# Condition BasedSet 5

## Practice Questions for CAT with Solutions

### 1. CAT - Condition Based

Each of six trains Train A through Train F – travels between exactly two cities from among six different cities – Chennai, Delhi, Kolkata, Bengaluru and Hyderabad – such that no two trains start from the same city and no two trains end at the same city.

Further, no two trains travel between the same pair of cities. It is also known that the travel time of each train defined as the number of hours that the train takes to travel from its origin to its destination, is a distinct positive integer less than 8.

The following information is known about the origins, destinations and travel times of the six trains:
1. The destination of Train A is the same as the origin of Train D, but neither of these trains travel either from Delhi or to Delhi.
2. The travel time of Train E is two hours more than that of Train C.
3. One of the trains starts from Chennai and goes to Hyderabad, with a travel time of three hours.
4. The travel time of Train F, which travels to Kolkata, is less than seven hours, while the travel time of the train which starts from Kolkata is two hours.
5. The travel time of Train B, which starts from Bengaluru, is the average of the travel times of the train which starts from Mumbai and the train which starts from Hyderabad.
6. The train which travels to Delhi starts from Kolkata, while Train D does not start from Hyderabad.
Q1. What is the travel time in hours of Train A?
Q2. What is the destination of Train B?
1. Delhi
2. Chennai
4. Mumbai
Q3. Which train starts from Hyderabad?
1. Train A
2. Train E
3. Train F
4. CBD

7 hours

d. Mumbai

c. Train F

### 2. CAT - Condition Based

Ajit is a statistician and a cricket lover. His friend Sujit, the president of the local cricket league, tells him about a recent match between two clubs in his league, HCC and PCC, in which a strange coincidence occurred during HCC’s first innings. HCC scored 616 runs losing just 5 wickets, and at different points during the innings, their score was 111 runs for 1 wicket, 222 for 2, 333 for 3, 444 for 4,and 555 for 5. Ajit was intrigued and asked for more details, but Sujit did not remember the entire score- board. He told Ajit whatever he could recall and based on that Ajit drew some tables (shown below, arranged in order of appearance of the batsmen, i.e. Rizvan was the opening batsman and Narender was the last to enter the field).

Fall of wickets:

• 1-2 (Ganesh, 1.1 overs)
• 2-138 (Rajiv, 40.1 overs)
• 3-313 (Jatin, 75.3 overs)
• 4-375 (Rizvan, 91.1 overs)
• 5-538 (Saurabh, 129.6 overs)

Breakup of extras conceded:

• Between 1st and 2nd wicket – 3 no balls, 2 leg byes
• Between 2nd and 3rd wicket – 1 leg bye
• Between 3rd and 4th wicket – 1 wide, 4 byes
• Between 4th and 5th wicket – 4 byes
• After 5th wicket – 2 leg byes

Note:

1. Each over consists of six balls. For example, 75.3 overs means 75 overs and 3 balls.
2. SR denotes Strike Rate, which equals runs scored divided by balls faced multiplied by 100.
3. The total balls faced by the batsmen are equal to 6 × number of overs + number of balls.
4. In the ‘Fall of wickets’, the first number denotes the wicket, the second number denotes the team score when that wicket fell and the brackets contain the name of the batsman dismissed and the total overs faced by the team at that time. For example, HCC lost their fourth wicket after 91 overs and 1 ball, at a total score of 375, when Rizvan was dismissed.
5. Fours and Sixes denotes the number of times a batsman scored four or six runs respectively off a single ball.
Q1. How many runs did Rizvan score?
Q2. Which batsman had the highest strike rate?
1. Rizvan
2. Jatin
3. Saurabh
4. Venkat
Q3. What was Saurabh’s score when Rizvan lost his wicket?
Q4. If one batsman hit exactly twelve fours, who scored the highest percentage of his runs by hitting fours and sixes?
1. Rizvan
2. Jatin
3. Saurabh
4. Venkat

202

b. Jatin

29

a. Rizvan

### 3. CAT - Condition Based

The function ‘Difference (N)’ takes a non negative integer N as a parameter and returns the absolute difference of N and the number obtained by reversing the digits of N. For a two digit natural number X with distinct digits, a set of six non negative integers {P, Q, R, S, T, U} is defined such that P = Difference(X), Q = Difference(P), R = Difference(Q), S = Difference(R), T = difference(S) and U = Difference(T)
Q1. If the value of T is not equal to zero, then what is the largest possible value for X?
1. 86
2. 90
3. 68
4. None of these
Q2. If d is the difference between the two digits of X and d = 4, then what is the sum of P, Q, R, S, T and U?
1. 128
2. 117
3. 136
4. 158
Q3. For any value of X, what is the maximum possible sum of T and U?
Q4. If X is greater than 50, then what is the maximum possible value of U?

