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Test Level 3: Missing Data - CAT MCQ


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10 Questions MCQ Test Level-wise Tests for CAT - Test Level 3: Missing Data

Test Level 3: Missing Data for CAT 2024 is part of Level-wise Tests for CAT preparation. The Test Level 3: Missing Data questions and answers have been prepared according to the CAT exam syllabus.The Test Level 3: Missing Data MCQs are made for CAT 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test Level 3: Missing Data below.
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Test Level 3: Missing Data - Question 1
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Directions: Read the following to answer the question.

The following table shows the results of Triangular Hockey Series played among the teams of India, Australia and England. The matches were played in such a manner that each team played against another at least once. The table has a few missing pieces of information.

Q. Calculate the total number of matches played in the whole series.

Detailed Solution for Test Level 3: Missing Data - Question 1

There are three teams playing in the hockey series. They are India, Australia and England.
According to the given condition, the matches were played in such a manner that each team played against another at least once, each team should play in 2 matches.


i.e. India Vs Australia, Australia Vs England and India Vs England.
Therefore, total 3 matches were played in the series.

Test Level 3: Missing Data - Question 2
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Directions: Read the following to answer the question.

The following table shows the results of Triangular Hockey Series played among the teams of India, Australia and England. The matches were played in such a manner that each team played against another at least once. The table has a few missing pieces of information.

Q. Identify the score card reading during India-England match, favouring India.

Detailed Solution for Test Level 3: Missing Data - Question 2

Checking the inning details of the given score board of the series, we have a clue i.e. India has drawn in one match, which means either won or lost in second match.
In the score board, India has scored 2 goals.
So, the possibilities for match drawn will be 0 - 0, 1 - 1 and 2 - 2.
As we know that total goals scored by all three teams are 12, so the total goals scored by England = 12 - (2 + 3) = 7

Possibility case 0 - 0:
Case 1:
1st match: India Vs Australia: 0 - 0
2nd match: India Vs England: 2 - 4
The score card 2 - 4 shows that India scored 2 goals and England scored 4 goals.
So, second match would be lost.

Case 2:
1st match: Australia Vs India: 0 - 0
2nd match: Australia Vs England: 3 - 7
The score card 3 - 7 shows that Australia scored 3 goals and England scored 7 goals.
As one of the matchs is drawn with India i.e. 0 - 0, second match would be lost against England i.e. 3 - 7.

Case 3:
1st match: India Vs England: 2 - 4
2nd match: Australia Vs England: 3 - 7
This case is not matched with the first 2 cases of 0 - 0, so the possibility case for 0 - 0 is wrong.

Possibility case 1 - 1:
Case 1:
1st match: India Vs Australia: 1 - 1
2nd match: India Vs England: 1 - 1
So, second match would be drawn. But, it is not given in favour of India.
Therefore, the possibility case for 1 - 1 is also wrong.

Possibility case 2 - 2:
Case 1:
1st match: India Vs Australia: 2 - 2
2nd match: India Vs England: 0 - 2
So, the second match would be lost to India and England scored 2 goals against India.

Case 2:
1st match: Australia Vs India: 2 - 2
2nd match: Australia Vs England: 1 - 5
It shows that Australia has lost in second match with 1 goal and England scored 5 goals against Australia.
From cases 1 and 2, we can clearly say that England scored 2 + 5 = 7 goals in total. It is completely matched with the given table.
Meanwhile, India and Australia have scored together = 0 + 1 = 1 goal against England.
Thus, the possibility case 2 - 2 is perfectly correct.
So, the table can be filled as follows.

During India Vs England match, the score card reading in favour of India is 0 - 2.

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Test Level 3: Missing Data - Question 3
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Directions: Read the following to answer the question.

The following table shows the results of Triangular Hockey Series played among the teams of India, Australia and England. The matches were played in such a manner that each team played against another at least once. The table has a few missing pieces of information.

Q. What is the mean average of goals scored by all three teams in the whole series?

Detailed Solution for Test Level 3: Missing Data - Question 3

From the given information, we can find that total number of goals scored by all teams is same as total number of goals against all teams.
Therefore, total number of goals against all teams = 4 + 7 + 1 = 12
Thus, total number of goals scored by all teams = 12
So, the mean average of goals scored by all three teams = 12/3 = 4

Test Level 3: Missing Data - Question 4
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Directions: Read the data and answer the following question.

Dance, music, cooking, karate, swimming and drawing classes are to be scheduled from 3rd April to 9th April, not necessarily in the same order. Each of them is held for 50 mins, 60 mins, 70 mins, 85 mins, 100 mins and 110 mins, but not necessarily in the same order. A class of 50 mins is scheduled on 9th April which is not Sunday as it is an off day. Dance class is for less than 70 mins and is scheduled immediately before karate class. There are two classes scheduled between swimming class, which is for 110 mins and cooking class, which is for 70 mins. Karate class is before Sunday and there are two days between Sunday and the dance class. Drawing class, which is for 85 mins, is not scheduled on 3rd April. Saturday's class is of 110 mins.

