Logical Reasoning & DI (LRDI) Test - 22

Let us start by tabulating the data available.

We have no information about the number of persons in each club. 

The sports-sports cell in the table represents the number of persons from sports club who stayed in sports club. Since we do not have this information (we have information only regarding the movement from one club to another), let us mark all such cells with X. 

The cell sports-dramatics (row-column) represents the number of students from sports club who left for dramatics club. Therefore, the cell sports-total will provide the number of students who left the sports club and the cell total-sports will provide the number of students who left other clubs for the sports club. 

The number of persons who moved from dramatics club to the sports club is the same as the number of persons who moved from the sports club to the dramatics club. The same is the case with sports club and literary club as well. Let us use ‘a’ to denote the number of persons who moved from the dramatics club to the sports club and ‘b’ to denote the number of persons who moved from sports club to literary club. The number of persons who moved out of sports and quiz clubs is the same. Let us denote it by ‘c’. 

A total of 21 students left one club for another. No person moved from the quiz club to sports club (quiz-sports = 0).

The number of persons who moved to the literary club is one more than the number of persons who moved to the sports club. Let the number of persons who moved to the literary club be ‘d+1’ and the number of persons who moved to the sports club be ‘d’.

The number of persons who left the quiz club for the dramatics club and the literary club is the same. Let us denote the number of persons who left the quiz club for dramatics club by ‘e’.  4 students moved out of dramatics club and 5 students moved out of literary club.

As we can see from the table, c+c+4+5 =21

⇒ c = 6 

The number of students who left other clubs for dramatics club is 4 more than the number of students who left other clubs for the quiz club.

Let the number of students who left other clubs for quiz club be ‘f’.

⇒ Number of students who left other clubs for dramatics club = f + 4.

The number of students who joined sports club is exactly half the number of students who left it. We know that 6 students left the sports club. Therefore, 3 students should have joined the sports club.  ⇒ d = 3

We can see from the table that e + e = 6 

⇒ e = 3 

Let us fill the vacant cells with variables from g to k. We get the following table.

f + f + 4 + 3 + 4 = 21

⇒ 2f = 10

f = 5

a+b = 3

a+b+i = 6

⇒ i = 3

a+h+j = 4 --------------(1)

b+h = 1 ----------------(2)

a+b = 3 ----------------(3)

b+g+k = 5 -------------(4)

j + k = 2 --------------(5)

a+g = 6 ---------------(6)

Let us rewrite every variable in terms of 'a'.

b = 3-a

g =6-a

Substituting these values in (4), we get,

3-a+6-a+k = 5

9-2a+k = 5

k = 2a-4

Substituting the value of 'k' in (5), we get,

j+2a-4 = 2

j = 6-2a

(1)⇒ a+h+j = 4

a + h + 6 - 2a = 4

⇒ h = a - 2

It has been given that at least one student moved from Sports to Literary club. Therefore, the value of 'a' cannot be 3.

We know that k=2a-4. Therefore, the value of 'a' should be at least 2. 

2 is the only value that falls within the range.

Solving the equations using a=2, we get the following table:

Number of persons who joined literary club = 4

Number of persons who left literary club = 5

Therefore, the required difference is 5-4 = 1.

Let us start by tabulating the data available.

We have no information about the number of persons in each club. 

The sports-sports cell in the table represents the number of persons from sports club who stayed in sports club. Since we do not have this information (we have information only regarding the movement from one club to another), let us mark all such cells with X. 

The cell sports-dramatics (row-column) represents the number of students from sports club who left for dramatics club. Therefore, the cell sports-total will provide the number of students who left the sports club and the cell total-sports will provide the number of students who left other clubs for the sports club. 

The number of persons who moved from dramatics club to the sports club is the same as the number of persons who moved from the sports club to the dramatics club. The same is the case with sports club and literary club as well. Let us use ‘a’ to denote the number of persons who moved from the dramatics club to the sports club and ‘b’ to denote the number of persons who moved from sports club to literary club. The number of persons who moved out of sports and quiz clubs is the same. Let us denote it by ‘c’. 

A total of 21 students left one club for another. No person moved from the quiz club to sports club (quiz-sports = 0).

The number of persons who moved to the literary club is one more than the number of persons who moved to the sports club. Let the number of persons who moved to the literary club be ‘d+1’ and the number of persons who moved to the sports club be ‘d’.

The number of persons who left the quiz club for the dramatics club and the literary club is the same. Let us denote the number of persons who left the quiz club for dramatics club by ‘e’.  4 students moved out of dramatics club and 5 students moved out of literary club.

As we can see from the table, c+c+4+5 =21

⇒ c = 6 

The number of students who left other clubs for dramatics club is 4 more than the number of students who left other clubs for the quiz club.

Let the number of students who left other clubs for quiz club be ‘f’.

⇒ Number of students who left other clubs for dramatics club = f + 4.

