# Free DI and LR - 02 Practice Test - CAT

What was India’s total score in the innings?

A. 360
B. 384
C. 400
D. 420

#### SOLUTION

Solution : C

The answer is fastest obtained by the process of elimination. Lets take for example, that 360 is the total, then saurav will score 54 runs, this implies that the number of 4’s he scores will not be an integral number (1403×54(4×100)) which is not integral. Similarly, the other options can be eliminated. 400 will be the total score

The number of 6’s scored by Sehwag in the innings is

A.

4

B.

3

C.

2

D.

5

#### SOLUTION

Solution : B

Once the total score is obtained as 400 the score table will look as follows.

PLAYERSCORESaurav60Sehwag40Sachin160Rahul80Others60

Number of 6’s scored by Sehwag= 45100×40= 186 = 3

The number of 4’s scored by Rahul in the innings is

A. 7
B. 6
C. 10
D. 8

#### SOLUTION

Solution : D

The number of 4’s scored by Rahul in the innings is, 40100 × 80 = 324 = 8

The total number of 6’s scored by India in the innings is

A.

14

B.

13

C.

10

D.

12

#### SOLUTION

Solution : A

The table is obtained as follows

PLAYERNo of 6'sSaurav1Sehwag3Sachin4Rahul2Others4

Total= 14

At most how many players of the Indian team could have failed to score any  runs in the innings , given that there were a total of 11 players in the team?

A. 3
B. 6
C. 5
D. 4

#### SOLUTION

Solution : C

Out of 11 players, 4 are top-scorers means that 7 players together can score a maximum of 39 each. Score left to distribute among 7 players= 60, can be distributed among 2 players, hence 7-2=5 will the max no. of players who will not score any runs

How many vehicles which were charged for parking were in the parking lot in the year 2003 ?

A.

65200

B.

71450

C.

80980

D.

none of these

#### SOLUTION

Solution : D

All vehicles other than others pay a parking fee.
2 wheelers = 14% of 200000 = 28000
3 wheelers = 17% of 50000 = 8500
Cars = 18% of 150000 = 27000
Vans = 16% of 75000 = 12000
Trucks 19% of 55000 = 10450
Total = 85950

In which of the following years was the maximum parking fee collected ?

A.

2005

B.

2002

C.

2001

D.

2003

#### SOLUTION

Solution : D

Calculate the parking fee for each of the years using the same logic as above 2005 = (16% of 200000) × 10 + (14% of 50000)× + (13% of 150000) × 30 + (15% of 75000) × 40 + (20% of 55000) × 50 = 2045000 2002 = (15% of 200000) × 10 + (16% of 50000)× 20 + (15% of 150000) × 30 + (17% of 75000) × 40 + (18% of 55000) × 50 = 2140000 2001 = (15% of 200000) × 10 + (16% of 50000) × 20 + (19% of 150000) × 30 + (17% of 75000) × 40 + (15% of 55000) × 50 = 2237500 2003 = (14% of 200000) × 10 + (17% of 50000) × 20 + (18% of 150000) × 30 + (16% of 75000) × 40 + (19% of 55000) × 50 = 2262500 Hence answer = 2003

By what percentage is the parking fee collected from trucks different from the parking fee collected by 2 wheeler in the given period of time?

A. 25.5
B. 62.31
C. 37.5
D. 45.1

#### SOLUTION

Solution : C

Parking fee collected by trucks can be calculated as = 55000 x 50=2750000
Parking fee collected by 2 wheelers can be calculated as= 200000 x 10 = 2000000
Percentage difference in fee collected from trucks different from the parking fee collected by 2 wheelers = (750000/2000000)*100 =37.5%

What is the percentage share of trucks in the total parking fee collected the year 2003?

A. 27
B. 23
C. 31
D. 28

#### SOLUTION

Solution : B

Amount contributed by trucks in the total fee collected in 2003 can be calculated as
Fee collected by trucks in 2003 = (19% of 55000) × 50 = 522500
Total fee collected in 2003 (refer the 1st question of this caselet) = 2262500
Percentage = 5225002262500×100=23.09%
Option B is the correct answer.

What is the percentage contribution of 2 wheeler and 3 wheeler to the parking fee in 2005 ?

A. 30
B. 22.5
C. 28
D. 45

#### SOLUTION

Solution : B

2 wheelers = (16 % of 200000)×10 = 320000
3 wheelers = (14 % of 50000)×20 = 140000
Total
=460000
total parking fee in 2005 (refer the 1st question of this caselet) = 2045000
Percentage contribution of 2 wheelers and 3 wheelers to the parking fee in 2005 = 4600002045000×100=22.5%

How many students definitely scored A+ in Test 5?

A. 10
B. 12
C. 13
D. 14

#### SOLUTION

Solution : B

Out of 15 candidates, except Alok, Ravi and Pankaj, all the others scored 10 points or A+ grade in test 5. Hence , [2].

The number of candidates who got A+ grade in at least two out of the five tests is:

A. Not more than 5
B. Not more than 6
C. Not more than 7
D. None of these

#### SOLUTION

Solution : C

Vijay, Sagar, Shekhar, Akshay, Salman and Vinod i.e. 6 candidates got A+ in at least two of the five tests. Paresh may or may not have scored 10 points in at least two out of the five tests.

Which of the following statements cannot be true?

A. Only two students secured the same grade in three consecutive tests.
B. Exactly five students did not get D grade in any of the tests.
C. The average score of the fifteen students in Test 2 is equal to 2.
D. The average score of the fifteen students in Test 3 is equal to 5.

#### SOLUTION

Solution : B

Shakhar scored A+ in tests 3, 4 and 5 and Pankaj scored D grade in tests 1, 2 and 3. Ravi may or may not have scored the same grades in three consecutive tests. Thus option [1] may or may not be true.

Ravi, Mohit, Sagar, Shakhar and Vinod did not score D grade in any of the tests.

Thus, option [2] is also true.

It is known that Ravi and Akshay secured equal grades in Test 3. So, which of the following statements is definitely true?

A. Everyone except Alok and Ravi got A+ grade in Test 5.
B. Exactly eight students got C grade in Test 2.
C. Exactly 6 students got less than A grade in Test 3.
D. None of these.

#### SOLUTION

Solution : C

The average score of the 15 candidates in tests 2 is 2715 = 1.8 or 3015 = 2 or 3315 = 2.2.

Thus, option [3] can be true.

The total score of all the 15 candidates in Test 3, except Ravi, Akshay and Paresh, is 56. Considering all the possibilities of the points scored by these three in Test 5, none of them add up to 19. Thus the average of 5 cannot be achieved.