1. There cannot be more than two candidates from a single department.
2. A candidate cannot vote for himself/herself.
3. Faculty members cannot vote for a candidate from their own department.
After the election, it was observed that Prof. Pakrasi received 3 votes, Prof. Qureshi received 14 votes, Prof. Ramaswamy received 6 votes and Prof. Samuel received 1 vote. Prof. Pakrasi voted for Prof. Ramaswamy, Prof. Qureshi for Prof. Samuel, Prof. Ramaswamy for Prof. Qureshi and Prof. Samuel for Prof. Pakrasi
Which two candidates can belong to the same department?
- Prof. Pakrasi and Prof. Qureshi
- Prof. Qureshi and Prof. Ramaswamy
- Prof. Pakrasi and Prof. Samuel
- Prof. Ramaswamy and Prof. Samuel
The Correct Option is A
Solution and Explanation
Given:
- Only 1 candidate is from O&Q ⇒ Non-candidates in O&Q = 4
- Departments vote as a block
- Minimum non-candidates = 1 (from B&H if 2 of 3 members are candidates)
- Prof. R received 5 votes from non-candidates
Possible groupings for 5 votes:
- (a) 5
- (b) 4 + 1 ⇒ O&Q (4) + B&H (1) ⇒ implies 2 candidates in B&H
- (c) 3 + 2 ⇒ Also implies 2 candidates in some small departments
Cases (b) and (c) violate the limit of 1 candidate from O&Q and make it hard to balance remaining departments.
Case (a) is only valid if all 5 votes came from a single department. That’s only possible in M&S (7 total members - 2 candidates = 5 voters).
So the department-wise breakdown becomes:
| F&A | M&S | O&Q | B&H | |
|---|---|---|---|---|
| Total members | 9 | 7 | 5 | 3 |
| Candidates | 0 | 2 | 1 | 1 |
| Non-candidates | 9 | 5 | 4 | 2 |
Now vote distribution by candidate:
| P | Q | R | S | |
|---|---|---|---|---|
| Total Votes | 3 | 14 | 6 | 1 |
| Self Vote | 1 (S) | 1 (R) | 1 (P) | 1 (Q) |
| From Non-candidates | 2 | 13 | 5 | 0 |
| Source Dept(s) | B&H | F&A + O&Q | M&S | — |
From M&S:
There are 2 candidates. Since R got 5 votes from M&S, R is not a candidate from M&S (his department voted for him).
So possible candidates from M&S are: (P, Q), (P, S), or (Q, S)
From vote data and department constraints, P and Q are the only consistent pair from M&S.
Therefore, final assignment cases:
| F&A | M&S | O&Q | B&H | |
|---|---|---|---|---|
| Case 1 | 0 | P, Q | R | S |
| Case 2 | 0 | P, Q | S | R |
Conclusion:
The correct pair of candidates from M&S is Prof. Pakrasi and Prof. Qureshi.
Correct answer: Option A: Prof. Pakrasi and Prof. Qureshi
Which of the following can be the number of votes that Prof. Qureshi received from a single department?
- 7
- 8
- 6
- 9
The Correct Option is D
Solution and Explanation
Here's the extracted data and reasoning:
1. Total Votes for Prof. Qureshi:
- Prof. Qureshi received a total of 14 votes in the election.
2. Voting Constraints:
- Each department votes as a block: all non-candidate members vote for the same candidate.
- A candidate cannot receive votes from their own department.
3. Department Sizes:
- F&A: 9 members
- M&S: 7 members
- O&Q: 5 members
- B&H: 3 members
4. Possible Voting Scenarios:
- Prof. Qureshi must have received votes from departments other than his own.
- The maximum votes he could receive from a single department is from F&A (9 votes).
- Since he got a total of 14 votes, it's plausible that he received 9 from F&A and the remaining 5 from another department (e.g., O&Q or M&S).
Conclusion:
- The maximum number of votes Prof. Qureshi could have received from a single department is 9.
Therefore, the correct answer is: Option 4: (9)
If Prof. Samuel belongs to B&H, which of the following statements is/are true?
Statement A: Prof. Pakrasi belongs to M&S.
Statement B: Prof. Ramaswamy belongs to O&Q.
Statement A: Prof. Pakrasi belongs to M&S.
Statement B: Prof. Ramaswamy belongs to O&Q.
- Only statement A
- Both statements A and B
- Neither statement A nor statement B
- Only statement B
The Correct Option is B
Solution and Explanation
To determine the truth of statements A and B based on the information that Prof. Samuel belongs to the B&H department, let’s analyze the constraints:
1. Departmental Composition:
- Each department has a limited number of faculty members.
- Only one candidate can be from the O&Q department.