d. None of these

b. 117

9

0

### 4. CAT - Condition Based

The marks of 6 students in H.S.C. (Commerce) are given. However some fields are blank. With the help of the clues, fill the blank fields and answer the questions that follow. The marks in each subject are out of 100. The passing percentage required in each subject is 35% and that required overall is 50%. Each student passes in each subject and also passes overall. The maximum marks scored in Accounts are 99 and those scored in Maths are 100. No two students got the same marks in the same subject and no student got the same marks in any two subjects. All marks are in integers.
It is also known that:
1. Marks scored by the 6 students in Economics are 6 consecutive numbers.
2. Chandan got the same overall percentage as one other student.
3. Marks obtained by Deepa in English are the average of the marks obtained by Ajay and Faruq in English.
4. Bipin’s marks in Hindi, Chandan’s marks in Economics, Faruq’s marks in O.C. and Ajay’s marks in Maths are the same.
5. Faruq’s marks in English are the same as Ajay’s marks in O.C. and both are individually 50% more than Esha’s marks in Hindi.
6. Chandan’s marks in English are the same as Deepa’s marks in O.C. and Deepa’s marks in English are the same as Chandan’s marks in O.C.
7. Faruq was ranked 4th in Maths.
8. Ajay’s marks in Hindi are the average of what Chandan and Esha scored in Hindi.
9. Marks scored by Bipin in Maths are just enough to get him a 3rd rank in Maths. x. Faruq scored 1 mark less in O.C. than Chandan.
10. Faruq got more marks in Economics than what Esha got in O.C.
11. Bipin’s marks in O.C. are the same as Esha’s marks in English. Both of these are the average of Chandan’s marks in English and Deepa’s marks in English.
12. Bipin managed to get the 1st rank in English by just 1 mark.
13. Deepa’s marks in Maths are less compared to Esha’s marks in Maths.
14. Esha’s score in Hindi is exactly half of her Maths score.
15. Esha’s marks in O.C. are 1 more than her marks in Economics.
16. Deepa’s marks in Accounts are 76% more than Esha’s marks in Hindi.
17. Five students got 90 or more in Maths.
18. Esha got 2 marks more in Economics than Deepa in English.

Q1. Who scored 99 in Accounts?
1. Faruq
2. Chandan
3. Deepa
4. Either Chandan or Faruq
Q2. How much did Bipin get in English?
1. 70
2. 78
3. 76
4. Cannot be determined
Q3. Who got the same overall total as Chandan?
1. Bipin
2. Faruq
3. Deepa
4. Either Deepa or Bipin
Q4. How much did Deepa get in Hindi?
1. 70
2. 72
3. 73
4. Either 72 or 73

b. Chandan

c. 76

c. Deepa

c. 73

### 5. CAT - Condition Based

Given below is a 4 × 4 crossword puzzle. Use the following clues to complete it:

Across
1. Number of terms in the expansion of (IIM + 1)71 which are definitely divisible by IIM7.
2. Number of zeroes with which P ends, where P is the product of first 100 multiples of 10.
4. The least number of terms that should be removed from ‘Q’ so that the sum of no two terms is a multiple of 3, where Q is the set of all three digit numbers.
Down
1. Sum of digits of (11111111)2.
3. Number of 3-digit numbers in which the digit in ten’s place is less than both the digit in hundred’s place and unit’s place.

Q1. What is the square of the last digit of 1-across?
Q2. What is the sum of all the digits of 2-across?
Q3. What is the middle digit in 3-down?

25

7

8

### 6. CAT - Condition Based

Kiran, an eccentric billionaire, hired three Private Investigators (PIs), Sherlock, Feluda and Hercules, and independently asked each of them to track the activities of the other two PIs, during the same period, for exactly n days. As part of their respective assignments, Kiran asked each of them to record the number of days that each of the other two PIs sent any e-mail from their respective e-mail accounts during these n days.
After the n days, each of the three PIs provided their respective reports which included information only about the other two PIs.

