Directions for questions 1 to 5: A test paper contains 50 questions. 4 marks are awarded for every correct answer and one mark is deducted for every wrong answer. Aryan, Bunny, Chetana and Divya appeared for this test and their scores are given in the following table. Further it is also known that Divya has scored the maximum marks. Complete the following table and answer the questions that follow.
1.Who answered the second highest number of questions correctly(No two students answered same number of questions correctly)?
(a) Aryan
(b) Bunny
(c) Chetana
(d) Divya
(e) Cannot be determined
2.Who answered the maximum number of questions incorrectly?
(a) Aryan
(b) Bunny
(c) Chetana
(d) Divya
(e) Cannot be determined
3.If all the questions attempted by Divya are not correct, then which of the following can be the score of Divya?
(a) 189
(b) 188
(c) 196
(d) 191
(e) Cannot be determined
4.If the average score of all the four students is a multiple of 5, then what is the total number of correct answers by all the four?
(a) 157
(b) 167
(c) 140
(d) 146
(e) Cannot be determined
5.If Divya got 4th rank among the four students with the maximum possible marks then what could be the maximum number of questions she attempted?
(a) 15
(b) 47
(c) 21
(d) 46
(e) Cannot be determined
Answers with explanation:
Directions for questions 1 to 5: Following is the complete chart:
1.Choice (c)
2.Choice (a)
3.Choice (d)
Since Divya scored maximum marks, hence his score is more than 187, but note that she cannot score all the scores more than 187, there are only some scores which she can score.
Thus only a score of 191 is possible.
4.Choice (a)
For being the average a multiple of 5 Divya must attempt 48 questions and also all of them must be correct. So total correct questions by four becomes = 16 + 46 + 47 + 48 = 157.
5.Choice (d)
In order to get maximum marks with lowest rank,Divya must score 59 with maximum attempts. Which could be realized by the equation 4x – y = 59. Which satisfies for x = 21 and y = 25. Hence the maximum question that he could attempt is 46.
Directions for questions 6 to 10: A team of 5 players A, B, C, D and E participated in a tournament and played four matches (1 to 4). The following table gives partial information about their individual scores and the total runs scored by the team in each match.
Each column has two values missing. These are the runs scored by the two lowest scorers in that match. None of the two missing values is more than 10% of the total runs scored in that match.
6.What is the maximum possible percentage contribution of A in the total runs scored in the four matches?
(a) 19.7%
(b) 19.9%
(c) 20.1%
(d) 20.2%
(e) Cannot be determined
7.What is the maximum possible percentage contribution of E in the total runs scored in the four matches?
(a) 18.2%
(b) 19.9%
(c) 18.6%
(d) 20.2%
(e) Cannot be determined
8.If the absolute difference between the total runs scored by A and C in the four matches is minimum possible then what is the ratio of A and C’s total runs scored by them in the four matches.
(a) 187:189
(b) 189:187
(c) 183:187
(d) 189:188
(e) Cannot be determined
9.If the absolute difference between the total runs scored by A and C in the four matches is minimum possible then what is the absolute difference between total runs scored by B and E in the four matches?
(a) 32
(b) 37
(c) 35
(d) 27
(e) Cannot be determined
10.The players are ranked 1 to 5 on the basis of the total runs scored by them in the four matches, with the highest scorer getting Rank 1. If it is known that no two players scored the same number of total runs, how many players are there whose ranks can be exactly determined?
(a) 0
(b) 1
(c) 3
(d) 5
(e) Cannot be determined
Answers with explanation:
6.Option (a)
Maximum possible runs scored by A in Match-1 = 27
Maximum possible runs scored by A in Match-3 = 19
Maximum possible percentage contribution:
(27+100+19+53)/(270+300+240+200)x100% = 199/1010x100% = 19.7%
7.Option (c)
Maximum possible runs scored by E in Match-2 = 30
Maximum possible runs scored by E in Match-4 = 20
Maximum possible percentage contribution:
(60+30+78+20)/(270+300+240+200)x100%
= 188/1010x100% = 18.6%
8.Option (b)
Maximum possible total runs scored by C in the four matches
= 27 + 30 + 110 + 20 = 187.
In such a case minimum possible total runs scored by A in the four matches = 23 + 100 + 13 + 53 = 189
Difference = 189 – 187 = 2 (minimum possible)
So Required ratio is 189:187
9.Option (b)
Maximum possible total runs scored by C in the four matches
= 27 + 30 + 110 + 20 = 187.
In such a case minimum possible total runs scored by A in the four matches
= 23 + 100 + 13 + 53 = 189.
Difference = 189 – 187 = 2 (minimum possible) Subsequently total runs scored by B in the four matches
= 88 + 65 + 19 + 52 = 224.
Also, total runs scored by E in the four matches
= 60 + 30 + 78 + 19 = 187
Absolute difference = 224 – 187 = 37
10.Option (c)
Individual ranges for total score:
A-> 189-199
B-> 218-224
C-> 182-187
D-> 223
E-> 187-188
Least total will be of C (Rank 5)
2nd least will be E (Rank 4)
Rank 3 must be of A.
It is not possible to determine the exact ranks of B and D.
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