In an office with 8 employees, the average rating of all employees is 30. The average rating of the top five employees is 38, and the average rating of the bottom three employees is 25. Which of the following is not possible?
Show Hint
- One of the top five employees has a rating of 50.
- The lowest rating among the bottom three employees is 20.
- The highest rating among the top five employees is 40.
- One of the bottom three employees has a rating of 24.
The Correct Option is C
Solution and Explanation
Total Ratings:
Total ratings of all employees:
\[ \text{Total} = 8 \times 30 = 240 \]
Top Five and Bottom Three Totals:
Total ratings of the top five employees:
\[ \text{Top Five Total} = 5 \times 38 = 190 \]
Total ratings of the bottom three employees:
\[ \text{Bottom Three Total} = 3 \times 25 = 75 \]
Verification of Totals:
The total ratings of all employees:
\[ \text{Sum of Top Five + Bottom Three} = 190 + 75 = 265 \]
This exceeds the total ratings of 240, so adjustments are required.
Analyze the Options:
(A) One of the top five employees has a rating of 50:
If one top employee has a rating of 50, the remaining total for the top four is:
\[ 190 - 50 = 140, \quad \text{Average for four} = \frac{140}{4} = 35 \]
This is possible, as the remaining ratings align with the data.
(B) The lowest rating among the bottom three employees is 20:
If one bottom employee has a rating of 20, the remaining total for the other two is:
\[ 75 - 20 = 55, \quad \text{Average for two} = \frac{55}{2} = 27.5 \]
This is possible, as the averages match.
(C) The highest rating among the top five employees is 40:
If the highest top employee rating is 40, then the remaining total for the other four is:
\[ 190 - 40 = 150, \quad \text{Average for four} = \frac{150}{4} = 37.5 \]
This contradicts the given average of 38, making this impossible.
(D) One of the bottom three employees has a rating of 24:
If one bottom employee has a rating of 24, the remaining total for the other two is:
\[ 75 - 24 = 51, \quad \text{Average for two} = \frac{51}{2} = 25.5 \]
This is possible, as it satisfies the conditions.
Thus, the correct answer is (C).
Top Questions on Average
- For predicting the straight-line trend in the sales of washing machines (in thousands) on the basis of 8 consecutive years' data, the company calculates 4-year moving averages. If the sales of washing machines for respective years are \( a, b, c, d, e, f, g, \) and \( h \), then which of the following averages will be computed?
(A) \( \frac{a + b + c + d}{4} \)
(B) \( \frac{a + c + d + e}{4} \)
(C) \( \frac{c + d + f + h}{4} \)
(D) \( \frac{b + c + d + e}{4} \)
Choose the correct answer from the options given below: - If the average of p numbers is q2 and that of q numbers is p2, then the average of (p+q) numbers is:
- The average of 101 consecutive odd numbers is 303. Find the largest number.
- If the average of six numbers is 18, and three of the numbers are 15, 20, and 25, what is the average of the remaining three numbers?
- The average of 5 consecutive even numbers is 24. What is the largest of these numbers?
Questions Asked in XAT exam
- Arya, a graduate from a reputable institute, got a job in an IT company but became bored after a year. Her best friend S, who worked at the same company, joined a top-tier B-school for an MBA, which tempted Arya to pursue the same path. Her friend assured her that an MBA would boost her career prospects and salary. Arya started preparing for an MBA while continuing her job, but the challenge of balancing preparation with work made her consider leaving the job.
- XAT - 2025
- Analytical Decision Making
- There’s a community 30 km outside of the main city. Mr. S started a grocery business in the community after winning the bid by offering way above the rent initially drafted by the community council. The community council, led by Mr. D, agreed to the offer with a performance review every three years. Mr. S also agreed to provide an additional 15% of his grocery sales to the council, banking on the prospect of selling in higher volumes. After setting up his business, Mr. S noticed that SUV owners in the community usually bought goods in bulk from the city once a week and used his store primarily for daily necessities and occasional big purchases like mixer grinders.
- XAT - 2025
- Analytical Decision Making
- Four reviewers (R1, R2, R3, R4) are in charge of reviewing products from companies A, B, C, and D. Each reviewer provides a rating between 1 and 5 for the products. Due to a technical glitch, the original ratings were deleted, and only the averages calculated for each product (A, B, C, D) and each reviewer (R1, R2, R3, R4) were saved. The data available is as follows:Tasks:
A B C D Average 3 4 4 ? 4 3 ? 5 ? 4 ? 3 3 ? 4 ? ? ? ? 4.25 4 4 4 4.25
1. What are the missing values in the table?
2. How were the missing values calculated?
3.Verify the correctness of the given averages for both rows and columns. - In an 8-week course, the teacher conducts a test every week, and the scores are in the range of 1–4. There are only two students enrolled in the course, \(R\) and \(S\). The following conditions are given:
- \(R\) and \(S\) scored the same on the first test.
- From the second test onwards, \(R\) consistently scored the same (a non-zero score).
- The total of the first three test scores of \(R\) equals the total of the first two test scores of \(S\).
- From the fifth test onwards, \(S\) scored the same as \(R\).
- The scores of \(S\) from the first two tests and all the remaining tests follow a geometric progression.
- XAT - 2025
- Algebra
- A bought a phone from a store and paid \(\frac{1}{6}\) of the price using UPI, \(\frac{1}{3}\) of the price in cash, and the remaining balance a year later. He also paid 10% interest on the remaining balance after one year. What was the original price of the phone?
- XAT - 2025
- Percentage