = S

Assume this is True. That means:
70 - (a-b) < 50
a - b > 20
a > 20 + b
20 + 2b < a+b
2b + 20 < 40
--> b < 10. b could be 5
a = 40 - b = 35.

70 - (a-b) = 70 - 30 = 40 < 50
--> S2 could be True

Assume this is False. That means the opposite:
b ≥ 10. b could be 12.
a = 40 - b = 28

70 - (a-b) = 70 - 16 = 54 > 50
--> S2 could be False

==> We cannot say S2 Must be True or Must be False
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chetan2u KarishmaB - Evaluation is different from receiving the feedback
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chetan2u KarishmaB - Evaluation is different from receiving the feedback

Care to elaborate on what exactly you mean by that or what you are implying?
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Eg in real life ppl do fill things up but they never recieve it once the leave the organisation - its just part of organisation records. So evaluating an employee is different from receiving a feedback
Bunuel

Care to elaborate on what exactly you mean by that or what you are implying?
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Eg in real life ppl do fill things up but they never recieve it once the leave the organisation - its just part of organisation records. So evaluating an employee is different from receiving a feedback

I think you are overthinking this. “Receive an evaluation” in option E simply means that a supervisor evaluation occurred, not that feedback was delivered or seen.
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