# Free DI and LR Practice Test - CAT

### Question 1

**In how many of these years, the aggregate number of marks allotted to all the topics is less than the aggregate number of marks allotted to all the topics in the year 1999 but more than aggregate number of marks allotted to all the topics in the year 2001?**

0

1

2

3

#### SOLUTION

Solution :A

As the aggregate of all the marks allotted to all the subjects across various years as following

Year199819992000200120022003Aggregate marks185165165150150150As we can see that there is no number between aggregate of year 1999 (165) and aggregate if year 2001 (150).

### Question 2

**Which topic has been allotted the second lowest aggregate number of marks over the given period?**

Arithmetic

Parajumbles

Analogies

Modern Maths

#### SOLUTION

Solution :C

The aggregate number of marks allotted to the topics over the

given period are as follows

Sl.noMarks160233310445051406140747850955101061123124313501449The second lowest aggregate number of marks is allotted to the topic Analogies.

### Question 3

**Four out of seven Chestnut High School Chess Academy students (A, B, C, D, E, F and G) are to be selected in a school chess team in such a way that if A is selected, then B cannot be in that team and if B is selected, then E cannot be in that team. If one of D and F is selected, then the other must be chosen. Which of the following statements must be true?**

If B is selected, then D must be chosen.

If A is selected, then C must be chosen.

If B is selected, then G must be chosen

C must be selected

#### SOLUTION

Solution :A

Option (A): If B is selected, then A and E cannot be selected. The other 3 must be from CDFG but D and F have to be together so the team will be B, D, F and any one of C or G. So D must be selected in the team, hence this Option is definitely TRUE.

Option(B): If A is selected B cannot be chosen. The other 3 members can be any 3 from C, D, E, F and G. This Option is not definitely TRUE.

Option (C): If B is selected, then A and E are ruled out. The other 3 can be chosen from C, D, F and G. Of this D and F must be chosen with the last member being either C or G. This Option is not definitely TRUE.

Option (D): C need not be chosen on every team. If we select DFEG, this is a valid team without C. Option(A)

### Question 4

On a certain sight-seeing tour, the ratio of the number of Indians to the number of Chinese was 5 to 2. What was the number of Americans on the sight-seeing tour?

(1) On the sight-seeing tour, the ratio of the number of Chinese to the number of Americans was 5 to 11.

(2) The number of Indians on the sight-seeing tour was less than 30

#### SOLUTION

Solution :C

Given Indians: Chinese = 5:2

(1) Chinese: Americans = 5:11, it is insufficient

(2) Indians<30; This alone is insufficientTogether, I:C:A = 25:10:22 (all have to be integers!) thus I=25 and A=22.

### Question 5

If N is a positive odd integer, what is the average of a certain set of N integers?

(1) The integers in the set are consecutive multiples of 3

(2) The median of the set of integers is 33

#### SOLUTION

Solution :C

(1) Insufficient. There is no way to find out the mean using this. Consider one set {3, 6, 9} and another {6, 9, 12}.

(2) Insufficient. Knowing that there is an odd number of terms in the set and that the median is 33 does not tell us what the mean is.(1&2) Sufficient. In an ordered set with an odd number of terms, the median is equal to the "middle" term. Moreover, in an equally distributed set of integers (in this case, consecutive multiples of 3) the median will be equal to the mean itself.

### Question 6

The correct response for which of the questions can be determined?

Second

Third

Fifth

Sixth

#### SOLUTION

Solution :A

We have

QuestionResponses(9 of them will be wrong)1AC D→Two wrong.2BA B→At least one wrong.3CA A→At least one wrong.4DB C→Two wrong.5CB B→At least one wrong.6AC C→At least one wrong.

### Question 7

Which of the following can be the correct responses for the first and fourth questions respectively?

(A, B) or (C, D)

(A, B) or (D, B)

(A, C) or (C, D)

(A, C) or (D, B)

#### SOLUTION

Solution :A

QuestionResponses(9 of them will be wrong)1AC D→Two wrong.2BA B→At least one wrong.3CA A→At least one wrong.4DB C→Two wrong.5CB B→At least one wrong.6AC C→At least one wrong.