Q. On which of the following days is the drawing class scheduled?
Detailed Solution for Test Level 3: Missing Data - Question 4

Test Level 3: Missing Data - Question 5
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Directions: Read the data and answer the following question.

Dance, music, cooking, karate, swimming and drawing classes are to be scheduled from 3rd April to 9th April, not necessarily in the same order. Each of them is held for 50 mins, 60 mins, 70 mins, 85 mins, 100 mins and 110 mins, but not necessarily in the same order. A class of 50 mins is scheduled on 9th April which is not Sunday as it is an off day. Dance class is for less than 70 mins and is scheduled immediately before karate class. There are two classes scheduled between swimming class, which is for 110 mins and cooking class, which is for 70 mins. Karate class is before Sunday and there are two days between Sunday and the dance class. Drawing class, which is for 85 mins, is not scheduled on 3rd April. Saturday's class is of 110 mins.

Q. Which of the following is correct?
Detailed Solution for Test Level 3: Missing Data - Question 5

Test Level 3: Missing Data - Question 6
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Directions: Read the data and answer the following question.

Dance, music, cooking, karate, swimming and drawing classes are to be scheduled from 3rd April to 9th April, not necessarily in the same order. Each of them is held for 50 mins, 60 mins, 70 mins, 85 mins, 100 mins and 110 mins, but not necessarily in the same order. A class of 50 mins is scheduled on 9th April which is not Sunday as it is an off day. Dance class is for less than 70 mins and is scheduled immediately before karate class. There are two classes scheduled between swimming class, which is for 110 mins and cooking class, which is for 70 mins. Karate class is before Sunday and there are two days between Sunday and the dance class. Drawing class, which is for 85 mins, is not scheduled on 3rd April. Saturday's class is of 110 mins.

Q. Wednesday is on
Detailed Solution for Test Level 3: Missing Data - Question 6

Test Level 3: Missing Data - Question 7
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Directions: Study the table carefully and answer the given question.

The following table shows the number of students in different engineering departments at seven IITs. Some of the data is missing from the table.

The above table is given for year 2014. In 2015, the intake of Mechanical Engineering at all the IITs together was increased by 10%, intake of Mineral Engineering was increased by 10% and intake of Chemical Engineering was increased by 8%. The intake of other departments remained the same as that of previous year.

Q. In 2014, all the students (in case total number of students was 55 or less) or only top 55 students from every department at each IIT received a scholarship of Rs. 2000. Out of the remaining, all the students (in case number of remaining students was 45 or less) or only the next 45 students from every department at each IIT received a scholarship of Rs. 1200. What is the total amount of scholarship awarded to students studying in Mining Engineering department at all the IITs together in 2014, if the total number of students in Mining Engineering at all the IITs together in 2015 was 600?
Detailed Solution for Test Level 3: Missing Data - Question 7

Total number of Mining Engineering students in 2014 at all the IITs = 600
Total number of Mining Engineering students at IIT Madras and IIT Kanpur = 600 – (95 + 155 + 65 + 90 + 140) = 55
So, all the Mining Engineering students at IIT Madras and IIT Kanpur received a scholarship of Rs. 2000 each. (As the number of students at each of the two IITs is less than 55)
Then, total scholarship amount awarded to Mining Engineering students = 55  6  2000 + (40 + 45 + 10 + 35 + 45)1200 = 6,60,000 + 2,10,000 = Rs. 8,70,000

Test Level 3: Missing Data - Question 8
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Directions: Study the table carefully and answer the given question.

The following table shows the number of students in different engineering departments at seven IITs. Some of the data is missing from the table.

The above table is given for year 2014. In 2015, the intake of Mechanical Engineering at all the IITs together was increased by 10%, intake of Mineral Engineering was increased by 10% and intake of Chemical Engineering was increased by 8%. The intake of other departments remained the same as that of previous year.

Q. What was the ratio of the total number of students in Mechanical Engineering at IIT Delhi and IIT Roorkee in 2014, if the total number of students in Mechanical Engineering at all the IITs in 2014 was 50% more than the total number of students at IIT Delhi in 2015 and IIT Delhi had 29 students more in Mechanical Engineering as compared to Mechanical students at IIT Roorkee in 2014?
Detailed Solution for Test Level 3: Missing Data - Question 8

