Directions: Study the following information carefully and answer the questions that follow: There is a matrix of 4*4. The rows are represented as %, $, # and @ from the first to the fourth in the same order and the columns are represented as 1 to 4 from the first to the fourth in the same order. Following operations are to be performed in the given order to obtain the whole matrix. 1. One diagonal of matrix is IBPS and the other diagonal is 2019 in the same order. Both have their first element in the first Column and 4th column respectively. 2. The immediate neighbor of any alphabet in the same row is the alphabetical position of that number. 3. The remaining places are to be filled by taking the difference between the two numbers surrounding that place in the same row. In the obtained matrix, the value of the sum of all digits in the second column would be less than that of the third column. The compiler of a PC will respond to the input by calculating the value of the string as per the following conditions. 1. If there are equal number of even and odd numbers in the string, then value of the string will be the absolute difference between all the even numbers and all the odd numbers. 2. If there are equal number of alphabets and numbers in the string, then the value of string will be the absolute difference between the alphabetical position of all the alphabets and all the numbers. 3. If there is only one even number in the string, then the value of string will be the addition of all the numbers in that string. 4. If there is a vowel in the string, then value of the string will be the alphabetical position of that vowel. 5. If none of the above mentioned conditions follow, then the value of the string will be obtained by subtracting the lowest number from the highest number in that string. Note: 1. The value of an input is obtained by adding the values of all the strings and then the digits in that value is added up to the point where it becomes a single digit number and then it is taken as an input. 2. If only a single string is given, then the digits in that value is added upto the point where it becomes a single digit number and then it is taken as input. 3. If the value of an input is a prime number, then the program will be executed. If the value of an input is an even number, then program will not be executed. If the value of an input is both even and prime number, then program will be executed but it will show an error. If the value of an input is other than the above mentioned values, then PC will hang. Let us assume a matrix: 1 2 3 4 % 1 2 C 4 $ J 6 7 8 # 9 10 T 12 @ O 14 15 16 AA = $3 @2 %1 #2, BB = @1 $3 %2 $3 denotes value in second row and column 3 which will be equal to 7. Therefore AA = 7 14 1 10 So, this is satisfying condition 1. Hence the sum = (14 + 10) – (7 + 1) = 16 BB = O 7 2 So, this is satisfying condition 4. Thus, frequency = alphabetical position of O = 15 The values of AA and BB are added, and the final frequency is 16 + 15 = 31 which is a two digit number, So again adding them 3 + 1 = 4, which is a non-prime even number so the program will not be executed. Consider the following four strings for all questions: AA = $2 #1 @3 #3 BB = @1 %4 @3 %3 CC = $4 @2 #4 %1 DD = %4 @2 @4 #2
What will be the value of string if all four signals given is taken as input?
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Analyzing the Problem and Constructing the Matrix
The problem requires us to first construct a 4x4 matrix based on a set of specific rules. The rows are labeled %, $, #, and @, and the columns are labeled 1, 2, 3, and 4.
The matrix construction rules are applied in the given order:
- One diagonal (%,1 to @,4) is IBPS, and the other diagonal (%,4 to @,1) is 2019.
- The immediate neighbor of any alphabet in the same row is the alphabetical position of that alphabet.
- Remaining places are filled by taking the difference between the two nearest numbers surrounding that place in the same row.
Let's build the matrix step-by-step:
Step 1: Apply Rule 1 (Diagonals)
Diagonal 1 (%,1 to @,4): %,1 = I, $,2 = B, #,3 = P, @,4 = S
Diagonal 2 (%,4 to @,1): %,4 = 2, $,3 = 0, #,2 = 1, @,1 = 9
| 1 | 2 | 3 | 4 | |
|---|---|---|---|---|
| % | I | 2 | ||
| $ | B | 0 | ||
| # | 1 | P | ||
| @ | 9 | S |
Step 2: Apply Rule 2 (Alphabetical Position of Neighbors)
If an alphabet is in a cell, its immediate empty horizontal neighbor(s) in the same row take the value of the alphabet's position in the English alphabet (A=1, B=2, ... Z=26).
- I at %,1: Immediate neighbor %2 is empty. %2 = AlphaPos('I') = 9.
- B at $,2: Immediate neighbors $,1 and $,3. $,3 is 0 (number). $,1 is empty. $,1 = AlphaPos('B') = 2.
- P at #,3: Immediate neighbors #,2 and #,4. #,2 is 1 (number). #,4 is empty. #,4 = AlphaPos('P') = 16.
- S at @,4: Immediate neighbor @,3 is empty. @,3 = AlphaPos('S') = 19.
Matrix after Rule 1 & 2:
| 1 | 2 | 3 | 4 | |
|---|---|---|---|---|
| % | I | 9 | 2 | |
| $ | 2 | B | 0 | |
| # | 1 | P | 16 | |
| @ | 9 | 19 | S |
Step 3: Apply Rule 3 (Difference of Nearest Numbers)
Remaining empty places are filled by the absolute difference between the two nearest numbers in the same row.
- %,3 is empty: Nearest numbers are %2 (9) and %4 (2). Difference = |9 - 2| = 7. %,3 = 7.