The number of students who joined sports club is exactly half the number of students who left it. We know that 6 students left the sports club. Therefore, 3 students should have joined the sports club.  ⇒ d = 3

We can see from the table that e + e = 6 

⇒ e = 3 

Let us fill the vacant cells with variables from g to k. We get the following table. 

f + f + 4 + 3 + 4 = 21

⇒ 2f = 10

f = 5

a+b = 3

a+b+i = 6

⇒ i = 3

a+h+j = 4 --------------(1)

b+h = 1 ----------------(2)

a+b = 3 ----------------(3)

b+g+k = 5 -------------(4)

j + k = 2 --------------(5)

a+g = 6 ---------------(6)

Let us rewrite every variable in terms of 'a'.

b = 3-a

g =6-a

Substituting these values in (4), we get,

3-a+6-a+k = 5

9-2a+k = 5

k = 2a-4

Substituting the value of 'k' in (5), we get,

j+2a-4 = 2

j = 6-2a

(1)⇒ a+h+j = 4

a + h + 6 - 2a = 4

⇒ h = a - 2

It has been given that at least one student moved from Sports to Literary club. Therefore, the value of 'a' cannot be 3.

We know that k=2a-4. Therefore, the value of 'a' should be at least 2. 

2 is the only value that falls within the range.

Solving the equations using a=2, we get the following table:

Number of members lost by sports club = 6 - 3 = 3.

Number of members gained by dramatics club = 9 - 4 = 5.

Number of members lost by literary club = 5 - 4 =1

Number of members lost by quiz club = 6 - 5 = 1.

As we can see, sports club lost the highest number of members.

Therefore, option C is the right answer. 

Since AB is a multiple of 11, and both A and B are greater than 4, they must be at least 5. So, the possible values for AB are:

55

66

77

88

99

Now, for each of the given values of AB, let us find out all possible values of C and D. Since any other multiple of AB in each case is a number having more than 2 digits, the only multiple is AB itself:

5555

6666

7777

8888

9999

The same is true for EF,

555555

666666

777777

888888

999999

Now for each of the values of ABCDEF, we can have 4 values of GH, 56, 67, 78, 89.

Hence, total number of possible cases = 4 x 5 = 20.

The festival began on the Monday evening and ended on the Sunday evening. Each day, only one band performed. Each band performed only once. The seven bands are - Cactus, Axis, Enigma, Boom, Fish, Dhoom and Bodhi Tree.

Bodhi Tree didn't precede any performance; so it performed on Sunday. Sid, the lead vocalist of the rock band Cactus, would perform only on Monday. Rupam of a fusion band with Fish performed on Wednesday. Angelina with Enigma refused to perform after Thursday and she didn't perform before Meet. So, Meet of a rock band performed on Tuesday and Angelina performed on Thursday. We can tabulate the results as follows :

Rupam is the only male among the lead vocalists of the fusion band, so the other two are females; hence, they should be Angelina and Bony.

Fusion band was performing on Wednesday and Thursday [Rupam, Angelina], so definitely it should be followed by a rock band [since all the three bands of the same genre were not allowed to perform consecutively]. So, rock band performed on Friday and fusion band performed on Saturday [by Bony]. So, Ali performed on Friday. Boom (a rock band) refused to perform immediately before or after Fish. So, it had to perform on Friday. The final arrangement is as follows:

If Bony was the lead vocalist of Axis, then Meet was the lead vocalist of Dhoom but not Boom.

22666689 - right

33996656 - wrong - EF is not a multiple of CD

99999912 - wrong - 1 is not allowed

22469234 - right

55555556 - right

44848434 - right

22489667 - right

33333332 - wrong - G should be less than H

44888845 - right

|3 - 6| = 3

The festival began on the Monday evening and ended on the Sunday evening. Each day, only one band performed. Each band performed only once. The seven bands are - Cactus, Axis, Enigma, Boom, Fish, Dhoom and Bodhi Tree.

Bodhi Tree didn't precede any performance; so it performed on Sunday. Sid, the lead vocalist of the rock band Cactus, would perform only on Monday. Rupam of a fusion band with Fish performed on Wednesday. Angelina with Enigma refused to perform after Thursday and she didn't perform before Meet. So, Meet of a rock band performed on Tuesday and Angelina performed on Thursday. We can tabulate the results as follows :

Rupam is the only male among the lead vocalists of the fusion band, so the other two are females; hence, they should be Angelina and Bony.

Fusion band was performing on Wednesday and Thursday [Rupam, Angelina], so definitely it should be followed by a rock band [since all the three bands of the same genre were not allowed to perform consecutively]. So, rock band performed on Friday and fusion band performed on Saturday [by Bony]. So, Ali performed on Friday. Boom (a rock band) refused to perform immediately before or after Fish. So, it had to perform on Friday. The final arrangement is as follows:

Boom performed on Friday and Meet performed on Tuesday.

Since we can use only prime digits, GH can only be 23.

AB can be 22, 33, 55, 77.

