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 correct option if both signals AA and DD is taken as input?
The program will be executed.
Detailed Solution for Matrix and String Logic Problem
The problem requires us to first construct a 4x4 matrix based on a set of rules and then evaluate given strings (AA and DD) using values from this matrix and another set of rules. Finally, we determine the program's execution outcome based on the resulting single-digit value.
Step 1: Constructing the 4x4 Matrix
The matrix has rows %, $, #, @ and columns 1, 2, 3, 4.
Rule 1: Diagonals
- Diagonal 1 (%,1 to @,4) is IBPS: %,1=I, $,2=B, #,3=P, @,4=S.
- Diagonal 2 (%,4 to @,1) is 2019: %,4=2, $,3=0, #,2=1, @,1=9.
Matrix after Rule 1:
| 1 | 2 | 3 | 4 | |
|---|---|---|---|---|
| % | I | 2 | ||
| $ | B | 0 | ||
| # | 1 | P | ||
| @ | 9 | S |
Rule 2: Immediate Neighbor of Alphabet
One immediate neighbor of an alphabet in the same row gets its alphabetical position value (I=9, B=2, P=16, S=19). Based on the need for Rule 3, the placement should facilitate difference calculation between two numbers.
- Row %: I at %,1 (pos 9). Neighbors %,2, %,3. %,4=2. To enable Rule 3 for %,3, %,2 must be 9.
- Row $: B at $,2 (pos 2). Neighbors $,1, $,3=0. $,1 is empty. $,1 must be 2.
- Row #: P at #,3 (pos 16). Neighbors #,2=1, #,4. #,4 is empty. #,4 must be 16.
- Row @: S at @,4 (pos 19). Neighbors @,2, @,3. @,1=9. To enable Rule 3 for @,2, @,3 must be 19.
Matrix after Rule 2 (strategic placement):
| 1 | 2 | 3 | 4 | |
|---|---|---|---|---|
| % | I | 9 | 2 | |
| $ | 2 | B | 0 | |
| # | 1 | P | 16 | |
| @ | 9 | 19 | S |
Rule 3: Difference between Surrounding Numbers
Remaining places between two numbers are filled by their absolute difference.
- Row %: %,3 is between %,2 (9) and %,4 (2). %,3 = |9-2| = 7.
- Row $: $,4 is next to 0 ($,3) and B ($,2). Not between two numbers. Rule 3 doesn't strictly apply.
- Row #: #,1 is next to 1 (#,2) and P (#,3). Not between two numbers. Rule 3 doesn't strictly apply.
- Row @: @,2 is between @,1 (9) and @,3 (19). @,2 = |9-19| = 10.
Matrix after applying Rule 3 where possible:
| 1 | 2 | 3 | 4 | |
|---|---|---|---|---|
| % | I | 9 | 7 | 2 |
| $ | 2 | B | 0 | |
| # | 1 | P | 16 | |
| @ | 9 | 10 | 19 | S |
The rules do not explicitly cover cells at the ends of rows ($4 and #1) that are not between two numbers. However, the column sum condition must hold for the final matrix. Let's consider a common pattern in such puzzles where the difference rule might extend to using the alphabetical position of an adjacent alphabet. If we assume $4 is the difference between 0 and B (pos 2), $4 = |0-2| = 2$. If #1 is the difference between 1 and P (pos 16), #1 = |1-16|=15. Let's test this completed matrix against the column sum condition.
| 1 | 2 | 3 | 4 | |
|---|---|---|---|---|
| % | I(9) | 9 | 7 | 2 |
| $ | 2 | B(2) | 0 | 2 |
| # | 15 | 1 | P(16) | 16 |
| @ | 9 | 10 | 19 | S(19) |
Column 2 numbers: 9 (%,2) + B(2) ($,2) + 1 (#,2) + 10 (@,2) = 9+2+1+10 = 22.
Column 3 numbers: 7 (%,3) + 0 ($,3) + P(16) (#,3) + 19 (@,3) = 7+0+16+19 = 42.
The sum of digits in column 2 (22) is less than that of column 3 (42). This assumed filling method satisfies the condition. So we proceed with this matrix.
Final Matrix Values (Alphabetical positions used where applicable):
| 1 | 2 | 3 | 4 | |
|---|---|---|---|---|
| % | I(9) | 9 | 7 | 2 |
| $ | 2 | B(2) | 0 | 2 |
| # | 15 | 1 | P(16) | 16 |
| @ | 9 | 10 | 19 | S(19) |
Step 2: Evaluate String AA = $2 #1 @3 #3
Get values from the matrix:
- $2 = B (Alphabetical position 2)
- #1 = 15
- @3 = 19
- #3 = P (Alphabetical position 16)
String AA values: {B, 15, 19, P}. Numerical values for calculation: {2, 15, 19, 16}.
Check string evaluation conditions:
- Condition 1 (Equal even/odd numbers): Numbers {15, 19, 16}. Odd: 15, 19 (2). Even: 16 (1). Not equal.
- Condition 2 (Equal alphabets/numbers): Alphabets {B, P} (2). Numbers {15, 19} (2). Equal. Condition 2 applies.
Value of string AA = Absolute difference between sum of alphabetical positions and sum of numbers.
Sum of alphabetical positions = 2 (for B) + 16 (for P) = 18.
Sum of numbers = 15 + 19 = 34.
Value of AA = |18 - 34| = |-16| = 16.
Step 3: Evaluate String DD = %4 @2 @4 #2
Get values from the matrix:
- %4 = 2
- @2 = 10
- @4 = S (Alphabetical position 19)
- #2 = 1
String DD values: {2, 10, S, 1}. Numerical values for calculation: {2, 10, 19, 1}.
Check string evaluation conditions:
- Condition 1 (Equal even/odd numbers): Numbers {2, 10, 1}. Even: 2, 10 (2). Odd: 1 (1). Not equal.
- Condition 2 (Equal alphabets/numbers): Alphabets {S} (1). Numbers {2, 10, 1} (3). Not equal.
- Condition 3 (Only one even number): Numbers {2, 10, 1}. Even numbers are 2 and 10 (two). Not one.
- Condition 4 (Vowel in string): String {2, 10, S, 1}. No vowel.
- Condition 5 (None of above): Applies.
Value of string DD = Subtract the lowest number from the highest number in the string.
Numbers in DD are {2, 10, 1}. Lowest = 1, Highest = 10.
Value of DD = 10 - 1 = 9.
Step 4: Calculate the Input Value
The input value is obtained by adding the values of all strings (AA and DD) and then summing the digits of the result until a single digit is obtained.
Sum of values = Value of AA + Value of DD = 16 + 9 = 25.
Sum of digits of 25 = 2 + 5 = 7.
The final single-digit input value is 7.
Step 5: Determine Program Execution Outcome
The outcome depends on the single-digit input value (7).
- If the value is a prime number, the program will be executed. (7 is prime)
- If the value is an even number, the program will not be executed. (7 is not even)
- If the value is both even and prime, it will execute with an error. (7 is not even)
- If none of the above, the PC will hang. (7 is prime, so it's covered by the first condition)
Since the input value 7 is a prime number, the program will be executed.
Conclusion
Based on the constructed matrix and the string evaluation rules, the input value derived from strings AA and DD is 7. As 7 is a prime number, the program will be executed.
The correct option is that the program will be executed.
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 will be the value of string if all four signals given is taken as input?
