# Free DI and LR Practice Test - CAT

### Question 1

How many teams in second round had the same score?

2

3

4

#### SOLUTION

Solution :C

4 teams in the second round had the same score. Hence option (c).

### Question 2

What can be the maximum number of points of a team after the second round?

8

15

9

22

#### SOLUTION

Solution :B

After the second round the maximum points of a team would be (5 + (4 + 3 + 3) (earned)) i.e. 15 points .This would happen when the top team of group A would defeat all the teams from group B. Hence option (b).

### Question 3

If two teams from each group qualify for the third round then what is the minimum points of the team from group A which qualifies?

9

6

5

#### SOLUTION

Solution :B

The minimum points with which a team would qualify, avoiding any contention would be with a single win and the points would be (3 + 3 (earned)) i.e. 6 points. Hence option (b).

### Question 4

The sum of the scores of the lower 3 teams of group B after the first round is.

6

12

5

4

#### SOLUTION

Solution :C

The sum of score of lower three teams of group B is 5 points. Hence option (c).

### Question 5

Which of the following could be the panel of judges selected to hear civil cases?

R, S, V

S, U, X

T, W, Y

V, X, Y

#### SOLUTION

Solution :C

T, W, Y. They satisfy the given conditions.

### Question 6

If X is the presiding judge of the panel selected for the civil cases, which of the following must be the other two members of that panel?

R & W

S & U

S & Y

U & V

#### SOLUTION

Solution :C

Since X is the presiding judge, the next experienced civil judge lower is seniority is Y and from the third geographical region is S.

### Question 7

Which of the following could be the panel of judges selected to hear criminal cases?

R, S, X

R, V, W

S, T, W

T, U, X

#### SOLUTION

Solution :A

Option (b) is eliminated as there have to be two judges experienced in criminal cases.

Option (c) is eliminated as S & W belong to the same region.

Option(d) is eliminated as T & X belong to the same region.

### Question 8

The judges selected to serve on any panel announced by the clerk of the court must include either:

R or U

R or Y

T or V

S or W

#### SOLUTION

Solution :D

The panel must include S or W as the second in seniority since the senior most will be the presiding judge and each panel should have two experienced judges in that particular field.

### Question 9

If the panel of judges hearing criminal cases consists of T, U & W and if U withdraws and is replaced, which of the following will be the presiding judge of the panel hearing criminal cases after U has been replaced?

R

S

Y

W

#### SOLUTION

Solution :A

Since U withdraws, the replaced one should be from that region i.e. either R or Y. Since T is in the panel, the presiding judge should be his senior.Hence it is R.

### Question 10

X is the set of all the students for whom the average grade point obtained was more than 3.0. How many students of the set X are there for whom the exact number of subjects in which they obtained a grade point of 5 can be determined?

4

5

3

6

#### SOLUTION

Solution :A

n(X) = 5

The candidates are X = {D, E, M, O, P}. Except O, for each other students, the information is given for at least 4 subjects. So grade point of 5th subject can be evaluated.

For O, Total grade point in remaining two subjects = 16 - 8 = 8.

There are two ways in which the two other grade points add up to 8 = 5 + 3 = 4 + 4.Hence for 'O' the same cannot determined. Hence option (a)

### Question 11

**For which of the following students, is it not possible to determine the exact number of subjects in which they obtained a grade point of 2?**

A

B

C

All of these

#### SOLUTION

Solution :D

Student A:

Total grade points (in remaining two subjects) = 10 - 4 = 6. Three possibilities exist.

(1)6 = 3 + 3

(2)6 = 4 + 2

(3) 6 = 5 + 1

Student A satisfies the given condition.

Student B:

Total grade points (in remaining three subjects) = 15 - 6 = 9. Possibilities .