### Question 8

If thereare three questions having same answers, then it can be

A or B

A or C

B or C

A, B or C

#### SOLUTION

Solution :D

QuestionResponses(9 of them will be wrong)1AC D→Two wrong.2BA B→At least one wrong.3CA A→At least one wrong.4DB C→Two wrong.5CB B→At least one wrong.6AC C→At least one wrong.

### Question 9

How many distinct cases for the correct responses of the questions exist?

4

6

8

10

#### SOLUTION

Solution :B

QuestionResponses(9 of them will be wrong)1AC D→Two wrong.2BA B→At least one wrong.3CA A→At least one wrong.4DB C→Two wrong.5CB B→At least one wrong.6AC C→At least one wrong.

### Question 10

For how many cases, D is an answer for at least one of the questions?

2

3

4

5

#### SOLUTION

Solution :B

### Question 11

Who lives in Mumbai?

B

D

E

Either (1) or (2)

#### SOLUTION

Solution :A

PersonCityCompanyADelhiRototecBMumbaiInfotecCChennaiTetratecDBangaloreSimotecEHyderabadQuetec

### Question 12

Which company does D work in?

Quetec

Rototec

Simotec

Either (1) or (2)

#### SOLUTION

Solution :C

PersonCityCompanyADelhiRototecBMumbaiInfotecCChennaiTetratecDBangaloreSimotecEHyderabadQuetec

### Question 13

In which city does the person who works in Tetratec live?

Delhi

Chennai

Hyderabad

Either (1) or (2)

#### SOLUTION

Solution :B

PersonCityCompanyADelhiRototecBMumbaiInfotecCChennaiTetratecDBangaloreSimotecEHyderabadQuetec

### Question 14

In which city does the person who works in Infotec live?

Chennai

Delhi

Mumbai

Either (1) or (2)

#### SOLUTION

Solution :C

PersonCityCompanyADelhiRototecBMumbaiInfotecCChennaiTetratecDBangaloreSimotecEHyderabadQuetec

### Question 15

For which company does the person who lives in Hyderabad work?

Quetec

Infotec

Tetratec

Rototec

#### SOLUTION

Solution :A

PersonCityCompanyADelhiRototecBMumbaiInfotecCChennaiTetratecDBangaloreSimotecEHyderabadQuetec

### Question 16

Mathew, Nathan, Olonga, Peter, Quine, Rafeal, Sutherland, Thomson and Udele are nine members in a family, who go to play to two different football clubs namely Liverpool and Chelsea. Each club can allow only three members of the same family. Peter has a priority and must be given preference by Liverpool or Chelsea. Rafeal and Nathan do not wish to go to the same club. Sutherland goes to Liverpool only and Thomson goes to Chelsea only. Olonga comes back saying that neither of the two clubs allowed him. Mathew does not go with Rafeal and Udele does not go with Quine. Nathan and Udele do not go together. If Quine, Rafeal and Sutherland go together and are allowed by one of the clubs, then who goes to play in which club, assuming that Mathew does not go to play?

Chelsea - Peter, Udele, Thomson or Peter, Nathan, Thomson

Chelsea - Peter, Mathew, Thomson or Peter, Nathan, Thomson

Liverpool - Mathew, Udele, Thomson or Nathan, Udele, Thomson

Liverpool - Peter, Udele, Thomson or Mathew, Udele, Thomson

#### SOLUTION

Solution :A

According to the condition that Sutherland goes to Liverpool only, Quine, Rafeal and Sutherland go to Liverpool. Thus Options (C) and (D) are not possible. Now, Peter is given preference and Thomson goes to Chelsea only thus possible answer options can be (A) and (B). Since Mathew does not play so Option (B) can be discarded. Thus option (A) is the answer.

### Question 17

Four people need to cross a bridge at night. They have one flashlight for the four of them, but the bridge is only wide enough for two to cross at a time. Because it's so dark, anyone crossing the bridge must do so with the flashlight. Person A can walk across in 1 minute. Person B takes 2 minutes; person C takes 5 minutes, and finally person D needs a full 10 minutes to cross. Naturally, if two people are crossing the bridge, they move with the speed of the slower person. What is the shortest amount of time it will take for all four to get to the other side?

