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X is a 30 digit number starting with the digit 4 followed by the digit 7. Then the number X3 will have
- a)92 digits
- b)91 digits
- c)90 digits
- d)93 digits
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
X is a 30 digit number starting with the digit 4 followed by the digit...
Minimum digits of x = 25x1023 = 25 digits
Minimum digits of x5 = (25x1023)5 = 122 digits
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Community Answer
X is a 30 digit number starting with the digit 4 followed by the digit...
Explanation:
To find the minimum number of digits in X5, we need to determine the minimum possible value of X.
Step 1:
Since X starts with the digit 2 followed by the digit 5, we can represent X as follows:
X = 25 + A
Here, A represents the remaining digits of X.
Step 2:
To find the minimum value of A, we need to consider the smallest possible value for each digit in A.
Since X is a 25-digit number, the remaining digits in A can be any digit from 0 to 9. However, to minimize the value of A, we need to choose the smallest possible digit for each position.
Therefore, A will be composed of ten 0s followed by fourteen 1s.
Step 3:
Now, let's calculate the minimum value of X:
X = 25 + A
X = 25 + 000000000011111111111111
Step 4:
To find the minimum value of X5, we need to determine the smallest possible value for the remaining digits after 25 in X5.
Since X5 is a number that starts with X and ends with 5, the remaining digits after 25 in X5 will be the same as A.
Therefore, X5 will have the same number of digits as A.
Step 5:
Now, let's calculate the number of digits in X5:
Number of digits in X5 = Number of digits in A
Number of digits in X5 = Number of digits in 000000000011111111111111
Number of digits in X5 = 10 + 14
Number of digits in X5 = 24
Conclusion:
Therefore, the number X5 will have a minimum of 24 + 1 = 25 digits. However, since X is a 25-digit number, the number X5 will actually have a minimum of 25 + 1 = 26 digits.
Therefore, the correct answer is option C) 122 digits.
To find the minimum number of digits in X5, we need to determine the minimum possible value of X.
Step 1:
Since X starts with the digit 2 followed by the digit 5, we can represent X as follows:
X = 25 + A
Here, A represents the remaining digits of X.
Step 2:
To find the minimum value of A, we need to consider the smallest possible value for each digit in A.
Since X is a 25-digit number, the remaining digits in A can be any digit from 0 to 9. However, to minimize the value of A, we need to choose the smallest possible digit for each position.
Therefore, A will be composed of ten 0s followed by fourteen 1s.
Step 3:
Now, let's calculate the minimum value of X:
X = 25 + A
X = 25 + 000000000011111111111111
Step 4:
To find the minimum value of X5, we need to determine the smallest possible value for the remaining digits after 25 in X5.
Since X5 is a number that starts with X and ends with 5, the remaining digits after 25 in X5 will be the same as A.
Therefore, X5 will have the same number of digits as A.
Step 5:
Now, let's calculate the number of digits in X5:
Number of digits in X5 = Number of digits in A
Number of digits in X5 = Number of digits in 000000000011111111111111
Number of digits in X5 = 10 + 14
Number of digits in X5 = 24
Conclusion:
Therefore, the number X5 will have a minimum of 24 + 1 = 25 digits. However, since X is a 25-digit number, the number X5 will actually have a minimum of 25 + 1 = 26 digits.
Therefore, the correct answer is option C) 122 digits.
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X is a 30 digit number starting with the digit 4 followed by the digit 7. Then the number X3will havea)92 digitsb)91 digitsc)90 digitsd)93 digitsCorrect answer is option 'C'. Can you explain this answer?
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