This is the second set under the CAT 2016 Sprint Preparation Series – LRDI 2. Over the next 5 days, we will be covering around 300 questions that we expect to come across in CAT 2016. The answers to LRDI Sprint CAT 2016 – Day 2 will be posted at the end of the day and will include the solution, possible traps and things to keep in mind come similar question types in CAT 2016. You may go through the entire series here: CAT 2016 Sprint Preparation Series by Learningroots
CAT 2016 Sprint Preparation Series – LRDI 2
Set 1
The table below provides certain demographic details of 30 respondents who were part of a survey. The demographic characteristics are: gender, number of children, and age of respondents. The first number in each cell is the number of respondents in that group. The minimum and maximum age of respondents in each group is given in brackets. For example, there are five female respondents with no children and among these five, the youngest is 34 years old, while the oldest is 49.
1. The percentage of respondents aged less than 40 years is at least
a. 10%
b. 16.67%
c. 20.0%
d. 30%
2. Given the information above, the percentage of respondents older than 35 can be at most
a. 30%
b. 73.33%
c. 76.67%
d. 90%
3. The percentage of respondents that fall into the 35 to 40 years age group (both inclusive) is at least
a. 6.67%
b. 10%
c. 13.33%
d. 26.67%
4. What is the ratio of the minimum number of respondents who are more than 30 years old to that of the maximum respondents who are less than 40 years old? (Note down your answer in the decimal notation of the ratio up to two significant digits. For example: If your answer is coming to 12:15, write it down as 0.80)
Set 2
A hedge fund has recently acquired four companies – BOB, MOB, ZOB and DOB. The sales of DOB are half that of BOB whereas the profits of DOB are double that of BOB. The expenses of ZOB are Rs 3 crores less than that of DOB whereas the profit of MOB is Rs 1 Crore less than that of ZOB. The expenses of BOB are three times that of DOB. It is also known that the sales of ZOB are Rs 15 crores or one-fourth that of MOB. The auditing firm has also reported that sales of DOB are Rs 10 crores more than that of ZOB and the expenses of BOB are 90% of its own sales.
5. The total sales of all the four companies is (Rs crores):
a. 200
b. 150
c. 125
d. 160
6. The expenses of BOB exceed that of ZOB by (Rs crores):
a. 34
b. 43
c. 33
d. 62
7. Which company had the maximum profits?
a. BOB
b. MOB
c. ZOB
d. DOB
8. The expenses of MOB exceed the profits of BOB by (Rs crores):
a. 51
b. 52
c. 53
d. 54
9. Total profits of the four companies are (Rs. Crores):
a. 15
b. 20
c. 25
d. 40
10. The profits of MOB form what percentage of the expenses of ZOB?
a. 16%
b. 20%
c. 15%
d. 23%
Set 3
Recently, the answers of a test held nationwide were leaked to a group of unscrupulous people. The investigative agency has arrested the mastermind and nine other people A, B, C, D, E, F, G, H and I in this matter. Interrogating them, the following facts have been obtained regarding their operation. Initially the mastermind obtains the correct answer-key. All the others create their answer-key in the following manner. They obtain the answer-key from one or two people who already possess the same. These people are called his/her ‘sources’. If the person has two sources, then he/she compares the answer-keys obtained from both sources. If the key to a question from both sources is identical, it is copied, otherwise it is left blank. If the person has only one source, he/she copies the source’s answers into his/her copy. Finally, each person compulsorily replaces one of the answers (not a blank one) with a wrong answer in his/her answer key.
The paper contained 200 questions; so the investigative agency has ruled out the possibility of two or more of them introducing wrong answers to the same question. The investigative agency has a copy of the correct answer key and has tabulated the following data. These data represent question numbers.
11. Which one among the following must have two sources?
a. A
b. B
c. C
d. D
12. How many people (excluding the mastermind) needed to make answer-keys before C could make his answer-key?
a. 2
b. 3
c. 4
d. 5
13. Both G and H were sources to
a. F
b. B
c. I
d. None of the nine
14. Which of the following statements is true?
a. C introduced the wrong answer to question 27.
b. E introduced the wrong answer to question 46.
c. F introduced the wrong answer to question 14.
d. H introduced the wrong answer to question 46.