- Prof. Samuel is confirmed to be from B&H, so no other candidate can belong to B&H.
2. Analysis of Statement A:
- Statement A: "Prof. Pakrasi belongs to M&S."
- M&S is a large department and can feasibly have one candidate.
- No restriction is violated if Prof. Pakrasi is from M&S.
⇒ Statement A is true.
3. Analysis of Statement B:
- Statement B: "Prof. Ramaswamy belongs to O&Q."
- Since only one candidate can be from O&Q and Prof. Samuel is in B&H, it is possible for Prof. Ramaswamy to be the sole O&Q candidate.
- This also maintains correct departmental representation.
⇒ Statement B is true.
4. Conclusion:
- Both statements A and B are consistent with the provided constraints.
Therefore, the correct answer is: Option 2: Both statements A and B.
What best can be concluded about the candidate from O&Q?
- It was either Prof. Ramaswamy or Prof. Samuel.
- It was Prof. Samuel.
- It was either Prof. Pakrasi or Prof. Qureshi.
- It was Prof. Ramaswamy.
The Correct Option is A
Solution and Explanation
To deduce which candidate might belong to the O&Q department, let’s apply the constraints:
1. Departmental Constraint:
- Only one candidate can belong to the O&Q department.
- O&Q has only 5 faculty members, making it smaller than F&A or M&S.
2. Process of Elimination:
- Prof. Pakrasi and Prof. Qureshi received a large number of votes.
- This suggests they were likely supported by large departments (such as F&A or M&S).
- Since O&Q is a small department, it is unlikely that either belongs to O&Q.
3. Remaining Candidates:
- That leaves Prof. Ramaswamy and Prof. Samuel.
- Based on available data, either of them could feasibly be from O&Q.
4. Conclusion:
- The candidate from O&Q is either Prof. Ramaswamy or Prof. Samuel.
Therefore, the correct answer is: Option 1: It was either Prof. Ramaswamy or Prof. Samuel.
Which of the following statements is/are true?
Statement A: Non-candidates from M&S voted for Prof. Qureshi.
Statement B: Non-candidates from F&A voted for Prof. Qureshi.
Statement A: Non-candidates from M&S voted for Prof. Qureshi.
Statement B: Non-candidates from F&A voted for Prof. Qureshi.
- Neither statement A nor statement B
- Both statements A and B
- Only statement A
- Only statement B
The Correct Option is D
Solution and Explanation
To determine the truth of each statement based on the information provided:
1. Voting Patterns and Departmental Rules:
- All non-candidates in each department voted for a single candidate who was not from their own department.
- Prof. Qureshi received a substantial number of votes (14 votes), suggesting that multiple departments voted for him.
2. Analysis of Statement A:
- Statement A: "Non-candidates from M&S voted for Prof. Qureshi."
- If M&S had voted for Prof. Qureshi, then all non-candidates in M&S must have done so (as per the rule).
- But based on vote distribution and the need to allocate total votes properly, it is unlikely that M&S voted for Prof. Qureshi.
⇒ Statement A is unlikely to be true.
3. Analysis of Statement B:
- Statement B: "Non-candidates from F&A voted for Prof. Qureshi."
- F&A is the largest department (9 members), and could account for a significant portion of Qureshi's 14 votes.
- This aligns with the possibility of multiple departments supporting Qureshi.
⇒ Statement B is likely to be true.
4. Conclusion:
- Only Statement B is supported by the data.
Thus, the correct answer is: Option 4: Only statement B.
Top Questions on Conclusion
- There are only four neighbourhoods in a city-Levmisto, Tyhrmisto,Pesmisto and Kitmisto. During the onset of a pandemic,the number of new cases of a disease in each of these neighbourhoods was recorded over a period of five days. On each day, the number of new cases recorded in any of the neighbourhoods was either 0,1,2 or 3.
The following facts are also known:
1. There was at least one new case in every neighbourhood on Day 1.
2. On each of the five days, there were more new cases in Kitmisto than in Pesmisto.
3. The number of new cases in the city in a day kept increasing during the five-day period. The number of new cases on Day 3 was exactly one more than that on Day 2.
4. The maximum number of new cases in a day in Pesmisto was 2 and this happenedonly once during the five-day period.
5. Kitmisto is the only place to have 3 new cases on Day 2.
6. The total numbers of new cases in Levmisto,Tyhrmisto,Pesmisto and Kitmisto over the five-day period were 12,12,5 and 14 respectively. - The Humanities department of a college is planning to organize eight seminars, one for each of the eight doctoral students - A, B, C, D, E, F, G and H. Four of them are from Economics, three from Sociology and one from Anthropology department. Each student is guided by one among P, Q, R, S and T. Two students are guided by each of P, R and T, while one student is guided by each of Q and S. Each student is guided by a guide belonging to their department.
