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12 Mar 2026, 06:09
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Age at Hire: 36
Years after Hire Date: 28
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.
Select for Age at Hire a possible age at hiring, and select Years after Hire Date the 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.
Select for Age at Hire a possible age at hiring, and select Years after Hire Date the 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.
| Age at Hire | Years after Hire Date | |
| 26 | ||
| 28 | ||
| 30 | ||
| 34 | ||
| 36 |
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Official Answer
Age at Hire: 36
Years after Hire Date: 28
12 Mar 2026, 06:09
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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
\(91 \le \text{Current age} + \text{Years of experience} \le 92\).
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 \(y\):
\(91 \le (a + y) + y \le 92\).
\(91 \le a + 2y \le 92 \).
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:
\(91 - 2y \le a \le 92 - 2y\).
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) --- \(91 - 2y \le a \le 92 - 2y\) (Range of \(a\) = Age at hire)
26 ------------------ \(39 \le a \le 40\)
28 ------------------ \(35 \le a \le 36\)
30 ------------------ \(31 \le a \le 32\)
34 ------------------ \(23 \le a \le 24\)
36 ------------------ \(19 \le a \le 20\)
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.
Correct answer:
Age at Hire "36"
Years after Hire Date "28"
Bunuel
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
\(91 \le \text{Current age} + \text{Years of experience} \le 92\).
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 \(y\):
\(91 \le (a + y) + y \le 92\).
\(91 \le a + 2y \le 92 \).
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:
\(91 - 2y \le a \le 92 - 2y\).
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) --- \(91 - 2y \le a \le 92 - 2y\) (Range of \(a\) = Age at hire)
26 ------------------ \(39 \le a \le 40\)
28 ------------------ \(35 \le a \le 36\)
30 ------------------ \(31 \le a \le 32\)
34 ------------------ \(23 \le a \le 24\)
36 ------------------ \(19 \le a \le 20\)
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.
Correct answer:
Age at Hire "36"
Years after Hire Date "28"
19 Apr 2026, 08:35
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But year at hire being 26 and years worked if it were 34, then the age at which she does get the award is 60 which is the first time she receives the award. If it were OA then 36+28 = 64? The question asks when do they first receive the award, so receiving the award at age 60 is the first time right? What did I miss here?
Bunuel