(1) 9 = 3 + 3 + 3

(2) 9 = 4 + 3 + 2

(3) 9 = 5 + 3 + 1

(4) 9 = 4 + 4 + 1

Student B satisfies the condition. Hence option (d)

### Question 12

**A maximum of how many students might have obtained a grade point of 3 in at least three subjects?**

0

1

2

3

#### SOLUTION

Solution :C

The only possible Students are

1) B= 1+3+3+3+5= 15

2) F= 3+3+3+4+4=17

### Question 13

**The number of students who obtained a grade point of 1 in exactly three subjects is at least**

0

1

2

3

#### SOLUTION

Solution :A

It is possible that no student scored a grade point of 1 in exactly 3 subjects. Hence option (a)

### Question 14

The maximum percentage decrease in market share of any product in any city for company A is Enter the answer in the box below as a two digit rounded percentage number. (If the answer is 30.66%, type in 31)

#### SOLUTION

Solution :From the table, the market share of CO in Kolkata has halved. It is the only product which shows such a drastic decrease in any city.

Hence, percentage of this decrease = 50%.

### Question 15

The city in which the minimum number of products increased their market shares in 1993 to 94 is (Write the name of the city in the box below, if the city is Chennai, write : Chennai )

#### SOLUTION

Solution :It is clear from the table that the market shares only increased by two cities Mumbai and Kolkata, on the other hand, Chennai has 1, while Delhi has none. So the answer is Delhi.

### Question 16

The number of products which doubled their market shares in one or more cities is

#### SOLUTION

Solution :From the given data in the table we can say that the market share is doubled for MT in Kolkata in 1993-94. So the answer is 1.

### Question 17

**Assuming there was no stock of trinkets in India at the beginning of 1991, which of the following statements is true for 1994?**

India would have exported trinkets

India would have imported trinkets

India would have neither exported nor imported trinkets

Insufficient data

#### SOLUTION

Solution :D

Since we do not know whether the excesses each year on exported or not, we cannot comment regarding 1994.

### Question 18

**In which year was the sale of trinkets as a percentage of domestic production the highest?**

1991

1992

1993

1994

#### SOLUTION

Solution :B

We have to check only for 1992 and 1993 and by observation, we can say it is 1992.

### Question 19

**If the production in 1995 is expected to go up by 10% over that of the previous year and the sales are expected to go down by 20%, what is the excess of domestic production over the sales of trinkets in 1995?**

#### SOLUTION

Solution :D

In 1995, production = 260 × 1.1 = 286 and Consumption = 240 × 0.8 = 192

This means excess of production

=286−192192=94192≈49%

### Question 20

**If the excess/shortfall in production with respect to the sales in any year is exported/imported in the same year, then in 1993 the imports form what percentage of the sales?**

#### SOLUTION

Solution :A

Imports in 1993 = (20260)×100=7.7%

### Question 21

**If the average sales per year from 1991 to 1994 was double the sales in 1990 and the domestic production in 1990 was 15% more than the average production from 1991 to 1994. The percentage excess of domestic production over sales in 1990 was closest to**

#### SOLUTION

Solution :C

Average sales from 1991 to 1994 =8754=218.75

Thus, sales in 1990 = 109.375

Now, average production from 1991 to 1994= 230

Production in 1990=15% more= 264.5 approximately

Thus, percentage excess of domestic production over sales = 264-109 = 155

There percentage excess over 1990's sales =(155110)×100=142.2%

### Question 22

The consumer price index in Bengaluru in 2010 relative to the year 2001 was 1.75, meaning that for every Indian rupee spent on consumer goods in 2001, Rs. 1.75 on average had to be spent in 2010. In Indian rupees, what was the increase in the price of Nick tennis shoes from 2001 to 2010, if these shoes' price increased precisely according to the consumer price index?

(1) The price of Brand Nick tennis shoes was Rs. 2001 in 2010.

(2) The ratio of the rupee increase in the price of Nick tennis shoes to the price of the shoes in 2010 was 3:7.

#### SOLUTION

Solution :A

From statement 1, If we know the price in the year 2010, we can find the price in the base year and we can calculate the increase

However, the second statement does not give us any useful information other than the ratio which is already given in the question stem. Hence, the question can be answered by using the data in statement 1 alone.