18

8

17

15

#### SOLUTION

Solution :A

Total amount of time required = 10+5+2+1 = 18 min

### Question 18

If it is known that South Africa won a match against Australia, then New Zealand tied their match with which of the following teams?

#### SOLUTION

Solution :C

Let us take the first letter of the name of each team to represent its name. Now, it is given

That

(i)A + I = 12

(ii)I + SA = 11

(iii)NZ + I = 10

(iv)I + P = 8

Adding the above four equations, we get :

A + SA + 4I + NZ + P = 41 ........(1)

The total number of games played is = 4 + 3 + 2 + 1 = 10

Each game is worth two points hence total points

= 10 × 2 = 20 or A + SA + I + NZ + P = 20 .......(2)

Comparing with equation (1) and (2) we get:

3I = 21 or I = 7 (3 wins, 1 tie)

A = 5, SA = 4, NZ = 3, P=1

(2 win, 1 tie) (2 wins) (1 win, 1 tie) (1 tie)

As there are two ties they must be between A, NZ, I and P, but not SA. Now we can have

the following possibilities of ties:Case I: I ties with A the NZ ties with P

TeamWinLoseTieA(SA/NZ),P(SA or NZ)ISA(A or NZ),P(A or NZ),I−ISA,NZ,P−ANZ(A or SA)(A or SA),IPP−A,SA,INZ

Case II: I ties with NZ,A ties with P

TeamWinLoseTieASA,NZIPSANZ,PA,I−INZ,P−NZNZPA,SAIP−I,SA,NZA

Case III: I ties with P,A ties with NZ.

TeamWinLoseTieASA,PINZSANZ,PA,I−IA,SA,NZ−PNZPSA,IAP−A,SA,NZI

Choice (c). SA wins against A only in Case I, in which NZ ties with P

### Question 19

How many total arrangements of wins and ties are possible?

#### SOLUTION

Solution :Let us take the first letter of the name of each team to represent its name. Now, it is given that

(i)A + I = 12

(ii)I + SA = 11

(iii)NZ + I = 10

(iv)I + P = 8

Adding the above four equations, we get :

A + SA + 4I + NZ + P = 41 ........(1)

The total number of games played is = 4 + 3 + 2 + 1 = 10

Each game is worth two points hence total points

= 10 × 2 = 20 or A + SA + I + NZ + P = 20 .......(2)

Comparing with equation (1) and (2) we get:

3I = 21 or I = 7 (3 wins, 1 tie)

A = 5, SA = 4, NZ = 3, P=1

(2 win, 1 tie) (2 wins) (1 win, 1 tie) (1 tie)

As there are two ties they must be between A, NZ, I and P, but not SA. Now we can have

the following possibilities of ties:Case I: I ties with A the NZ ties with P

TeamWinLoseTieA(SA/NZ),P(SA or NZ)ISA(A or NZ),P(A or NZ),I−ISA,NZ,P−ANZ(A or SA)(A or SA),IPP−A,SA,INZ

Case II: I ties with NZ,A ties with P

TeamWinLoseTieASA,NZIPSANZ,PA,I−INZ,P−NZNZPA,SAIP−I,SA,NZA

Case III: I ties with P,A ties with NZ.

TeamWinLoseTieASA,PINZSANZ,PA,I−IA,SA,NZ−PNZPSA,IAP−A,SA,NZI

Choice (c). Total number of arrangements

Case I = 2

Case II = 1

Case III = 1

--------

4

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### Question 20

**Which of the following teams totaled the third highest in points?**

#### SOLUTION

Solution :B

Third highest points are scored by South Africa

### Question 21

Which of the following statements must be true?

#### SOLUTION

Solution :C

Choice (c). Only South Africa must have won against Pakistan, as others have a chance of tying a match with Pakistan.