15. Which of the following two groups of people had identical sources?
I. A, D and G II. E and H
a. Only I
b. Only II
c. Neither I nor II
d. Both I and II
Set 4
Four families decided to attend the marriage ceremony of one of their colleagues. One family has no kids, while the others have at least one kid each. Each family with kids has at least one kid attending the marriage. Given below is some information about the families, and who reached when to attend the marriage.
· The family with two kids came just before the family with no kids.
· Shanthi who does not have any kids reached just before Sridevi’s family.
· Sunil and his wife reached last with their only kid.
· Anil is not the husband of Joya.
· Anil and Raj are fathers.
· Sridevi’s and Anita’s daughters go to the same school.
· Joya came before Shanthi and met Anita when she reached the venue
· Raman stays the farthest from the venue.
· Raj said his son could not come because of his exams.
16. Who among the following arrived third?
a. Shanthi
b. Sridevi
c. Anita
d. Joya
17. Name the correct pair of husband and wife.
a. Raj and Shanthi
b. Sunil and Sridevi
c. Anil and Sridevi
d. Raj and Anita
18. Of the following pairs, whose daughters go to the same school?
a. Anil and Raman
b. Sunil and Raman
c. Sunil and Anil
d. Raj and Anil
19. Whose family is known to have more than one kid for certain?
a. Raman’s
b. Raj’s
c. Anil’s
d. Sunil’s
Solutions:
1. Probably the easiest set of the day. From the set who have 0 children, we get at least 1 male and 1 female who will be less than 40 for sure. Similarly, 1 male and 1 female from those who had 1 child, 1 male and 1 female from those who had 2 children and 2 males and 1 female from those who had 3 children. So, 9 people in total out of 30 so 30%.
2. Similar to the first one, we get 1 + 4 + 7 + 7 + 3 + 0 + 1 = 23 out of 30 so 76.67%.
3. 1 + 1 + 1 + 1 = 4 out of 30 or 13.33%
4. More than 30 years old is 22 at minimum and less than 40 years old is 25 at maximum. So, the ratio will be 22:25 or 0.88
5. In the simplest form the table will look like this:
From the given information, x = 25 crores, so sales of BOB are 50 crores and expenses of BOB are 45 crores. So, z = 15 and y = 5. Also, k = 3. So, the new table will look like this:
Total sales is 150 crores.
6. 45 – 12 = 33 crores.
7. DOB had the maximum profits.
8. 58 – 5 = 53 crores.
9. 5 + 2 + 3 + 10 = 20 crores.
10. 2/12 = 16.67% so option a.
11. An extremely interesting question. The fun fact is that, this was asked in the re-test that was conducted post the CAT 2003 leak and so, it was pretty much relatable. Another fun fact is that, the solution would probably take less space than the first paragraph of the question.
As A, D and G have only one incorrect answer, they were the ones who had got the paper from the mastermind. Now, if we look at E, we see that he has marked 46 and 90 as the wrong answers and so, he would have got the paper from A. Similarly, H got it from A. If we look at F now, there is a funny thing that has happened. Although F has got 14 and 46 wrong, if he had only one source i.e. A, there would be no ambiguity in the blank answers column. However, as F has skipped questions 90 and 92, it is obvious that he has a couple of sources who had different answers for questions 90 and 92 viz. E and H. Similarly, C and I would also have multiple sources as they have something under the blank answers column. It can also be seen that C copied from I and then changed 56 as his wrong answer. Also, I copied from D and E and so left 17, 46 and 90 blank. B copied from E and G. The table would look as below:
Option b.
12. Option c.
13. Option d.
14. As F copied from A, F had 46 wrong from A’s set. So, he would have introduced 14 as the wrong answer into the system. Option c.
15. Option d.
16. Again, an easy set with too much data. The table would look as follows:
Option a
17. Option b is correct.
18. Option c is correct.
19. Option b is correct.
Hope you liked the sets. Stay tuned for a fresh set tomorrow!
You may go through the entire series here: CAT 2016 Sprint Preparation Series by Learningroots.