When AB is 22, ABCDEFGH can be 22222223

When AB is 33, ABCDEFGH can be 33333323

When AB is 55, ABCDEFGH can be 55555523

When AB is 77, ABCDEFGH can be 77777723

Hence, only 4 codes.

The festival began on the Monday evening and ended on the Sunday evening. Each day, only one band performed. Each band performed only once. The seven bands are - Cactus, Axis, Enigma, Boom, Fish, Dhoom and Bodhi Tree.

Bodhi Tree didn't precede any performance; so it performed on Sunday. Sid, the lead vocalist of the rock band Cactus, would perform only on Monday. Rupam of a fusion band with Fish performed on Wednesday. Angelina with Enigma refused to perform after Thursday and she didn't perform before Meet. So, Meet of a rock band performed on Tuesday and Angelina performed on Thursday. We can tabulate the results as follows :

Rupam is the only male among the lead vocalists of the fusion band, so the other two are females; hence, they should be Angelina and Bony.

Fusion band was performing on Wednesday and Thursday [Rupam, Angelina], so definitely it should be followed by a rock band [since all the three bands of the same genre were not allowed to perform consecutively]. So, rock band performed on Friday and fusion band performed on Saturday [by Bony]. So, Ali performed on Friday. Boom (a rock band) refused to perform immediately before or after Fish. So, it had to perform on Friday. The final arrangement is as follows:

'Cactus, Axis/Dhoom, Fish, Enigma, Boom, Dhoom/Axis' is a possible performance sequence.

AB = 22, Possible values of CD are 22, 24, 26, 28, 42, 44, 46, 48, 62, 64, 66, 68, 82, 84, 86, 88.

AB = 33, Possible values of CD are 33, 36, 39, 63, 66, 69, 93, 96, 99.

AB = 44, Possible values of CD are 44, 48, 84, 88.

AB = 55, Possible values of CD are 55.

AB = 66, Possible values of CD are 66.

AB = 77, Possible values of CD are 77.

AB = 88, Possible values of CD are 88.

AB = 99, Possible values of CD are 99.

For the following values of ABCD, we get these values of EF.

ABCD = 2222, EF = 22, 44, 66, 88

ABCD = 2224, EF = 24, 48, 72, 96

ABCD = 2226, EF = 26, 52, 78

ABCD = 2228, EF = 28, 56, 84

ABCD = 2242, EF = 42, 84

ABCD = 2244, EF = 44, 88

ABCD = 2246, EF = 46, 92

ABCD = 2248, EF = 48, 96

ABCD = 2262, EF = 62

ABCD = 2264, EF = 64

ABCD = 2266, EF = 66

ABCD = 2268, EF = 68

ABCD = 2282, EF = 82

ABCD = 2284, EF = 84

ABCD = 2286, EF = 86

ABCD = 2288, EF = 88

ABCD = 3333, EF = 33, 66, 99

ABCD = 3336, EF = 36, 72

ABCD = 3339, EF = 39, 78

ABCD = 3363, EF = 63

ABCD = 3366, EF = 66

ABCD = 3369, EF = 69

ABCD = 3393, EF = 93

ABCD = 3396, EF = 96

ABCD = 3399, EF = 99

ABCD = 4444, EF = 44, 88

ABCD = 4448, EF = 48, 96

ABCD = 4484, EF = 84

ABCD = 4488, EF = 88

ABCD = 5555, EF = 55

ABCD = 6666, EF = 66

ABCD = 7777, EF = 77

ABCD = 8888, EF = 88

ABCD = 9999, EF = 99

Total cases = 54.

Each one will have 23, 34, 45, 56, 67, 78, 89 i.e 7 cases with it.

54 x 7 = 378

1. Assign Fixed Performances:

• Monday: Cactus (Rock) - Sid
• Wednesday: Fish (Fusion) - Rupam
• Sunday: Bodhi Tree (Home band)

2. Determine Possible Days for Remaining Bands:

• Angelina (Enigma) must perform on or before Thursday.
• Meet must perform before Angelina.
• Boom cannot perform on Tuesday or Thursday (immediately before or after Fish).
• Ali (with Boom) cannot perform on Saturday.

3. Schedule the Bands:

• Tuesday: Meet's band (Rock)
• Thursday: Enigma (Fusion) - Angelina
• Friday: Boom (Rock) - Ali
• Saturday: Dhoom (Fusion) - Bony

• Counting Fusion and Rock Band Consecutive Performances:

• Monday (Rock) → Tuesday (Rock): Same genre.
• Tuesday (Rock) → Wednesday (Fusion): 1st Rock-Fusion transition.
• Wednesday (Fusion) → Thursday (Fusion): Same genre.
• Thursday (Fusion) → Friday (Rock): 2nd Fusion-Rock transition.
• Friday (Rock) → Saturday (Fusion): 3rd Rock-Fusion transition.

• Total Transitions between Fusion and Rock bands from Monday to Saturday: 3