# Free DI and LR Practice Test - CAT

### Question 1

**The athletes from FRG and USA decided to run a 4 × 100 m relay race for their respective countries with the country having three athletes borrowing the athlete from CZE. Assume that all the athletes ran their stretch of the relay race at the same speed as in Decathlon event. How much more time did the FRG relay team take as compared to the USA team?**

0.18

0.27

0.78

0.00

#### SOLUTION

Solution :B

Total time taken by FRG team = (10.95 + 10.85 + 10.58 + 10.72) = 43.10

Total time taken by USA team = (10.78 + 10.75 + 10.94 + 10.36) = 42.83Difference = 0.27.

### Question 2

**What is the least that Daisy Thompson must get in Score 2 that ensures him a bronze medal?**

5309

5296

5271

5270

#### SOLUTION

Solution :B

First ranked person has a total score of 8905 and second ranked person has a score of 8897. Therefore he must get a score of greater than 8880 but less than 8897. Presently he is scoring 582 + 3003 = 3585. Therefore, if he gets a score of 5296, his total score would become 3585 + 5296 = 8881, which would ensure him a bronze medal.

### Question 3

The number of commodities that experienced a price decline for two or more consecutive year is

#### SOLUTION

Solution :The commodities that experienced a price decline for and two or more consecutive year were rice, egg, onion, dal and chilies.

### Question 4

**For which commodities did a price increase immediately follow a price decline only one is this period?**

#### SOLUTION

Solution :C

The given condition is satisfied only for the commodity onion.

### Question 5

**The cost in rupees per tonne of oil moved by rail and road happens to be roughly**

3

1.5

4.5

4.8

#### SOLUTION

Solution :B

Volume transported by rail and road = (22 + 9) = 31% of 12 = 3.72 million tones

Cost of transportation by rail and road = (12 + 6) = 18% of 30 = Rs 5.4 million.⇒Cost in Rs per tonne = 5.43.72= 1.45 or 1.5

### Question 6

**From the charts given, it appears that the cheapest mode of transport is**

Road

Rail

Pipeline

Ship

#### SOLUTION

Solution :A

Cheapest mode of transportation has least cost per tonne

Road = 622= 0.27, Rail = 129 = 1.33, Pipeline = 6549= 1.32, Ship = 109= 1.11It is clear that cheapest made of transportation is Road.

### Question 7

What is the simple annual growth rate of patients from 2007 to 2010?

#### SOLUTION

Solution :(500−200)200 × 1003 = 50%

### Question 8

**What is the ratio of Doctors in 2007 to nurses in 2010?**

43 : 28

2 : 1

10 : 7

2 : 5

#### SOLUTION

Solution :A

430: 280= 43: 28.

### Question 9

In which year the percentage increase in the number of females over the previous year is the highest?

1996

1999

2004

2005

#### SOLUTION

Solution :D

### Question 10

**In 2002, if the ratio of number of educated males to professionally educated females was 5:4. If the number of educated males increased by 25% in 2003. What is the percentage change in number of uneducated females in 2003?**

+25%

+30%

+34%

+56%

#### SOLUTION

Solution :D

Number of educated people in 2002 = 545 million

Number of educated female in 2002

49 × 545 million= 242.22 million

Number of uneducated female in 2002 = 107.78 million

Number of educated male in 2002

59 × 545 million = 302.78 million

Number of educated male in 2003 = 378.475 million

Number of educated female in 2003 = 181.525 million

Number of uneducated female in 2003 = 168.475 million

Hence, required percentage change

60.695107.78 × 100 = 56%

### Question 11

**In the year 2005, total production living in urban area is equal to sixty eight percent of educated population. The ratio of number of people living in urban areas to people living in rural areas is 43:12 in 2010. What is the ratio of the rural population in 2005 to that in 2010?**

0.8

0.47

2.05

None of these

#### SOLUTION

Solution :C

Population living in urban area in 2005 = 0.68 × 600 = 408 million.

Population living in rural area in 2005 = 492 million.

