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Numerical - 15 May 2025
Vignesh Srinivasan
Module 18 of 8
Read the following and answer the questions 1 to 4
An agency entrusted to accredit colleges looks at four parameters: faculty quality (F), reputation (R), placement quality (P), and infrastructure (I). The four parameters are used to arrive at an overall score, which the agency uses to give an accreditation to the colleges. In each parameter, there are five possible letter grades given, each carrying certain points: A (50 points), B (40 points), C (30 points), D (20 points), and F (0 points). The overall score for a college is the weighted sum of the points scored in the four parameters. The weights of the parameters are 0.1, 0.2, 0.3 and 0.4 in some order, but the order is not disclosed. Accreditation is awarded based on the following scheme:
Eight colleges apply for accreditation, and receive the following grades in the four parameters (F, R, P, and I):
It is further known that in terms of overall scores:
1. High Q is better than Best Ed;
2. Best Ed is better than Cosmopolitan; and
3. Education Aid is better than A-one.
[CAT 2018 Slot 2]
1) What is the weight of the faculty quality parameter?
(1) 0.1
(2) 0.3
(3) 0.2
(4) 0.4
2) How many colleges receive the accreditation of AAA?
Answer:
3) What is the highest overall score among the eight colleges?
Answer:
4) How many colleges have overall scores between 31 and 40, both inclusive?
(1) 2
(2) 1
(3) 0
(4) 3
Read the following and answer the questions that follow
A new game show on TV has 100 boxes numbered 1, 2, . . . , 100 in a row, each containing a mystery prize. The prizes are items of different types, a, b, c, . . . , in decreasing order of value. The most expensive item is of type a, a diamond ring, and there is exactly one of these. You are told that the number of items at least doubles as you move to the next type. For example, there would be at least twice as many items of type b as of type a, at least twice as many items of type c as of type b and so on. There is no particular order in which the prizes are placed in the boxes.
[CAT 2019 Slot 1]
5) What is the minimum possible number of different types of prizes?
Answer:
6) What is the maximum possible number of different types of prizes?
Answer:
7) Which of the following is not possible?
(1) There are exactly 30 items of type b.
(2) There are exactly 75 items of type e.
(3) There are exactly 60 items of type d.
(4) There are exactly 45 items of type c.
8) You ask for the type of item in box 45. Instead of being given a direct answer, you are told that there are 31 items of the same type as box 45 in boxes 1 to 44 and 43 items of the same type as box 45 in boxes 46 to 100.
What is the maximum possible number of different types of items?
(1) 4
(2) 6
(3) 3
(4) 5
Details for Questions 1 to 4 are provided below
Fuel contamination levels at each of 20 petrol pumps P1, P2, …, P20 were recorded as either high, medium, or low.
1. Contamination levels at three pumps among P1 – P5 were recorded as high.
2. P6 was the only pump among P1 – P10 where the contamination level was recorded as low.
3. P7 and P8 were the only two consecutively numbered pumps where the same levels of contamination were recorded.
4. High contamination levels were not recorded at any of the pumps P16 – P20.
5. The number of pumps where high contamination levels were recorded was twice the number of pumps where low contamination levels were recorded.
[CAT 2018 Slot 1]
9) Which of the following MUST be true?
(1) The contamination level at P10 was recorded as high.
(2) The contamination level at P12 was recorded as high.
(3) The contamination level at P20 was recorded as medium.
(4) The contamination level at P13 was recorded as low.
10) What best can be said about the number of pumps at which the contamination levels were recorded as medium?
(1) More than 4
(2) Exactly 8
(3) At most 9
(4) At least 8
11) If the contamination level at P11 was recorded as low, then which of the following MUST be true?
(1) The contamination level at P12 was recorded as high.
(2) The contamination level at P15 was recorded as medium.
(3) The contamination level at P18 was recorded as low.
(4) The contamination level at P14 was recorded as medium.
12) If contamination level at P15 was recorded as medium, then which of the following MUST be FALSE?
(1) Contamination levels at P13 and P17 were recorded as the same.
(2) Contamination levels at P10 and P14 were recorded as the same.
(3) Contamination levels at P11 and P16 were recorded as the same.