### Question 23

A group of college students decide to contribute equally to the purchase of a Rs. 36 gift for their friend. How many people are in the group? (1) The number of people in the group is equal to the size of each person's contribution, in rupees. (2) If three more people joined the group, each person's individual contribution would fall by Rs.2.

#### SOLUTION

Solution :B

From statement 1 (Sufficient)

Let n be the number of people and x be the amount contributed by each person. Hence, from statement (1) n = x

Is is given that n2=36 ⇒ n=6

From statement 2(Sufficient) the new number of people is n + 3, and the new contribution is x - 2. The product will still be 36.

Now substitute in 36n for x:

Thus, we know that 36 = (n + 3)(x - 2). We also still know that 36 = nx, or 36n. Let's expand the new equation and swap out x.

36 = (n + 3)(x - 2) =nx + 3x - 2n - 6

Since nx equals 36, we can substitute in 36 for nx as follows:

36 = 36 + 3x - 2n - 6

6 = 3x - 2n

6=3(36n)−2n

6=108n−2n 2n2+6n−108=0

Solving this, n=6.

### Question 24

Who is the actress in director Beta's movie starring V?

O

M

P

O or M

#### SOLUTION

Solution :C

UVWXALPHAM/OPMO/MBETAMPNNGAMMAO/MOMM/ODELTANMPNc. P

- N is doing 2 movies with X and no movies with directors Alpha and Gamma. Thus N and X are the lead pairs in movies by director Beta and director and director Delta.
- Director Delta has 2 movies with N and 1 with M and P each.
- P has no movie with U.
- M and V have a movie with director Delta.
- => P and W are the lead pair in a movie by director Delta, so are U and N.
- Director Beta has 2 movies with N, 1 with M and 1 with P.
- P has no movie being made with U, and W has only 1 movie with P, directed by Delta
- => V and P are the lead pair in a movie by Director Beta.
- U has only one movie with N.
- => U and M are the lead pair in a movie by Director Beta and so are W and N, and X and N.
- V has 2 movies with P and Director Gamma has none with P.
- => V and P have lead pair roles in Director Alpha's movie.
- => V and O work together for Director Gamma's movie.
- W has two movies with M, most preferably with directors Alpha and Gamma.
- So, remaining are the movies of U and X with each of M and O. These movies are directed by Director Alpha and Director Gamma.

### Question 25

W and N are the lead pair in which director's movie?

Gamma

Beta

Delta

Beta or Gamma

#### SOLUTION

Solution :B

b. Beta

### Question 26

M and X are the lead pair in which director's movie?

Alpha

Gamma

Beta

Alpha or Gamma

#### SOLUTION

Solution :D

d. Alpha or Gamma

### Question 27

From the data provided, the lead pairs of how many movies can be exactly determined?

16

15

14

12

#### SOLUTION

Solution :D

d. 12

### Question 28

Who plays the lead actor opposite O in director Gamma's movie?

X

U

U and X

(V and U) or (V and X)

#### SOLUTION

Solution :D

d. (V and U) or (V and X)

### Question 29

To pass to the next level (Batch A) in a school's sports team, students in the intermediate batch (Batch B) at Premier High School have to pass both a written and a practical test. Everyone has to take the tests, and no one failed both tests. If 30% of the students of Batch B who passed the written test did not pass the practical, how many Batch B students at Premier High School go to Batch A?

(1) There are 188 Batch B students at Premier High School.

(2) 20% of the Batch B students who passed the practical test failed the written test.

if the question can be answered by using any of the statements alone but not by using the other statement alone.

if the question can be answered by using either of the statements alone.

if the question can be answered only by using both the statements together.

if the question cannot be answered

#### SOLUTION

Solution :C

For an overlapping set question, we can use a double-set matrix to organize the information and solve. The two sets in this question are the practical test (pass/fail) and the written test (pass/fail).

(1) INSUFFICIENT: If we add the total number of students to the information from the question, we do not have enough to solve for .7

x.