Rural population in 2010 = 1255 × 1100 = 240 millionHence, required ratio = 492240 = 2.05

### Question 12

The average mark obtained by all students in Electric Machines is

#### SOLUTION

Solution :Subjects→Students↓Signal and SystemsElectric MachinesPower ElectronicsControl SystemAnalog ElectronicNetwork AnalysisTotal MarksA243018607548255B216060459052328C1772395810560351D156645805168325E207860646072354F198445786664356Total marks116390267385447364Average marks = 3906 = 65

### Question 13

**What is the approximate percentage marks obtained by D in all the subjects together?**

45.5%

60.5%

56.5%

50.6%

#### SOLUTION

Solution :C

Subjects→Students↓Signal and SystemsElectric MachinesPower ElectronicsControl SystemAnalog ElectronicNetwork AnalysisTotal MarksA243018607548255B216060459052328C1772395810560351D156645805168325E207860646072354F198445786664356Total marks116390267385447364

Percentage marks = 325575× 100 = 56.52%

### Question 14

**The total marks obtained by E in "Network Analysis” and "Control System”are what percent more than the total marks obtained by B in "Signal and Systems” and "Power Electronics”?**

77.9%

70.9%

60.9%

67.9%

#### SOLUTION

Solution :D

Subjects→Students↓Signal and SystemsElectric MachinesPower ElectronicsControl SystemAnalog ElectronicNetwork AnalysisTotal MarksA243018607548255B216060459052328C1772395810560351D156645805168325E207860646072354F198445786664356Total marks116390267385447364

Percentage increase = 5581 × 100 = 67.9%

### Question 15

**If any student gets more than 60 marks in Electric Machines and more than 75 marks in Analog Electronic, he can get 100% scholarship. How many students will get 100% scholarship?**

One

Two

Three

Four

#### SOLUTION

Solution :A

Subjects→Students↓Signal and SystemsElectric MachinesPower ElectronicsControl SystemAnalog ElectronicNetwork AnalysisTotal MarksA243018607548255B216060459052328C1772395810560351D156645805168325E207860646072354F198445786664356Total marks116390267385447364

Only C got more than 60 marks in Electric Machines and more than 75 marks in Analog Electronic

### Question 16

Which of the following statement(s) is/are correct?

I. Chandan and Dinesh gave a presentation on Classroom learning vs experiential learning on Friday and Tuesday respectively.

II. Anil and Eklavya gave a presentation on Time management and The Lehmann Crash respectively on Tuesday.

Only I

Only II

Both I and II

Neither I nor II

#### SOLUTION

Solution :D

Let the five students be A,B,C,D and E. We can make a table based on the given conditions(Once the initial conditions are met, we just need to ensure that each one of A,B,C,D and E are present in every row and column, without overlap, highlighted ones are given in the question)

### Question 17

On which topic did Eklavya give a presentation on Friday?

Classroom learning vs experiential learning

Business & Ethics

Time Management

Cannot be determined

#### SOLUTION

Solution :B

Let the five students be A,B,C,D and E. We can make a table based on the given conditions (Once the initial conditions are met, we just need to ensure that each one of A,B,C,D and E are present in every row and column, without overlap, highlighted ones are given in the question)

### Question 18

On which day of the week did Anil give a presentation on Globalization?

Friday

Thursday

Saturday

Cannot be determined

#### SOLUTION

Solution :B

Let the five students be A,B,C,D and E. We can make a table based on the given conditions (Once the initial conditions are met, we just need to ensure that each one of A,B,C,D and E are present in every row and column, without overlap, highlighted ones are given in the question)

### Question 19

On which day of the week did Dinesh give a presentation on Time Management?

Friday

Thursday

Saturday

Monday

#### SOLUTION

Solution :A

Let the five students be A,B,C,D and E. We can make a table based on the given conditions (Once the initial conditions are met, we just need to ensure that each one of A,B,C,D and E are present in every row and column, without overlap, highlighted ones are given in the question)

### Question 20

If F is not selected to attend the retirement dinner, then exactly how many different groups of four are there each of which would be an acceptable selection?

One

Two

Three

Four

#### SOLUTION

Solution :C

Since the second condition states "either E or F must be selected...," we can infer from the new supposition (F is not selected) and the second condition (either E or F, but not both, is selected) that E is selected. And since E is selected, we know from the third condition that C is selected. In other words every acceptable selection must include both C and E.

We are now in a good position to enumerate the groups of four which would be acceptable selections. The first condition specifies that either A or B, but not both, must be selected. So you need to consider the case where A (but not B) is selected and the case in which B (but not A) is selected. Let's first consider the case where A (but not B) is selected. In this case, G is not selected, since the fourth condition tells you that if B is not selected, then G cannot be selected either. Since exactly four people must be selected, and since F, B, and G are not selected, D, the only remaining person, must be selected. Since D's selection does not violate any of the conditions or the new supposition, E, C, A, and D is an acceptable selection; in fact, it is the only acceptable selection when B is not selected. So far we have one acceptable selection, but we must now examine what holds in the case where B is selected.

Suppose that B is selected. In this case A is not selected, but G may or may not be selected. If G is selected, it is part of an acceptable selection -- E, C, B, and G. If G is not selected, remembering that A and F are also not selected, D must be selected. This gives us our final acceptable selection -- E, C, B, and D.

Thus there are exactly three different groups of four which make up acceptable selections, and (C) is the correct option.

### Question 21

There is only one acceptable group of four that can be selected to attend the retirement dinner if which one of the following pairs of people is selected?

C and G

B and D

D and G

C and E

#### SOLUTION

Solution :C

AECD

AFCD

BECD

BECG

BFCD

BFCG

BFDG

### Question 22

If the gymnasts march immediately ahead of the veterans, then which one of the following could be the fourth group?

Gymnasts

musicians

puppeteers

veterans

#### SOLUTION

Solution :D

Only two conditions are possible because we know "exactly one group marches behind the fire-fighters but ahead of the veterans." And Gymnasts can occupy either 3rd or 5th place.

1st2nd3rd4th5th6thFire-fightersGymnastsVeteransFire-fightersGymnastsVeterans

### Question 23

If the jugglers are the fifth group, then which one of the following must be true?

The musicians are the sixth group

The fire-fighters are the first group

The veterans are the second group

The gymnasts are the third group

#### SOLUTION

Solution :A

Only two conditions are possible because we know At least two groups march behind the puppeteers but ahead of the musicians.

1st2nd3rd4th5th6thPuppeteersFire-fightersGymnastsVeteransjugglersmusiciansGymnastsfire-FightersPuppeteersVeteransJugglersMusicians

### Question 24

Which one of the following groups CANNOT march immediately behind the gymnasts?

fire-fighters

jugglers

musicians

puppeteers

#### SOLUTION

Solution :B

Only Jugglers group cannot march immediately behind the gymnasts

### Question 25

What is the highest percentage decrease over the preceding year in the automobile production? (Write your answer till 2^{nd} decimal place. For e.g 2.03)

#### SOLUTION

Solution :Total Automobile Production is as follows:

Year 2004: 800 + 500 + 475 = 1775

Year 2005: 700 + 550 + 450 = 1700

Year 2006: 1025 + 675 + 475 = 2175

Year 2007: 1200 + 650 + 475 = 2325

Year 2008: 1250 + 600 + 350 = 2200

2005 and 2008 show a decrease in automobile production.

Percentage decrease for 2005 = 1775−17001775 × 100 = 4.23%

Percentage decrease for 2008 = 2325−22002325 × 100 = 5.38%

### Question 26

If the ratio of the domestic sale price of a commercial vehicle, a passenger vehicle, and a three wheeler is 5:3:2 then what percent of earnings (approximately to nearest natural number) is contributed by commercial vehicle segment to the overall earnings from domestic sales during the period 2004-2008?

#### SOLUTION

Solution :Total domestic sale for the year 2004-2008:

Commercial vehicles: 450 + 500 + 625 + 600 + 550 = 2725

Passenger vehicles: 700 + 675 + 900 + 1050 + 975 = 4300

Three wheelers: 300 + 350 + 400 + 375 + 350 = 1775

∴ Ratio of the total sale price of commercial vehicles, passenger vehicles and three wheelers = (5 × 2725) : (3 × 4300) : (2 × 1775)

Contribution of commercial vehicles to the overall earnings = (5×2725)(5×2725)+(3×4300)+(2×1775) ×100 ≈ 45%

### Question 27

Which year exhibited highest percentage increase over the preceding year in the automobile sales?

#### SOLUTION

Solution :Sales is as follows:

Year 2004 = 1450

Year 2005 = 1525

Year 2006 = 1925

Year 2007 = 2025

Year 2008 = 1875

### Question 28

Who among them is lying?

Vinita

Sunita

Amita

cannot be determined

#### SOLUTION

Solution :A

Let us assume that Amita is lying and Sunita and Vinita are telling the truth

Then Sunita is not the youngest => from Vinita's 2nd statement, Vinita is not the eldest.

Since Amita is lying, so from her 3rd statement, Amita is not the eldest.

Now, since Sunita is not the youngest and Vinita is elder to Sunita => Sunita is not the eldest.

Also, since, Amita is not the eldest => Vinita has to be the eldest.

But, from her 2nd statement, Vinita is not the eldest; so, our assumption is incorrect

as per our assumption Sunita isn't lying which means our assumption is incorrect.

Let us assume that Sunita is lying and Amita and Vinita are telling the truths.

Then, from Amita's 1st statement, Sunita is the youngest. Since, Sunita is lying so, from Sunita's 2nd statement, Vinita is not elder to her, so this means that Vinita is either of the same age as her or younger than her. From Vinita's 1st statement, Sunita cannot be of the same age as Vinita => Sunita should be elder than Vinita but also Sunita is the youngest => contradiction => our assumption is incorrect => Sunita isn't lying.

Since, neither Amita nor Sunita is lying => Vinita must be lying.

Vinita is lying and Sunita and Amita are telling the truths.

Sunita is the youngest and all are above 24 years of age and Vinita is elder to Sunita. So, the least possible age for Sunita is 25 years and Amita and Vinita are more than 25 years of age => as per Sunita's 1st statement, Vinita is 26 years old.

Since, Vinita is lying and Sunita is the youngest, so from her 2nd statement, Vinita is not the eldest => Amita is the eldest. Since, Vinita is 26 years of age and Vinita is elder to Sunita and the least possible age for Sunita is 25 years => Sunita is 25 years of age.

Amita is the eldest.

### Question 29

What is Amita's age?

25

26

28

22

#### SOLUTION

Solution :C

Let us assume that Amita is lying and Sunita and Vinita are telling the truth

Then Sunita is not the youngest => from Vinita's 2nd statement, Vinita is not the eldest.

Since Amita is lying, so from her 3rd statement, Amita is not the eldest.

Now, since Sunita is not the youngest and Vinita is elder to Sunita => Sunita is not the eldest.

Also, since, Amita is not the eldest => Vinita has to be the eldest.

But, from her 2nd statement, Vinita is not the eldest; so, our assumption is incorrect

as per our assumption Sunita isn't lying which means our assumption is incorrect.Let us assume that Sunita is lying and Amita and Vinita are telling the truths.

Then, from Amita's 1st statement, Sunita is the youngest. Since, Sunita is lying so, from Sunita's 2nd statement, Vinita is not elder to her, so this means that Vinita is either of the same age as her or younger than her. From Vinita's 1st statement, Sunita cannot be of the same age as Vinita => Sunita should be elder than Vinita but also Sunita is the youngest => contradiction => our assumption is incorrect => Sunita isn't lying.Since, neither Amita nor Sunita is lying => Vinita must be lying.

Vinita is lying and Sunita and Amita are telling the truths.

Sunita is the youngest and all are above 24 years of age and Vinita is elder to Sunita. So, the least possible age for Sunita is 25 years and Amita and Vinita are more than 25 years of age => as per Sunita's 1st statement, Vinita is 26 years old.

Since, Vinita is lying and Sunita is the youngest, so from her 2nd statement, Vinita is not the eldest => Amita is the eldest. Since, Vinita is 26 years of age and Vinita is elder to Sunita and the least possible age for Sunita is 25 years => Sunita is 25 years of age.

Amita is the eldest.

### Question 30

What is Sunita's age?

24

25

26

cannot be determined

#### SOLUTION

Solution :B

Let us assume that Amita is lying and Sunita and Vinita are telling the truth

Then Sunita is not the youngest => from Vinita's 2nd statement, Vinita is not the eldest.

Since Amita is lying, so from her 3rd statement, Amita is not the eldest.

Now, since Sunita is not the youngest and Vinita is elder to Sunita => Sunita is not the eldest.

Also, since, Amita is not the eldest => Vinita has to be the eldest.

But, from her 2nd statement, Vinita is not the eldest; so, our assumption is incorrect

as per our assumption Sunita isn't lying which means our assumption is incorrect.Let us assume that Sunita is lying and Amita and Vinita are telling the truths.

Then, from Amita's 1st statement, Sunita is the youngest. Since, Sunita is lying so, from Sunita's 2nd statement, Vinita is not elder to her, so this means that Vinita is either of the same age as her or younger than her. From Vinita's 1st statement, Sunita cannot be of the same age as Vinita => Sunita should be elder than Vinita but also Sunita is the youngest => contradiction => our assumption is incorrect => Sunita isn't lying.Since, neither Amita nor Sunita is lying => Vinita must be lying.

Vinita is lying and Sunita and Amita are telling the truths.

Sunita is the youngest and all are above 24 years of age and Vinita is elder to Sunita. So, the least possible age for Sunita is 25 years and Amita and Vinita are more than 25 years of age=> as per Sunita's 1st statement, Vinita is 26 years old.

Since, Vinita is lying and Sunita is the youngest, so from her 2nd statement, Vinita is not the eldest => Amita is the eldest. Since, Vinita is 26 years of age and Vinita is elder to Sunita and the least possible age for Sunita is 25 years => Sunita is 25 years of age.

Amita is the eldest.

### Question 31

What is Vinita's age?

24

26

cannot be determined

#### SOLUTION

Solution :B

Let us assume that Amita is lying and Sunita and Vinita are telling the truth

Then Sunita is not the youngest => from Vinita's 2nd statement, Vinita is not the eldest.

Since Amita is lying, so from her 3rd statement, Amita is not the eldest.

Now, since Sunita is not the youngest and Vinita is elder to Sunita => Sunita is not the eldest.

Also, since, Amita is not the eldest => Vinita has to be the eldest.

But, from her 2nd statement, Vinita is not the eldest; so, our assumption is incorrect

as per our assumption Sunita isn't lying which means our assumption is incorrect.

Let us assume that Sunita is lying and Amita and Vinita are telling the truths.

Then, from Amita's 1st statement, Sunita is the youngest. Since, Sunita is lying so, from Sunita's 2nd statement, Vinita is not elder to her, so this means that Vinita is either of the same age as her or younger than her. From Vinita's 1st statement, Sunita cannot be of the same age as Vinita => Sunita should be elder than Vinita but also Sunita is the youngest => contradiction => our assumption is incorrect => Sunita isn't lying.

Since, neither Amita nor Sunita is lying => Vinita must be lying.

Vinita is lying and Sunita and Amita are telling the truths.

Sunita is the youngest and all are above 24 years of age and Vinita is elder to Sunita. So, the least possible age for Sunita is 25 years and Amita and Vinita are more than 25 years of age=> as per Sunita's 1st statement, Vinita is 26 years old.

Since, Vinita is lying and Sunita is the youngest, so from her 2nd statement, Vinita is not the eldest => Amita is the eldest. Since, Vinita is 26 years of age and Vinita is elder to Sunita and the least possible age for Sunita is 25 years => Sunita is 25 years of age.

Amita is the eldest.

### Question 32

Ms. Jasmine likes to let her students choose who their partners will be; however, no pair of students may work together more than seven class periods in a row. "A” and "B” have studied together seven class periods in a row. "C” and "D” have worked together three class periods in a row. "C” does not want to work with "A”. Who should be assigned to work with "B”?

"C”

"A”

"D”

Cannot be determined

#### SOLUTION

Solution :A

"B” should be assigned to study with "C”. "B” cannot be assigned with "A”, because they have already been together for seven class periods. If "B” is assigned to work with "D”, that would leave "A” with "C”, but "C” does not want to work with "A”