Each seminar is to be scheduled in one of four consecutive 30-minute slots starting at 9:00 am, 9:30 am, 10:00 am and 10:30 am on the same day. More than one seminars can be scheduled in a slot, provided the guide is free. Only three rooms are available and hence at the most three seminars can be scheduled in a slot. Students who are guided by the same guide must be scheduled in consecutive slots.
The following additional facts are also known.
1. Seminars by students from Economics are scheduled in each of the four slots.
2. A’s is the only seminar that is scheduled at 10:00 am. A is guided by R.
3. F is an Anthropology student whose seminar is scheduled at 10:30 am.
4. The seminar of a Sociology student is scheduled at 9:00 am.
5. B and G are both Sociology students, whose seminars are scheduled in the same slot. The seminar of an Economics student, who is guided by T, is also scheduled in the same slot.
6. P, who is guiding both B and C, has students scheduled in the first two slots.
7. A and G are scheduled in two consecutive slots. - Ten musicians (A, B, C, D, E, F, G, H, I and J) are experts in at least one of the following three percussion instruments: tabla, mridangam, and ghatam. Among them, three are experts in tabla but not in mridangam or ghatam, another three are experts in mridangam but not in tabla or ghatam, and one is an expert in ghatam but not in tabla or mridangam. Further, two are experts in tabla and mridangam but not in ghatam, and one is an expert in tabla and ghatam but not in mridangam.
The following facts are known about these ten musicians.
1. Both A and B are experts in mridangam, but only one of them is also an expert in tabla.
2. D is an expert in both tabla and ghatam.
3. Both F and G are experts in tabla, but only one of them is also an expert in mridangam.
4. Neither I nor J is an expert in tabla.
5. Neither H nor I is an expert in mridangam, but only one of them is an expert in ghatam. - A large store has only three departments, Clothing, Produce, and Electronics. The following figure shows the percentages of revenue and cost from the three departments for the years 2016, 2017 and 2018. The dotted lines depict percentage levels. So for example, in 2016, 50% of store's revenue came from its Electronics department while 40% of its costs were incurred in the Produce department.
In this setup, Profit is computed as (Revenue – Cost) and Percentage Profit as Profit/Cost × 100%.
It is known that
1. The percentage profit for the store in 2016 was 100%.
2. The store’s revenue doubled from 2016 to 2017, and its cost doubled from 2016 to 2018.
3. There was no profit from the Electronics department in 2017.
4. In 2018, the revenue from the Clothing department was the same as the cost incurred in the Produce department. - Princess, Queen, Rani and Samragni were the four finalists in a dance competition. Ashman, Badal, Gagan and Dyu were the four music composers who individually assigned items to the dancers. Each dancer had to individually perform in two dance items assigned by the different composers. The first items performed by the four dancers were all assigned by different music composers. No dancer performed her second item before the performance of the first item by any other dancers. The dancers performed their second items in the same sequence of their performance of their first items.
The following additional facts are known.
i. No composer who assigned item to Princess, assigned any item to Queen.
ii. No composer who assigned item to Rani, assigned any item to Samragni.
iii. The first performance was by Princess; this item was assigned by Badal.
iv. The last performance was by Rani; this item was assigned by Gagan.
v. The items assigned by Ashman were performed consecutively. The number of performances between items assigned by each of the remaining composers was the same.
Questions Asked in CAT exam
- A shop wants to sell a certain quantity (in kg) of grains. It sells half the quantity and an additional 3 kg of these grains to the first customer. Then, it sells half of the remaining quantity and an additional 3 kg of these grains to the second customer. Finally, when the shop sells half of the remaining quantity and an additional 3 kg of these grains to the third customer, there are no grains left. The initial quantity, in kg, of grains is
- CAT - 2024
- Algebra
- Gopi marks a price on a product in order to make 20% profit. Ravi gets 10% discount on this marked price, and thus saves Rs 15. Then, the profit, in rupees, made by Gopi by selling the product to Ravi, is
- CAT - 2024
- Profit and Loss
- If m and n are natural numbers such that n > 1, and mn = 225 × 340, then m − n equals
- CAT - 2024
- Exponents and Powers
- Five jumbled up sentences (labelled 1, 2, 3, 4 and 5), related to a topic, are given below. Four of them can be put together to form a coherent paragraph. Identify the odd sentence and key in the number of that sentence as your answer.
- CAT - 2024
- Para Jumbles
- \( 10^{68} \) is divided by 13, the remainder is is
- CAT - 2024
- Divisibility and Remainder