Suppose the total numbers of Mechanical Engineering students at IIT Delhi and IIT Roorkee in 2014 are y and z, respectively.
So, y - z = 29 ...(1)
Then, total number of students at IIT Delhi in 2014 = y + 174 + 225 + 95 + 80 = y + 574
And total number of students at IIT Delhi in 2015 = 1.1y + 174 + 225  1.08 + 95 + 80  1.1
= 1.1y + 174 + 243 + 95 + 88 = 1.1y + 600 ...(2)
Total number of Mechanical Engineering students at all the seven IITs in 2014 = y + z + 100 + 150
+ 220 + 190 + 220 = y + z  + 880 ...(3)
Then, from equations (2) and (3),
1.5(1.1y + 600) = y + z + 880
⇒ 1.65y + 900 = y + z + 880 
⇒ 0.65y - z = -20
⇒ 0.65y - y + 29 = -20 (from equation 1)
⇒ - 0.35y = -49
⇒ y = 140 and z = 111
Hence, ratio of the total number of students in Mechanical Engineering at IIT Delhi and IIT Roorkee in 2014 = 140 : 111

Test Level 3: Missing Data - Question 9
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Directions: The following table shows some incomplete information about the runs scored by four batsmen in four innings.

Additional information:
1. Average runs scored in the 1st innings for all the players were 67.5.
2. Paramjeet's average runs for all 4 innings were 1.5 times the runs scored by Jeetu in 1st innings.
3. Sachin's average runs were 72.5 in all four innings.
4. Total runs scored by Dhooni in all the four innings were 300.
5. The runs scored in 2nd innings were 10 less than the runs scored in 1st innings for all the players.
6. Paramjeet and Dhooni scored the same runs in 4th innings.
7. Sum of runs scored by all the players in the 4th innings is 270.

Q. Who scored the least in the 2nd innings?
Detailed Solution for Test Level 3: Missing Data - Question 9

 (i) Average runs scored in the 1st innings = 67.5
Total score = 67.5 × 4 = 270.0
(ii) Average runs of Sachin = 72.5
Total runs of Sachin = 72.5 × 4 = 290
So, the runs made by Sachin in 3rd innings = 290 - 80 - 70 - 80 = 60
(iii) Total score in the 4th innings = 270 (from 7)
Now, let Paramjeet`s, Dhooni`s and Jeetu`s scores in 4th innings be x, x and y.
=> 2x + y + 80 = 270
=> 2x + y = 190 ..…(i)
Let Jeetu`s and Dhooni`s scores in 1st innings be p and q, respectively.
=> p + q + 80 + 60 = 270
=> p + q = 130 ..…(ii)
From 2:
i.e. 6p - x = 170 ..….(iii)
From 5: Jeetu`s and Dhooni`s scores in 2nd innings are p - 10 and q - 10, respectively.
=> Jeetu`s total runs = 220
=> p + p - 10 + 60 + y = 220
2p + y = 170 ..….(iv)
Solving (i) and (iv), we get 2x - 2p = 20 ……(v)
Solving (iii) and (v), we get x = 46 and p = 36
From (i) and (ii),
y = 98 and q = 94
Thus,

In 2nd innings, Jeetu Malik scored the lowest.

Test Level 3: Missing Data - Question 10
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Directions: The following table shows some incomplete information about the runs scored by four batsmen in four innings.

Additional information:
1. Average runs scored in the 1st innings for all the players were 67.5.
2. Paramjeet's average runs for all 4 innings were 1.5 times the runs scored by Jeetu in 1st innings.
3. Sachin's average runs were 72.5 in all four innings.
4. Total runs scored by Dhooni in all the four innings were 300.
5. The runs scored in 2nd innings were 10 less than the runs scored in 1st innings for all the players.
6. Paramjeet and Dhooni scored the same runs in 4th innings.
7. Sum of runs scored by all the players in the 4th innings is 270.

Q. Who scored the lowest runs in the 1st innings?
Detailed Solution for Test Level 3: Missing Data - Question 10

(i) Average runs scored in the 1st innings = 67.5
Total score = 67.5 × 4 = 270.0
(ii) Average runs of Sachin = 72.5
Total runs of Sachin = 72.5 × 4 = 290
So, the runs made by Sachin in 3rd innings = 290 - 80 - 70 - 80 = 60
(iii) Total score in the 4th innings = 270 (from 7)
Now, let Paramjeet`s, Dhooni`s and Jeetu`s scores in 4th innings be x, x and y.
=> 2x + y + 80 = 270
=> 2x + y = 190 ..…(i)
Let Jeetu`s and Dhooni`s scores in 1st innings be p and q, respectively.
=> p + q + 80 + 60 = 270
=> p + q = 130 ..…(ii)
From 2:
i.e. 6p - x = 170 ..….(iii)
From 5: Jeetu`s and Dhooni`s scores in 2nd innings are p - 10 and q - 10, respectively.
=> Jeetu`s total runs = 220
=> p + p - 10 + 60 + y = 220
2p + y = 170 ..….(iv)
Solving (i) and (iv), we get 2x - 2p = 20 ……(v)
Solving (iii) and (v), we get x = 46 and p = 36
From (i) and (ii),
y = 98 and q = 94
Thus,

Lowest runs were scored in 1st innings by Jeetu Malik.

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