In a certain company, each of the five managers has six technicians

Question

In a certain company, each of the five managers has six technicians reporting to him or her. Each of the 30 technicians reports to exactly one of the five managers. In April, each manager will evaluate not only each technician reporting to him or her but also each of the other managers. How many evaluations will the managers perform in total?

A. 30
B. 45
C. 50
D. 60
E. 150

A. 30
B. 45
C. 50
D. 60
E. 150

odiodeserunt · Answer

1 manager reviews : 6 technicians + 4 other managers = 10 reviews
5 managers review : 5*10 =50 reviews
 Option C is the correct answer

poojaarora1818 · Answer

Solution:

Each of the five Managers evaluate six technicians as 5 * 6 =30

Each of the manager is evaluated by each of the other managers =4 * 5 =20

Adding both 30+20= 50

Answer C

nemoexplicabo · Answer

This is a great counting problem that tests your ability to break down a word problem into clear categories. The key is carefully reading what each manager evaluates and then multiplying correctly.

Let me walk through the setup first:

We have 5 managers and 30 technicians total. Each manager supervises 6 technicians (since 5 managers × 6 technicians each = 30 total technicians). The question tells us that in April, each manager will evaluate two groups of people:
1. Each technician reporting to them
2. Each of the other managers

Step 1: Count evaluations of technicians

Each manager evaluates their own 6 technicians.
Since there are 5 managers, that's 5 × 6 = 30 technician evaluations.

Step 2: Count evaluations of other managers

Each manager evaluates "each of the other managers." If there are 5 managers total, then "the other managers" means the 4 managers who are not themselves.

So each manager evaluates 4 other managers.
Since there are 5 managers doing this, that's 5 × 4 = 20 manager evaluations.

Step 3: Add them together

Total evaluations = Technician evaluations + Manager evaluations
Total = 30 + 20 = 50 evaluations

Answer: C

Common traps to avoid:

A common mistake is forgetting that each manager evaluates the OTHER managers, not all 5 managers including themselves. If you counted 5 managers × 5 evaluations, you'd get 25 manager evaluations instead of 20, leading to answer D (55 or 60). Another pitfall is double-counting. Each manager-to-manager evaluation happens once (Manager A evaluates Manager B is one evaluation, not two). We're counting from the perspective of who is doing the evaluating, which is why we multiply by 5.

Key takeaway: On combination and counting problems, always identify what's being counted and from whose perspective. Break the problem into clear categories (technician evaluations vs. manager evaluations), count each category separately, then combine. Writing out "each manager does X + Y" helps you see the structure clearly and catch errors before you calculate the final answer!

In a certain company, each of the five managers has six technicians

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

In a certain company, each of the five managers has six technicians

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards