# Free DI and LR Practice Test - CAT

### Question 1

Fulham lost its game with a Scoreline (GF-GA) of

0-1

1-2

1-3

2-3

#### SOLUTION

Solution :A

Fulham scored 3 goals 1 each of the drawn games and 3 goals were scored against them 1 each for 3 drawn games.

Hence it must have lost a game 0-1 because the number of goals scored against Fulham is 4 and goals scored by fulham are 3.

### Question 2

How many goals has Chelsea scored in its 4 games?

2

3

6

4

#### SOLUTION

Solution :D

The goal difference of all teams must add up to 0.Hence GD of Chelsea = -2

If 6 goals have been scored against it, it must have scored 4 goals.

### Question 3

How many games have been played till now?

20

12

10

7

#### SOLUTION

Solution :B

There are 24 entries against matches played. But in a match there are 2 teams participating hence there is a entry against each team and hence counted twice. This means in all 242=12 matches played.

### Question 4

Find the number of goals scored in the game between Chelsea and Sunderland.

4

1

2

3

#### SOLUTION

Solution :D

Sunderland scored 3 goals 1 each of the drawn games and 3 goals were scored against them 1 each for 3 drawn games.

Hence it must have lost a game 1 - 2 because the number of goals scored against Sunderland is 5 and goals scored by Sunderland are 4.Therefore Sunderland lost its game to Chelsea 1 - 2. Hence number of goals scored in this game is 3.

### Question 5

**Which of the following teams did Aston villa beat?**

#### SOLUTION

Solution :B

Aston villa draws against Chelsea and Chelsea beats Sunderland.

Hence both Manchester United and Birmingham City must have beaten Chelsea. So Aston villa must beat Fulham.

### Question 6

What is the maximum possible aggregate amount that could have been spent at the college canteen by all the mentioned four students?

Rs. 85

Rs. 86

Rs. 87

Rs. 88

Rs. 89

#### SOLUTION

Solution :B

The max possible amount will be with following combination:

(6,5.5), (6,5), (6,4) & (5.5,5)

And the total maximum amount is 86.

### Question 7

If the total amount spent by C is more than D but less than B, then what is the possible list of items that C could have had at the canteen?

P, S

P, Q

P, R

Either (1) or (3)

#### SOLUTION

Solution :D

The total amount spent by C is more than D (20) but less than B(23). Which means that the total amount spent by C can be either 21 i.e. P and R or 22 i.e. S and P. Hence, option (d) is the correct choice.

### Question 8

How many students out of the four mentioned students had 'S' at the canteen?

1

2

3

Cannot be determined

#### SOLUTION

Solution :D

From the given data, it is confirmed that 2 people B and D definitely had S. Also A did not have S but we cannot say anything about C and therefore, either 2 friends or 3 friends would have had S. Hence, option (d), i.e. Cannot be determined is the correct choice.

### Question 9

If A spent a total of Rs. 21, then which of the following items A could have had at the canteen?

R, S

R, P

P, S

Q, S

#### SOLUTION

Solution :B

A could have had R and P as 2R+2P=21.

Option (b)

### Question 10

Two of the exams fall on

Monday

Tuesday

Friday

Saturday

#### SOLUTION

Solution :D

There can be two cases for the scheduled day of exams, since on every unique day of the week, there is atleast one exam:

Case I: Mon Tue Thur Sat Mon Wed Fri

This is not possible as exams end on Saturday.Case IIMonWedFriSatTueThursSatPhyChemCompBioMathEcoEngOrChemCompPhy/MathBioEngEcoMath/PhyOrEngEconMathBioChemCompPhyOrPhy/MathEcoEngBioMath/PhyChemComp

The filling is done in sequence

Bio ¦ (Chem, comp) ¦ _ _ _

So the correct options are (d), (a), (a) (b) and (b) respectively.

### Question 11

How many days are between the schedules of English and Economics?

1

2

4

cannot be determined

#### SOLUTION

Solution :A

There can be two cases for the scheduled day of exams, since on every unique day of the week, there is atleast one exam:

Case I: Mon Tue Thur Sat Mon Wed Fri

This is not possible as exams end on Saturday.

Case IIMonWedFriSatTueThursSatPhyChemCompBioMathEcoEngOrChemCompPhy/MathBioEngEcoMath/PhyOrEngEconMathBioChemCompPhyOrPhy/MathEcoEngBioMath/PhyChemComp

### Question 12

How many days are between the schedules of Economics and Biology?

2

4

5

cannot be determined

#### SOLUTION

Solution :A

There can be two cases for the scheduled day of exams, since on every unique day of the week, there is atleast one exam:

Case I: Mon Tue Thur Sat Mon Wed Fri

This is not possible as exams end on Saturday.

