At a certain company, the bonus pool is divided among a group of emplo

Question

At a certain company, the bonus pool is divided among a group of employees consisting entirely of engineers and managers so that each engineer receives a bonus of e dollars and each manager receives a bonus of m dollars. Is m at least 20% greater than e?

(1) At least 20% of the employees in the group are managers.
(2) The total amount awarded to managers is at least 20% greater than the total amount awarded to engineers.

PCSund · Answer

e and m represents the amount awarded to each employee per group which means that we need the total amount awarded to the group and the number of group members in each group to make an assessment.

1) Not sufficient

No information about the bonus amount

2) Not sufficient

No information about number of employees

1+2) Not sufficient

let's first maximize difference by assuming only 20% of employees are managers and they receive all the bonus available. m is 20% greater than e

Next, let's minimize by assuming all but one employee are managers (remember, 1) states at least 20% of employees are managers). If we now also minimize the amount awarded to managers here, and since we have many more managers than engineers, the total sum for the managers will be split among managers whereas one engineer receives a large bonus. m is now smaller than e

TestPrepUnlimited · Answer

Is  m > 120\%*e ?

Statement 1:

The distribution of employees is currently irrelevant to how much each person receives. Insufficient.

Statement 2:

We need to know the relation between the number of managers vs the number of engineers.

Combined:

Let there be x managers and y engineers. We know  4x > y  since we must have at least 20% managers and at most 80% engineers.

x*m > 120\%*(y*e)  and  4x > y . There is no conclusion from combining these two inequalities so insufficient.

Ans: E

sayan640 · Answer

MartyMurray   KarishmaB  Would you like to explain this question ?

KarishmaB · Answer

Question: Is m >= 1.2e?

(1) At least 20% of the employees in the group are managers.

All this says is that out of 100 employees, at least 20 are managers. It is possible that 20 are managers and 80 are engineers. 
It is possible that 50-50 are managers and engineers. It is possible that 80 are managers and 20 are engineers. 
No info about m and e.

Not sufficient.

(2) The total amount awarded to managers is at least 20% greater than the total amount awarded to engineers.
  
Say number of engineers = E
Total amount received by engineers = Ee
Total amount received by managers >= 1.2*Ee
- It is possible that m = e and number of managers is 1.2E.
- It is possible that m = 1.2e and number of managers is E.
It is possible that m > 1.2e and number of managers is less than E.

Not sufficient.

Using both statements together, all 3 cases discussed in statement 2 are still possible.

Answer (E)

sayan640 · Answer

Hi  KarishmaB

There is no relationship mentioned in your solution between E and e.
Can you please check whether my method is correct or not ?

We need to find whether m > 6/5 e ?

Statement 1 says -  (1) At least 20% of the employees in the group are managers.

Since no info has been provided about the dollars , statement 1 is not sufficient.

Statement 2 says - (2) The total amount awarded to managers is at least 20% greater than the total amount awarded to engineers.

Lets say , the no. of Managers = x and no. of engineers = y 
 mx > 6/5 * ye
No relationship about x and y and hence no relationship can be found about m and e. 
 x can be a very big number say 200 and y can be a small number i.e 100. 
 then 200m > 6e ; Hence m and e can be anything. m can either be greater than 6/5 e or even lesser than it.  
 Statement 2 is not sufficient.

With both statement 1 and 2 ,

Lets say , the no. of Managers = 20P and no. of engineers = 80P

Hence 20p m > 6/5 * 80p* e 
 m > 24/5 e ...hence m can be greater than 6/5 e.

But if , the no. of Managers = 90P and no. of engineers = 10P

90 pm > 6/5 * 10 p * e 
 m > 6/45 e 
 
m is greater than a number smaller than e.  
 hence m can be greater than 6/5 *e or not. Not sufficient.

E is the answer.

can you please verify  KarishmaB

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At a certain company, the bonus pool is divided among a group of emplo

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