(2) INSUFFICIENT: If we add the fact that 20% of the

Batch B who passed thepractical testfailed the written test to the original matrix from the question, we can come up with the relationship .7x= .8y. However, that is not enough to solve for .7x.

(1) AND (2) SUFFICIENT: If we combine the two statements we get a matrix that can be used to form two relationships between

xandy:

This would allow us to solve for

xand in turn find the value of .7x, the number Batch B students who went to Batch A. The correct answer is C

### Question 30

In Green
Glen Layout last July, what was the average (arithmetic mean) home sale price?

(1) In Green
Glen Layout last July, there were 100 homes sold for a total of $51 million.

(2) In Green
Glen Layout last July, condominiums accounted for 60% of the home sales, and
the average condominium price was $450,000.

if the question can be answered by using any of the statements alone but not by using the other statement alone.

if the question can be answered by using either of the statements alone.

if the question can be answered only by using both the statements together.

if the question cannot be answered

#### SOLUTION

Solution :D

A suitable rephrase of this question is "What was thesum of the homes sale prices, and how many homes were sold?”

Statement (1):Insufficient

Seems SUFFICIENT as this statement tells us the sum of the home sale prices and the

number of homes sold. Thus, the average home price is 51,000,000/100=510,000.

But we are not sure how many homes were there overall (may be more than 100). So

INSUFFICIENT.

Statement (2) INSUFFICIENT:

This statement tells us the average condominium price, but not all of

the homes sold in Green Glen Layout last July were condominiums. From this statement, we don't know anything about the other 40% of homes sold in Green Glen Layout, so we cannot calculate theaverage home sale price

We have some information about the ratio of number of condominiums to noncondominiums

sold, 60%:40%, or 6:4, or 3:2, which could be used to pick working

numbers for the total number of homes sold. However, the average still cannot be

calculated because we don't have any information about the non-condominium prices.The correct answer is option (d)

### Question 31

Last year, the five employees of Alpha Ltd. took an average of 16 vacation days each. What was the average number of vacation days taken by the same employees this year?

(1) Three employees had a 50% increase in their number of vacation days, and two employees had a 50% decrease.

(2) Three employees had 10 more vacation days each, and two employees had 5 fewer vacation days each.

if the question can be answered by using any of the statements alone but not by using the other statement alone.

if the question can be answered by using either of the statements alone.

if the question can be answered only by using both the statements together.

if the question cannot be answered

#### SOLUTION

Solution :A

number of vacation days by the number of employees. Since we know the total number of

employees, we can rephrase the question as: How many total vacation days did the

employees of Alpha Ltd. take this year?

(1) INSUFFICIENT: Since we don't know the specific details of how many vacation days

each employee took the year before, we cannot determine the actual numbers that a 50%

increase or a 50% decrease represent. For example, a 50% increase for someone who took

40 vacation days last year is going to affect the overall average more than the same

percentage increase for someone who took only 4 days of vacation last year.

(2) SUFFICIENT: If three employees took 10 more vacation days each, and two employees

took 5 fewer vacation days each, then we can calculate how the number of vacation days

taken this year differs from the number taken last year:

(10 more days/employee)(3 employees) - (5 fewer days/employee)(2 employees) = 30

days - 10 days = 20 days

20 additional vacation days were taken this year.

In order to determine the total number of vacation days taken this year (i.e., in order to

answer the rephrased question), we need to determine the number of vacation days taken

last year. The 5 employees took an average of 16 vacation days each last year, so the total

number of vacation days taken last year can be determine by taking the product of the two:

(5 employees)(16 days/employee) = 80 days

80 vacation days were taken last year. Hence, the total number of vacation days taken

this year was 100 days.

Note: It is not necessary to make the above calculations -- it is simply enough to know that

you have enough information in order to do so (i.e., the information given is sufficient)!

### Question 32

All the 6 sides of a cube are colored. Now this cube is broken into smaller cubes, witheach side 14 the size of the side of the larger cube. How many of the smaller cubes will have all three sides colored?

4

8

6

cannot be determined

#### SOLUTION

Solution :B

Eight. At corners of the cube.