Case IIMonWedFriSatTueThursSatPhyChemCompBioMathEcoEngOrChemCompPhy/MathBioEngEcoMath/PhyOrEngEconMathBioChemCompPhyOrPhy/MathEcoEngBioMath/PhyChemComp

### Question 13

The schedule of which of the following subjects can be uniquely determined?

English

Biology

Economics

none of these

#### SOLUTION

Solution :B

Case I: Mon Tue Thur Sat Mon Wed Fri

This is not possible as exams end on Saturday.

### Question 14

In how many different ways, the schedule of all exams are possible?

4

6

7

8

#### SOLUTION

Solution :B

Case I: Mon Tue Thur Sat Mon Wed Fri

This is not possible as exams end on Saturday.

### Question 15

The number of cars sold in the D segment is same as the number of cars sold by which of the following manufacturers?

P

Q

R

S

#### SOLUTION

Solution :C

Let the numbers of cars sold by different manufactures is as shown below.

P - a

Q - b

R - c

S - d

T - e

PQRSTB0.24a0.16b0.32c0.24d0.28eB+0.16a0.24b0.10c0.16d0.08eC0.18a0.24b0.15c0.32d0.12eD0.36a0.20b0.35c0.24d0.48eE0.06a0.16b0.08c0.04d0.04e

Let the numbers of cars sold by different segments is as shown below.

B - v

B+ - w

C - x

D - y

E - z

BB+CDEP0.15v0.20w0.15x0.18y0.15zQ0.05v0.15w0.10x0.05y0.20zR0.40v0.25w0.25x0.35y0.40zS0.225v0.30w0.40x0.18y0.15zT0.175v0.10w0.10x0.24y0.10z

From the above two tables, we can say that number of cars sold in the D segment is same as the number of cars sold by manufacture R.

### Question 16

What is the ratio of number of cars sold by Q to that of T?

2:3

1:2

3:4

4:9

#### SOLUTION

Solution :B

Let the numbers of cars sold by different manufactures is as shown below.

P - a

Q - b

R - c

S - d

T - e

PQRSTB0.24a0.16b0.32c0.24d0.28eB+0.16a0.24b0.10c0.16d0.08eC0.18a0.24b0.15c0.32d0.12eD0.36a0.20b0.35c0.24d0.48eE0.06a0.16b0.08c0.04d0.04e

Let the numbers of cars sold by different segments is as shown below.

B - v

B+ - w

C - x

D - y

E - z

BB+CDEP0.15v0.20w0.15x0.18y0.15zQ0.05v0.15w0.10x0.05y0.20zR0.40v0.25w0.25x0.35y0.40zS0.225v0.30w0.40x0.18y0.15zT0.175v0.10w0.10x0.24y0.10z

From the above two tables, the ratio of number of cars sold by Q to that of T is 1:2.

### Question 17

What is the ratio of number of cars sold by S in the E segment to that of P in the B segment?

1:4

1:3

2:5

5:6

#### SOLUTION

Solution :A

Let the numbers of cars sold by different manufactures is as shown below.

P - a

Q - b

R - c

S - d

T - e

PQRSTB0.24a0.16b0.32c0.24d0.28eB+0.16a0.24b0.10c0.16d0.08eC0.18a0.24b0.15c0.32d0.12eD0.36a0.20b0.35c0.24d0.48eE0.06a0.16b0.08c0.04d0.04e

Let the numbers of cars sold by different segments is as shown below.

B - v

B+ - w

C - x

D - y

E - z

BB+CDEP0.15v0.20w0.15x0.18y0.15zQ0.05v0.15w0.10x0.05y0.20zR0.40v0.25w0.25x0.35y0.40zS0.225v0.30w0.40x0.18y0.15zT0.175v0.10w0.10x0.24y0.10z

From the above two tables, the ratio of number of cars sold by S in the E segment to that of P in the B segment is 1:4.

### Question 18

Which were the two houses that played the finals?

#### SOLUTION

Solution :B

Red and Blue

### Question 19

How many matches did Red house win in the first round?

4

1

2

3

#### SOLUTION

Solution :D

Red will win 3 matches in the first round

### Question 20

Which house stood 5th at the tournament?

#### SOLUTION

Solution :D

gray house stands 5th

### Question 21

What is the difference between the no of matches won by team ranked 1 and team ranked 4 in the entire tournament?

#### SOLUTION

Solution :B

b.difference between number of matches won by blue house and yellow house

= 6 - 4 = 2

### Question 22

What is the difference between the final standings of Blue house and Gray house?

1

2

3

4

#### SOLUTION

Solution :D

4

### Question 23

**How many extra pen drives does Cyrus usually sell every month?**

10

50

35

20

#### SOLUTION

Solution :B

Cyrus generally sells 50 drives extra every month. Option b

Similarly, Diya sells 10 extra drives every month.