(4) Contamination level at P14 was recorded to be higher than that at P15.
An agency entrusted to accredit colleges looks at four parameters: faculty quality (F), reputation (R), placement quality (P), and infrastructure (I). The four parameters are used to arrive at an overall score, which the agency uses to give an accreditation to the colleges. In each parameter, there are five possible letter grades given, each carrying certain points: A (50 points), B (40 points), C (30 points), D (20 points), and F (0 points). The overall score for a college is the weighted sum of the points scored in the four parameters. The weights of the parameters are 0.1, 0.2, 0.3 and 0.4 in some order, but the order is not disclosed. Accreditation is awarded based on the following scheme:
Eight colleges apply for accreditation, and receive the following grades in the four parameters (F, R, P, and I):
It is further known that in terms of overall scores:
1. High Q is better than Best Ed;
2. Best Ed is better than Cosmopolitan; and
3. Education Aid is better than A-one.
[CAT 2018 Slot 2]
1) What is the weight of the faculty quality parameter?
(1) 0.1
(2) 0.3
(3) 0.2
(4) 0.4
2) How many colleges receive the accreditation of AAA?
Answer:
3) What is the highest overall score among the eight colleges?
Answer:
4) How many colleges have overall scores between 31 and 40, both inclusive?
(1) 2
(2) 1
(3) 0
(4) 3
Read the following and answer the questions that follow
A new game show on TV has 100 boxes numbered 1, 2, . . . , 100 in a row, each containing a mystery prize. The prizes are items of different types, a, b, c, . . . , in decreasing order of value. The most expensive item is of type a, a diamond ring, and there is exactly one of these. You are told that the number of items at least doubles as you move to the next type. For example, there would be at least twice as many items of type b as of type a, at least twice as many items of type c as of type b and so on. There is no particular order in which the prizes are placed in the boxes.
[CAT 2019 Slot 1]
5) What is the minimum possible number of different types of prizes?
Answer:
6) What is the maximum possible number of different types of prizes?
Answer:
7) Which of the following is not possible?
(1) There are exactly 30 items of type b.
(2) There are exactly 75 items of type e.
(3) There are exactly 60 items of type d.
(4) There are exactly 45 items of type c.
8) You ask for the type of item in box 45. Instead of being given a direct answer, you are told that there are 31 items of the same type as box 45 in boxes 1 to 44 and 43 items of the same type as box 45 in boxes 46 to 100.
What is the maximum possible number of different types of items?
(1) 4
(2) 6
(3) 3
(4) 5
Details for Questions 1 to 4 are provided below
Fuel contamination levels at each of 20 petrol pumps P1, P2, …, P20 were recorded as either high, medium, or low.
1. Contamination levels at three pumps among P1 – P5 were recorded as high.
2. P6 was the only pump among P1 – P10 where the contamination level was recorded as low.
3. P7 and P8 were the only two consecutively numbered pumps where the same levels of contamination were recorded.
4. High contamination levels were not recorded at any of the pumps P16 – P20.
5. The number of pumps where high contamination levels were recorded was twice the number of pumps where low contamination levels were recorded.
[CAT 2018 Slot 1]
9) Which of the following MUST be true?
(1) The contamination level at P10 was recorded as high.
(2) The contamination level at P12 was recorded as high.
(3) The contamination level at P20 was recorded as medium.
(4) The contamination level at P13 was recorded as low.
10) What best can be said about the number of pumps at which the contamination levels were recorded as medium?
(1) More than 4
(2) Exactly 8
(3) At most 9
(4) At least 8
11) If the contamination level at P11 was recorded as low, then which of the following MUST be true?
(1) The contamination level at P12 was recorded as high.
(2) The contamination level at P15 was recorded as medium.
(3) The contamination level at P18 was recorded as low.
(4) The contamination level at P14 was recorded as medium.
12) If contamination level at P15 was recorded as medium, then which of the following MUST be FALSE?
(1) Contamination levels at P13 and P17 were recorded as the same.
(2) Contamination levels at P10 and P14 were recorded as the same.
(3) Contamination levels at P11 and P16 were recorded as the same.
(4) Contamination level at P14 was recorded to be higher than that at P15.