- $,4 is empty: Nearest numbers are $,1 (2) and $,3 (0). Difference = |2 - 0| = 2. $,4 = 2.
- #,1 is empty: Nearest numbers are #,2 (1) and #,4 (16). Difference = |1 - 16| = 15. #,1 = 15.
- @,2 is empty: Nearest numbers are @,1 (9) and @,3 (19). Difference = |9 - 19| = 10. @,2 = 10.
The complete matrix is:
| 1 | 2 | 3 | 4 | |
|---|---|---|---|---|
| % | I | 9 | 7 | 2 |
| $ | 2 | B | 0 | 2 |
| # | 15 | 1 | P | 16 |
| @ | 9 | 10 | 19 | S |
Verification: Column Sum Condition
Sum of digits in numbers in Column 2: 9 (@%) + 1 (#) + (1+0) (@) = 9 + 1 + 1 = 11.
Sum of digits in numbers in Column 3: 7 (@%) + 0 (@$) + (1+9) (@) = 7 + 0 + 10 = 17.
Is 11 < 17? Yes. The condition is satisfied by this matrix.
Calculating String Values
Now we find the values for the given strings AA, BB, CC, and DD from the constructed matrix and calculate their individual values based on the given string value conditions.
- AA = $2 #1 @3 #3 → B, 15, 19, P
- BB = @1 %4 @3 %3 → 9, 2, 19, 7
- CC = $4 @2 #4 %1 → 2, 10, 16, I
- DD = %4 @2 @4 #2 → 2, 10, S, 1
String Value Conditions (applied in order):
- Equal number of even and odd numbers: Absolute difference between sum of evens and sum of odds.
- Equal number of alphabets and numbers: Absolute difference between sum of alphabetical positions of alphabets and sum of numbers.
- Only one even number: Sum of all numbers.
- Vowel present: Alphabetical position of that vowel.
- None of the above: Highest number - Lowest number.
Value of AA = B, 15, 19, P
- Numbers: 15 (Odd), 19 (Odd). Evens: 0, Odds: 2. (Condition 1 fails)
- Alphabets: 2 (B, P), Numbers: 2 (15, 19). Equal number of alphabets and numbers (2 each). (Condition 2 applies)
- Value = |(AlphaPos('B') + AlphaPos('P')) - (15 + 19)| = |(2 + 16) - (15 + 19)| = |18 - 34| = |-16| = 16.
Value of AA = 16.
Value of BB = 9, 2, 19, 7
- Numbers: 9 (Odd), 2 (Even), 19 (Odd), 7 (Odd). Evens: 1 (2), Odds: 3 (9, 19, 7). (Condition 1 fails)
- Alphabets: 0, Numbers: 4. (Condition 2 fails)
- Only one even number (2). (Condition 3 applies)
- Value = Sum of all numbers = 9 + 2 + 19 + 7 = 37.
Value of BB = 37.
Value of CC = 2, 10, 16, I
- Numbers: 2 (Even), 10 (Even), 16 (Even). Evens: 3 (2, 10, 16), Odds: 0. (Condition 1 fails)
- Alphabets: 1 (I), Numbers: 3 (2, 10, 16). (Condition 2 fails)
- More than one even number. (Condition 3 fails)
- Vowel present (I). (Condition 4 applies)
- Value = Alphabetical position of the vowel 'I' = 9.
Value of CC = 9.
Value of DD = 2, 10, S, 1
- Numbers: 2 (Even), 10 (Even), 1 (Odd). Evens: 2 (2, 10), Odds: 1 (1). (Condition 1 fails)
- Alphabets: 1 (S), Numbers: 3 (2, 10, 1). (Condition 2 fails)
- More than one even number. (Condition 3 fails)
- No vowels present (2, 10, S, 1). (Condition 4 fails)
- None of the above conditions follow. (Condition 5 applies)
- Value = Highest number - Lowest number. Numbers are 2, 10, 1. Highest = 10, Lowest = 1. Difference = 10 - 1 = 9.
Value of DD = 9.
Calculating the Final Input Value
The value of the input is obtained by adding the values of all the strings and then adding the digits in that value up to a single-digit number.
Total value = Value(AA) + Value(BB) + Value(CC) + Value(DD)
Total value = 16 + 37 + 9 + 9 = 71.
Reduce to a single digit by summing digits:
7 + 1 = 8.
The single-digit value of the input is 8.
Conclusion
The value of the string if all four signals given is taken as input is the single-digit sum derived from the total value of the individual strings. This single-digit value is 8.
Important Questions from Conditional Matrix
Select the set in which the numbers are related in the same way as are the numbers of the following sets.
(30, 14, 8)
(84, 12, 36)
Select the option in which the numbers are related in the same way as are the numbers of the following sets.
(NOTE: Operations should be performed on the whole numbers, without breaking down the numbers into its constituent digits. E.g. 13 – Operations on 13 such as adding /deleting /multiplying etc. to 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is not allowed)
(24, 8, 96)
(36, 4, 72)
What is the value of input if only signal AA and BB is taken into account?
What is the correct option if only signal CC is taken into account?
What is the correct option if both signals AA and DD is taken as input?