In March, either 35 extra drives are sold instead of 20 or 50 extra dries are sold instead of 35.

If, 35 extra drives were sold instead of 20, the total number of drives would be

500+520+555+(555+20)+(555+40).......

= 1020+10/2(2*555+9*20)=7470

But noone has sold 7470 drives by the end of the year. If 50 extra drives were sold instead of 35, the total number of drives would be

500+535+585+(585+35)+(585+70)...= 8460 drives

Arundati generally sells 35 extra drives and 50 drives instead of 35 are sold in March. Similarly, Bhavna generally sells 20 extra drives and sells 35 extra drives instead of 20 in October and Diya generally sells 10 extra drives and sells 20 extra drives instead of 10 in July

### Question 24

How many pen drives did Arundati sell till the end of April?

#### SOLUTION

Solution :B

Arundati sold 500+535+585+620= 2240 drives by april. Option b

### Question 25

How many extra pen drives does Diya usually sell every month as compared to the previous month?

10

50

35

20

cannot be determined

#### SOLUTION

Solution :A

Diya usually sold 10 extra drives every month. option a

### Question 26

Had there been no anomaly in the selling patterns of the four, how many pen drives more/less would the four together sell in the year?

50

65

70

55

60

#### SOLUTION

Solution :B

Had there been no anomaly, the four would have sold 9300+8310+660+7320=31590 pen drives in a year. But they sell 8460+7365+8980+6720= 31525 drives in the year. Thus they sold 65 drives less. Option b

### Question 27

How many pen drives did Cyrus sell in the month of March?

500

600

650

625

660

#### SOLUTION

Solution :B

Cyrus sold 50 extra drives every month and showed an anomaly in May. He sold 500+50+50=600 cards in March, option b

### Question 28

How many high school educated people do not play football?

#### SOLUTION

Solution :Number of high school education who do not play football

5+(x−6)2=10

### Question 29

How many people having middle school, but not high school, education play only football ?

#### SOLUTION

Solution :Number of people having middle school education but not high school education who play only football =(x−6)2=11.

### Question 30

The Stock broker in the Dalal street shop sells two kinds of shares: T32 and V45. Each investor buys exactly one share. If there were 300 investors yesterday, what fraction of V45 sold yesterday were bought by female investors?

1. 12 of all shares sold yesterday were T32 and 13 of all investors yesterday were male.

2. Yesterday, twice as many T32 were bought by females as there were V45 bought by males.

#### SOLUTION

Solution :C

Statement (1):Insufficient. From the first statement we know that 150 shares and 150 T32 are sold the previous day.

M F Total T 150(1/2 OF 100)V 150Total100200300

(1/3 of 300)

Statement (2): INSUFFICIENT:

M F Total T 2x Vx Total 300

(1/3 of 300)

Statement (2): INSUFFICIENT.

M F Total T 2x150Vx 150Total 100200300

we still cannot find out what is asked

Statements (1) and (2) together: SUFFICIENT. Combining the tables above, we get the following:

Thus, 2x + (150 - x) = 200

x + 150 = 200

x= 50 and the chart can be completed as follows

M F Total T50100150V50100150Total 100200300

### Question 31

Given that p and q belong to a set of natural numbers

If set S = {7, q , 12, 8, p , 9}, is p + q greater than 18?

(1) The range of set S is less than 9.

(2) The average of p and q is less than the average of set S.

#### SOLUTION

Solution :B

(1) INSUFFICIENT: Statement (1) tells us that the range of S is less than 9. The range of a set is the positive difference between the smallest term and the largest term of the set. We cannot get a definite answer from this data

Let p = 7 and q = 7. The range ofSis less than 9 and p + q < 18, so we conclude YES.

Let p = 10 and q = 10. The range of S is less than 9 and p + q > 18, so we conclude NO.Because this statement does not allow us to answer definitively Yes or No, it is insufficient.

(2) SUFFICIENT: Statement (2) tells us that the average of p and q is less than the average of the set S. Writing this as an inequality:

p+q2<7+8+9+12+p+q6

p+q2<36+p+q6

3(p+q)<36+(p+q)

2(p+q)<36

p+q<18Therefore, statement (2) is SUFFICIENT to determine whether p + q > 18.

### Question 32

Vaidehi's teacher asks her to find out the average(Arithmetic Mean) of 3 integers x,y and z, given that x

1. (x + y)z = 5

2. (x + z) < 3

#### SOLUTION

Solution :D

We get two values even on combining both cases.

Case 1: x = -3, y = 4, z = 5 x + z = 2 < 3 x + y + z = 6

Case 2: x = -3, y = -2, z = -1 x + z = -4 < 3 x + y + z = -6Hence both statements together are also insufficient