The following is known about the information in their reports:

1. According to Sherlock’s report, the number of days on which both of the other two PIs sent e-mails was 50, while the number of days on which only Feluda sent e-mails was 34.
2. According to Feluda’s report, the number of days on which only Hercules sent e-mails was 34, while the number of days on which only Sherlock sent e-mails was 27.
3. According to Hercules’ report, the number of days on which both of the other two PIs sent e-mails was 43, while the number of days on which only Sherlock sent e-mails was 29 and the number of days on which none of the other two sent e-mails was 21.
4. At least one of the three persons sent an e-mail on each of the n days.
Q1. What is the value of n?
Q2. On how many days during the given period did both Sherlock and Feluda send e-mails but Hercules did not?
Q3. On how many days during the given period did Hercules send e-mails but Feluda did not?
1. 29
2. 34
3. 27
4. 21
Q4. What is the maximum number of consecutive days during the given period on which Hercules could have sent an e-mail?
1. 77
2. 78
3. 79
4. 81

134

6

a. 29

c. 79

### 7. CAT - Condition Based

Tetra is a company that manufactures and sells chairs. At the beginning of each month, the stock of chairs in the inventory is calculated. The stock at the beginning of any month is calculated as follows:

The table below provides the stock of chairs at the beginning of each month in 2017.

It is also known that, in any month, the number of chairs manufactured was either half the number of chairs sold or thrice the number of chairs sold. There was no stock left in the inventory at the end of the year.

Q1. In how many months during the year were more than 50000 chairs sold?
Q2. In which month during the year were the highest number of chairs manufactured?
Q3. What is the average number of chairs sold per month (approximately) during the year?
Q4. In which of the following months was the percentage increase in the number of chairs sold as compared to the previous month the highest?
1. November
2. September
3. July
4. February

5

March

54167

d. February

### 8. CAT - Condition Based

Six institutes together conducted a common written test for admission into them. The test had four sections with the maximum marks in each section being 100. The following table gives the aggregate as well as the sectional cut off marks fixed by the six different institutes. A student will get calls from the institute only if he/she get marks greater than or equal to the cut off marks in each of the sections and his/her aggregate marks is at least equal to the aggregate cut off marks as specified by the institute.

Q1. Reshma got calls from all the institutes. What could be the minimum marks obtained by her?
Q2. In which month during the year were the highest number of chairs manufactured?
Q3. What is the average number of chairs sold per month (approximately) during the year?
Q4. Ramesh got calls from two institutes. What could be the maximum aggregate marks obtained by him?

362

50

370

383

### 9. CAT - Condition Based

After a recent outbreak of the T1T1 flu virus, many people went to the three most renowned hospitals – Jaslok, Wockhardt, Hinduja – in Mumbai. These patients underwent treatment for the flu, but some had to be kept in the Intensive Care Unit [ICU] for intensive treatment while the others were kept in the General ward. The data showing the number of patients in each ward from the three hospitals is as shown:

After successful treatments the patients were sent home. A few months later, the National Centre for Disease Control (NCDC) asked for data on males and females affected by T1T1 and admitted in each ward of each hospital. However, the hospitals only had partial records, as shown below

One of the doctors, however, remembered the following:
1. The number of females admitted in Wockhardt and the number of males admitted to the general ward (across hospitals) were in the ratio 1:2.
2. The number of males in the ICU and the number of males in Hinduja were consecutive primes.
Q1. The male to female patient ratio in Hinduja Hospital was _______
Q2. What is the ratio of males in ICU in Wockhardt to the females in General ward in Jaslokti Assume that the female patients in ICU are equally split among the three hospitals?
Q3. By what percentage are the females in ICU more than the males in ICU?
Q4. The ratio of the ratio of males in ICU to females in General to the ratio of males in General to the females in ICU is?

11 : 5

4 : 3

71.4%

14/27

### 10. CAT - Condition Based

Four aircraft manufacturing companies – ABC, XYZ, PQR, and FGH – manufactured a certain number of aircraft. It is known that, by the end of the year 1999, the four companies had manufactured a total of exactly 18 aircraft and by the end of 2001, the four of them had manufactured a total of exactly 35 aircraft. The following information is known about the number of aircraft manufactured by the companies:

1. The number of aircraft that XYZ manufactured during 2000 was the same as the number of aircraft that ABC manufactured during 2001, which was more than the number of aircraft that PQR manufactured during 2001.
2. By the end of 1999, ABC and FGH had manufactured 3 and 5 aircrafts, respectively.
3. Even though PQR did not manufacture any aircraft during 2001, each of PQR, ABC and FGH had manufactured the same number of aircraft by the end of 2001.
4. The number of aircraft that FGH during 2001 was the same as that during 2000, which was twice the number of aircraft in which ABC manufactured during 2001.
5. The number of aircraft that PQR manufactured during 2000 was the same as the number of aircraft that XYZ manufactured during 2001.
Q1. How many aircrafts PQR had by end of 2000?
Q2. How many aircrafts ABC made during 2001?
Q3. Aircrafts made by ABC was what percentage more that that of PQR for the year 1999?

9

1

-50%