### Question 22

The buyer who is most dissimilar in his preferences to C is

A

B

#### SOLUTION

Solution :A

The dissimilarity of choices for two people would be measured by sum of the absolute value of difference in rankings given by the two people to each of the five parameters.

E.g. Dissimilarity for A and C would be |3-1|+|1-5|+|4-3|+|2-4|+|5-2|=12.If we find the dissimilarity values for all pairs of people, the table would be as follows.

E D C B A1281210B2810C86D10

### Question 23

Which of the following pair of buyers are most dissimilar in their preferences?

#### SOLUTION

Solution :D

Option D is the correct answer.

### Question 24

The dissimilarity in the preferences of D is the least with

A

B

C

E

#### SOLUTION

Solution :C

Option C is the correct answer.

### Question 25

Among the following pairs of buyers, the pair which is identical in its level of dissimilarity in preferences with the pair A and D is

#### SOLUTION

Solution :C

Option C is the correct answer.

### Question 26

Which of the following statements is true?

Sarath eats 2 potato bites

Sarath eats 4 potato bites

Danny eats 6 potato bites

Barney eats 4 potato bites

#### SOLUTION

Solution :D

PersonBiscutsPotato bitesKetchup and jamSarath10xMerlin42xDanny51√Barney84xIrwin66√

### Question 27

Which one of the following statements is true?

Danny eats 5 biscuits

Irwin eats 8 biscuits

Barney eats 1 biscuit

Barney eats 6 biscuits

#### SOLUTION

Solution :A

PersonBiscutsPotato bitesKetchup and jamSarath10xMerlin42xDanny51√Barney84xIrwin66√

### Question 28

Which of the following statements is true?

Merlin eats 8 biscuits and 4 potato bites but no ketchup and jam.

The person who eats 5 biscuits and 1 potato bite does not take ketchup and jam.

The person who eats equal number of potato bites and biscuits also takes ketchup and jam

The person who eats 4 biscuits and 2 potato bites also takes ketchup and jam

#### SOLUTION

Solution :C

PersonBiscutsPotato bitesKetchup and jamSarath10xMerlin42xDanny51√Barney84xIrwin66√

### Question 29

The flow of oil in the pipeline joining units A and D will be (in litres )

#### SOLUTION

Solution :As the pipeline AB is working at its full capacity it must be transferring 2500 litres of oil. Out of which 1200 litres is taken by B, 700 litres is taken by C, and 400 litres oil taken by E. Remaining 200 litres will go to D but D's requirement is 700 litres so AD must be carrying 500 litres.

### Question 30

How many of the given the pipeline segments are carrying less than 20% of their capacity

#### SOLUTION

Solution :As the pipeline AB is working at its full capacity it must be transferring 2500 litres of oil. Out of which 1200 litres is taken by B, 700 litres is taken by C, and 400 litres oil taken by E. Remaining 200 litres will go to D but D's requirement is 700 litres so AD must be carrying 500 litres.

20% of 2500 is 500. By observing the figure, the pipes where the flow is less than 500 are CE and CD i.e., 2 pipes.

### Question 31

If the difference between the capacity of a pipeline and the amount of oil flowing in it is called as the slack in that pipeline, what is the slack in the pipeline connecting units C and D (in litres)?

#### SOLUTION

Solution :As the pipeline AB is working at its full capacity it must be transferring 2500 litres of oil. Out of which 1200 litres is taken by B, 700 litres is taken by C, and 400 litres oil taken by E. Remaining 200 litres will go to D but D's requirement is 700 litres so AD must be carrying 500 litres.

Again from the figure, the slack in the pipeline connecting C and D is 2300 litres.

### Question 32

There are three boxes, one contains only apples, one contains only oranges, and one contains both apples and oranges. The boxes have been incorrectly labeled such that no label identifies the actual contents of the box it labels. Opening just one box, and without looking in the box, you take out one piece of fruit. By looking at the fruit, you can immediately label all of the boxes correctly. Which box did you open?

Containing apple

Containing oranges

Containing both apples and oranges

Cannot be determined

#### SOLUTION

Solution :C

Containing both orange and apple.