At a small architecture firm, the average (arithmetic mean) age of the

Question

At a small architecture firm, the average (arithmetic mean) age of the employees at the end of 2025 was 30 years. At the beginning of 2026, one new employee joined the firm and one existing employee left, so the total number of employees remained the same. What was the new average (arithmetic mean) age of the employees after this change?

(1) The employee who left was 2 years older than the new employee who joined.
(2) The employee who left was 30 years old.

Bunuel · Accepted Answer

GMAT Club Official Solution:

At a small architecture firm, the average (arithmetic mean) age of the employees at the end of 2025 was 30 years. At the beginning of 2026, one new employee joined the firm and one existing employee left, so the total number of employees remained the same. What was the new average (arithmetic mean) age of the employees after this change?

(1) The employee who left was 2 years older than the new employee who joined.

Let the number of employees be n. Then the total age at the end of 2025 was 30n.

Statement (1) says the employee who left was 2 years older than the new employee who joined. So the total age decreased by 2. That makes the new average:

(30n - 2)/n = 30 - 2/n

Since n is unknown, the new average cannot be determined.

Not sufficient.

(2) The employee who left was 30 years old.

This tells us only that the employee who left was 30 years old. But we still do not know the age of the new employee who joined, so we cannot determine the new average.

Not sufficient.

(1)+(2) From (1), the new average is 30 - 2/n. (2) tells us that the employee who left was 30 years old, but since the new average depends on n, not on the age of the employee who left, the new average still cannot be determined. Not sufficient.

Answer: E.

Adit_ · Answer

IMO E.

Statement 1:

We get an equation like:

(30x- +y)/x
y gets cancelled out but we can't eliminate x here which is the number of employees.
INSUFFICIENT.

Statement 2:

Just knowing age of person leaving is clearly not enough.
INSUFFICIENT.

Combining the two:
Even after combining, we notice that statement 2 actually does nothing to help us.
y gets cancelled after all and knowing the age of the person leaving adds nothing to the equation.
INSUFFICIENT.

Answer:  Option E

odionam · Answer

This Question would be easier if one thing kept in mind i.e here total no. of employee is not given so we can't calculate actual average with given statements. Because adding or subtracting will impact on overall avg so Answer is E 
2nd thing if question were asked whether avg increase or decrease we can easily deduce it from statement 1.

BongBideshini · Answer

Let the number of employees = N, Total age at end of 2025 = 30N
At the beginning of 2026, one employee leaves (age = L) & One new employee joins (age = J)
New total age=30N - L + J
New average (30N - L + J) / N 
= 30 + (J - L)/N

Statement (1) 
J - L = -2
New average:
30 - 2/N
We do not know N
 Statement (1) is not sufficient.

Statement (2) 
L = 30

New average = 30 + (J - 30)/N
Cannot determine exact value.
 Statement (2) is not sufficient.

Statements (1) and (2) Together

L = 30
So, J = 28
New average:
30 - 2/N
Still need N

Statements together are not sufficient.

Ans E

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