A company makes a certain retirement package available to each

Question

A company makes a certain retirement package available to each employee starting on the anniversary of their hiring date when the sum of the employee’s age and the number of years she/he has worked for the company first equals or exceeds 91.

From the available options, select a possible age  at hiring  and number of years after being hired for an employee on the date when this retirement package is  first  made available to her/him. Make only two selections, one in each column.

RonPurewal · Accepted Answer

Official Solution:

First let’s investigate the required condition (age + years with the company ≥ 91) a little more closely. Every additional year worked by an employee increases  BOTH  the employee’s age  AND  years of experience by 1, so the sum of these will go up by 2 for each additional year worked. Accordingly,  the package becomes available when this sum becomes either 91 or 92.

In other words, the required condition is

91 ≤ Current age + Years of experience ≤ 92

The variables in the columns, however, are not  current  age and years of experience—they’re age  AT HIRE  and years of experience. Let’s define variables for these: say the employee was a years old when hired, and has now worked y years for the company.

With these choices, the employee’s  CURRENT  age is (a + y) years, and therefore we can write the required condition in terms of a and y:

91 ≤ (a + y) + y ≤ 92 
91 ≤ a + 2y ≤ 92

If we solve this inequality for one of the variables, we’ll get a ‘formula’ into which we can plug the available numbers and get the workable values for the other variable. Solving for a is straightforward—just subtract 2y from each component of the inequality:

91 – 2y ≤ a ≤ 92 – 2y

We can now plug each of the five available values into this inequality for y, which will tell us the values of a that, together with that y-value, should solve the problem. Only one of those results should contain any of the other available values, and that pair of values will be our solution.

y (Years of exp) --- 91 – 2y ≤ a ≤ 92 – 2y (Range of a = Age at hire)
26 ------------------ 39 ≤ a ≤ 40
28 ------------------ 35 ≤ a ≤ 36
30 ------------------ 31 ≤ a ≤ 32
34 ------------------ 23 ≤ a ≤ 24
36 ------------------ 19 ≤ a ≤ 20

The second row contains the possibility a = 36, which is one of the available choices; none of the other possible ranges for  a  contains any of the choices.

So, the solution is that unique possibility: 
 Age at Hire = 36, 
Years after Hire Date = 28.

aditya1818 · Answer

Looking at the question, the equation will be as below:

x+2y >=91 
where x= Age at Hire
and y= Years after hire date

Now possible values of x=(26,28,30,34,36)
for each values of x as above and solving x+2y >=91 will give y >= mn.ab(some decimal)
so it won't be available for decimal points and so we will have to look for values greater than (mn.ab) which will be integers and so in that case it won't be  first  made available

so now take 92 instead of 91 and then check if any exact value of "x" satisfies it.

for x+2y=92; x=36 and y=28 satisfies ( I first picked x=26 and solved mentally for y in x+2y=92 and was checking whether that value of "y" was there in the table or not and so on did for x=(28,30,34,36) and eventually x=36 got the desired result with the table)

and so for x=36 and y=28 retirement package is first made available to her/him

Dereno · Answer

Retirement package is available on the anniversary of hiring date.

Sum of employees age + Number of years worked >= 91 .

Let’s assume a person is being born, after a particular time period say x years, the person is being employed.

Let the age of the person at the time of employment be = age of hire.

The person works for y years = number of years worked.

At the time of anniversary, the number of years worked = y years.

And, the corresponding age at the time of anniversary = (age of hire +y) years.

Substituting in the equation we get

(Age of hire + y) + y >= 91

Age of Hire + 2y >= 91.

91 being a big number, , let the age of hire be 36.

2y should be greater than or equal to (91-36) = 55 years.

Thus, y >= (55/2) , which is 27.5

Hence, the value of y = 28.

Age of Hire = 36

Number of years worked = 28

doloribusnobis · Answer

RonPurewal

Can somebody please explain why the  age of   hire – 26  and  years after   hire date - 34  is not an answer?
Clearly,  26 + 2(34) = 94 , and  26 + 34 = age 60  comes before  36 + 28 = age 64.

RonPurewal · Answer

We need figures for the year in which the sum (Age + Years Employed)  FIRST  reaches 91 or greater.

With these numbers, you have a 60-year-old who's been with the company for 34 years. The problem is that, in the  previous  year, this employee would have been 59 years old with 33 years at the company—where 59 + 33 = 92 ≥ 91. So, the package would have been offered to that employee at age 59 after 33 years (which doesn't match any available pair of options), not at age 60 after 34 years.

A company makes a certain retirement package available to each

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