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 is the value of input if only signal AA and BB is taken into account?
8
Understanding the Matrix Construction Rules
The problem describes how to construct a 4x4 matrix based on several rules applied in a specific order. The rows are labeled %, $, #, and @, and columns are 1, 2, 3, and 4.
- Diagonal 1: The diagonal from %,1 to @,4 is IBPS.
- Diagonal 2: The diagonal from %,4 to @,1 is 2019.
- Immediate Neighbor Rule: The immediate horizontal neighbor of any alphabet in the same row gets the numerical value equal to the alphabetical position of that alphabet. This rule is applied after placing the diagonals.
- Remaining Places Rule: Any remaining empty cell is filled by taking the absolute difference between the two numbers surrounding that place in the same row. This rule is applied after the neighbor rule.
The instruction also states that the sum of all digits in the second column is less than that of the third column in the final matrix. This constraint helps confirm the correct matrix.
Step-by-Step Matrix Construction
Let's build the matrix following the rules:
Step 1: Place the Diagonals
- %,1 = I
- $,2 = B
- #,3 = P
- @,4 = S
- %,4 = 2
- $,3 = 0
- #,2 = 1
- @,1 = 9
Partial Matrix after Step 1:
| 1 | 2 | 3 | 4 | |
|---|---|---|---|---|
| % | I | 2 | ||
| $ | B | 0 | ||
| # | 1 | P | ||
| @ | 9 | S |
Step 2: Apply Immediate Neighbor Rule (for alphabets)
For each alphabet cell, its immediate horizontal neighbor (if empty) gets its alphabetical position:
- I at %,1 (pos 9). Neighbor %,2 is empty. %,2 gets 9.
- B at $,2 (pos 2). Neighbor $,1 is empty. $,1 gets 2. Neighbor $,3 is 0 (already filled).
- P at #,3 (pos 16). Neighbor #,4 is empty. #,4 gets 16. Neighbor #,2 is 1 (already filled).
- S at @,4 (pos 19). Neighbor @,3 is empty. @,3 gets 19.
Partial Matrix after Step 2:
| 1 | 2 | 3 | 4 | |
|---|---|---|---|---|
| % | I | 9 | 2 | |
| $ | 2 | B | 0 | |
| # | 1 | P | 16 | |
| @ | 9 | 19 | S |
Step 3: Apply Remaining Places Rule (difference between surrounding numbers)
Remaining empty cells are %,3, $,4, #,1, @,2. A cell is filled with the difference between two numbers surrounding it in the same row.
- %,3 is empty, between 9 (%,2) and 2 (%,4). %,3 gets |9 - 2| = 7.
- $,4 is empty. The numbers in row $ are 2 ($,1) and 0 ($,3). If "surrounding" means any two numbers in the row, $,4 gets |2 - 0| = 2.
- #,1 is empty. The numbers in row # are 1 (#,2) and 16 (#,4). #,1 gets |1 - 16| = 15.
- @,2 is empty, between 9 (@,1) and 19 (@,3). @,2 gets |9 - 19| = 10.
Final Constructed Matrix:
| 1 | 2 | 3 | 4 | |
|---|---|---|---|---|
| % | I | 9 | 7 | 2 |
| $ | 2 | B | 0 | 2 |
| # | 15 | 1 | P | 16 |
| @ | 9 | 10 | 19 | S |
Let's verify the constraint: Sum of digits in Col 2 < Sum of digits in Col 3.
- Col 2 values: 9, B, 1, 10. Treating alphabets B and P as their positions for sum calculation (B=2, P=16): 9, 2, 1, 10. Sum = 9 + 2 + 1 + 10 = 22. Sum of digits in Col 2 = 9 + 2 + 1 + 1 + 0 = 13.
- Col 3 values: 7, 0, P, 19. Treating P as 16: 7, 0, 16, 19. Sum = 7 + 0 + 16 + 19 = 42. Sum of digits in Col 3 = 7 + 0 + 1 + 6 + 1 + 9 = 24.
13 < 24. The constraint is satisfied, confirming the matrix construction.
Calculating String Values
The value of an input string is calculated based on specific conditions applied in a particular order. Based on the example provided, the likely precedence of rules is 4 > 1 > 3 > 2 > 5.
- If a vowel is in the string, value is the alphabetical position of that vowel (Rule 4).
- If there are equal number of even and odd numbers in the string, value is the absolute difference between sum of even numbers and sum of odd numbers (Rule 1, interpreting "numbers" based on example).
- If there is only one even number in the string, value is the sum of all numbers (Rule 3, implying among numbers).
- If there are equal number of alphabets and numbers in the string, value is the absolute difference between sum of alphabetical positions of alphabets and sum of numbers (Rule 2).
- Otherwise, value is the highest number minus the lowest number (Rule 5).
We need to find the values for strings AA and BB.
String AA = $2 #1 @3 #3
Getting values from the matrix:
- $2 = B (alphabetical position 2)
- #1 = 15
- @3 = 19
- #3 = P (alphabetical position 16)
String AA values are: B, 15, 19, P. This string contains 2 alphabets (B, P) and 2 numbers (15, 19).
Check String Value Rules for AA (B 15 19 P):
- Rule 4 (Vowel)? No vowels (B, P).
- Rule 1 (Equal E/O numbers)? Numbers are 15 (Odd), 19 (Odd). 0 Even, 2 Odd. Not equal counts.
- Rule 3 (Only one even number)? Numbers are 15, 19. No even numbers.
- Rule 2 (Equal alphabet/number counts)? String has 2 alphabets and 2 numbers. Yes, counts are equal. Apply Rule 2.
Value(AA) = |(Sum of alphabetical positions of alphabets) - (Sum of numbers)|
Alphabetical positions of alphabets in AA: B=2, P=16. Sum = 2 + 16 = 18.
Numbers in AA: 15, 19. Sum = 15 + 19 = 34.
Value(AA) = |18 - 34| = |-16| = 16.
String BB = @1 %4 @3 %3
Getting values from the matrix:
- @1 = 9
- %4 = 2
- @3 = 19
- %3 = 7
String BB values are: 9, 2, 19, 7. This string contains only numbers.
Check String Value Rules for BB (9 2 19 7):
- Rule 4 (Vowel)? No alphabets, so no vowel.
- Rule 1 (Equal E/O numbers)? Numbers are 9(Odd), 2(Even), 19(Odd), 7(Odd). 1 Even, 3 Odd. Not equal counts.
- Rule 3 (Only one even number)? Yes, only 2 is even among the numbers. Apply Rule 3.
Value(BB) = Sum of all numbers = 9 + 2 + 19 + 7 = 37.
Calculating the Final Input Value
The input value is obtained by adding the values of all strings taken into account (AA and BB).
Total Value = Value(AA) + Value(BB) = 16 + 37 = 53.
The digits in this value are added up to the point where it becomes a single digit number.
53 → 5 + 3 = 8.
The final single-digit input 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 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?
What will be the value of string if all four signals given is taken as input?
