**Data for Questions 1 to 4 : **
Some friends went to Netram Sweets. Following is the information about the number of rosogollas they ate:

i. Gimmy ate 8 less than Akshit.

ii. Dileep and Raj together ate 37.

iii. Jugal ate 8 more than Dileep.

iv. Akshit ate 5 more than Dileep.

v. Akshit and Gimmy together ate 40

1. How many rosogollas did Raj eat?

a) 18

b) 24

c) 68

d) 27

Explanation: A + G = 40 __________ (1)

A + D = 5 ___________ (2)

J + D = 8 ____________ (3)

This means that A is 3 less than J.

D + R = 37_______ (4)

A – G = 8 ________ (5)

Using (1) and (5) we get A = 24 and G = 16,

Hence D = 19, J = 27 and R = 18

R = 18. Option (a) is correct

2. Jugal and Dileep together ate how many rosogollas?

a) 46

b) 36

c) 40

d) None of these

Explanation: 27 + 19 = 46. Option (a) is correct (Refer explanation of Question 1)

3. What is the difference between number of rosogollas eaten by Dileep and Raj?

a) 1

b) 2

c) 3

d) Data inadequate

Explanation: 19 – 18 = 1. Option (a) is correct (Refer explanation of Question 1)

4. If the cost of each rosogolla is ` 2, what was the total amount they had to pay?

a) 208

b) 200

c) 198

d) None of these

Explanation: 24 + 16 + 19 + 27 + 18 → 104 * 2 = 208

Option (a) is correct (Refer explanation of Question 1)

**Data for Questions 5 to 8 : **
Coach Johan sat with the score cards of Indian players from the 3 games in a one-day cricket tournament where the same set of players played for India and all the major batsmen go out. John summarised the batting performance through three figures, one for each game. In each figure, the three outer triangles communicate the number of runs scored by the three top scorers from India. K, R, S, V and Y represent Kaif, Rahul, Saurav, Virender and Yuvraj respectively. The middle triangle in each diagram denotes the percentage of total score that was scored by the top three Indian scorers in that game. No two players score the same number of runs in the same game. John also calculated two batting indices for each players based on his scores it he tournament; the R-index of a batsman is the difference between his highest and lowest scores in the 3 games while the M-index is the middle number, if his scores are arranged in a non-increasing order

Batting performance of five Indian Batsmen in three Games of One-day International Cricket Tournament.

5. For how many Indian players is it possible to calculate the exact M-Index?

a) 0

b) 1

c) 2

d) More than 2

Explanation: Runs scored by top three batsmen against Pakistan = 40 + 130 + 28

= 198

90% = 198

100% = 220 runs

The rest of the players made only 22 runs.

Runs scored by top three batsmen against South Africa = 51 + 75 + 49

= 175

70% = 175

100% = 250

The rest of the players made only 75 runs

Runs scored by top three batsmen against Australia = 55 + 87 + 50 = 192

80% = 192

100 = 240

The rest of the players made only 48 runs Y→ 40 + South Africa + 87 = 127 + runs scored against South Africa.

V → 130 + South Africa + Australia =130 + runs scored against South Africa + Australia

K → 28 + 51 + Australia = 79 + Runs scored against Australia.

S → Pakistan + 75 + 50 = 125 + Runs scored against Pakistan.

R → Pakistan + 49 + 55 = 104 + Runs scored against Pakistan.

For Yuvraj, middle index cannot be determined as we don’t know the exact runs scored by him against South Africa.

Same is the case with Virendra and Kaif.

For Saurav the middle index will be 50 because whatever runs he scores against Pakistan, they could be maximum 22 or minimum zero. This will not affect the middle number 50.

For Rahul middle index will be 49. (Same logic)

Option (c) is correct

6. Among the players mentioned, who can have the lowest R-index from the tournament?

a) Only Kaif, Rahul or Yuvraj

b) Only Kaif or Rahul

c) Only Kaif or Yuvraj

d) Only Kaif

Explanation: R-Index → Difference between highest and lowest score.

For Yuvraj minimum R-index can be 87 – 40 = 47

For Virendra minimum R-index can be 130 – 48 = 82

For Kaif minimum R-index can be 51 – 28 = 23

For Sourav 75 – 22 = 53

For Rahul 55 – 22 = 33

\ It is Kaif who can have minimum R-index

Option (d) is correct

7. How many players among those listed definitely scored less than Yuvraj in the tournament?

a) 0

b) 1

c) 2

d) More than 2

Explanation: No. of players who definitely scored less than Yuvraj is 1.

In the worst case if we suppose that Yuvraj scored zero against South Africa, so we have to find how many players definitely scored less than 127.

This could be only Rahul who can score maximum 22 runs against Pakistan and will be able to get a score of 126, which is less than 127.

Option (b) is correct

8. Which of the players had the best M-index from the tournament?

a) Rahul

b) Saurav

c) Virendra

d) Yuvraj

Explanation: Saurav’s middle index is the best

Option (b) is correct