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How many two-digit numbers, with a non-zero digit in the units place, are there which are more than thrice the number formed by interchanging the positions of its digits?
Correct answer is '6'. Can you explain this answer?
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Verified Answer
How many two-digit numbers, with a non-zero digit in the units place, ...
Let 'ab' be the two digit number. Where b ≠ 0.
We will get number 'ba' after interchanging its digit.
It is given that 10a+b > 3*(10b + a)
7a > 29b
If b = 1, then a = {5, 6, 7, 8, 9}
If b = 2, then a = {9}
If b = 3, then no value of 'a' is possible. Hence, we can say that there are a total of 6 such numbers.
We will get number 'ba' after interchanging its digit.
It is given that 10a+b > 3*(10b + a)
7a > 29b
If b = 1, then a = {5, 6, 7, 8, 9}
If b = 2, then a = {9}
If b = 3, then no value of 'a' is possible. Hence, we can say that there are a total of 6 such numbers.
Most Upvoted Answer
How many two-digit numbers, with a non-zero digit in the units place, ...
Problem:
How many two-digit numbers, with a non-zero digit in the units place, are there which are more than thrice the number formed by interchanging the positions of its digits? Correct answer is '6'. Can you explain this answer?
Solution:
To find the required numbers, we need to consider the following cases:
Case 1: Units digit is 1
If the units digit is 1, the tens digit must be greater than 3 for the number to be more than thrice the number formed by interchanging the positions of its digits. There are 6 such numbers: 41, 51, 61, 71, 81, and 91.
Case 2: Units digit is 2
If the units digit is 2, the tens digit must be greater than 6 for the number to be more than thrice the number formed by interchanging the positions of its digits. There are no such numbers.
Case 3: Units digit is 3
If the units digit is 3, the tens digit must be greater than 9 for the number to be more than thrice the number formed by interchanging the positions of its digits. There are no such numbers.
Case 4: Units digit is 4
If the units digit is 4, the tens digit must be greater than 12 for the number to be more than thrice the number formed by interchanging the positions of its digits. There are no such numbers.
Case 5: Units digit is 5
If the units digit is 5, the tens digit must be greater than 15 for the number to be more than thrice the number formed by interchanging the positions of its digits. There are no such numbers.
Case 6: Units digit is 6
If the units digit is 6, the tens digit must be greater than 18 for the number to be more than thrice the number formed by interchanging the positions of its digits. There are no such numbers.
Case 7: Units digit is 7
If the units digit is 7, the tens digit must be greater than 21 for the number to be more than thrice the number formed by interchanging the positions of its digits. There are no such numbers.
Case 8: Units digit is 8
If the units digit is 8, the tens digit must be greater than 24 for the number to be more than thrice the number formed by interchanging the positions of its digits. There are no such numbers.
Case 9: Units digit is 9
If the units digit is 9, the tens digit must be greater than 27 for the number to be more than thrice the number formed by interchanging the positions of its digits. There are no such numbers.
Therefore, there are a total of 6 numbers that satisfy the given conditions.
How many two-digit numbers, with a non-zero digit in the units place, are there which are more than thrice the number formed by interchanging the positions of its digits? Correct answer is '6'. Can you explain this answer?
Solution:
To find the required numbers, we need to consider the following cases:
Case 1: Units digit is 1
If the units digit is 1, the tens digit must be greater than 3 for the number to be more than thrice the number formed by interchanging the positions of its digits. There are 6 such numbers: 41, 51, 61, 71, 81, and 91.
Case 2: Units digit is 2
If the units digit is 2, the tens digit must be greater than 6 for the number to be more than thrice the number formed by interchanging the positions of its digits. There are no such numbers.
Case 3: Units digit is 3
If the units digit is 3, the tens digit must be greater than 9 for the number to be more than thrice the number formed by interchanging the positions of its digits. There are no such numbers.
Case 4: Units digit is 4
If the units digit is 4, the tens digit must be greater than 12 for the number to be more than thrice the number formed by interchanging the positions of its digits. There are no such numbers.
Case 5: Units digit is 5
If the units digit is 5, the tens digit must be greater than 15 for the number to be more than thrice the number formed by interchanging the positions of its digits. There are no such numbers.
Case 6: Units digit is 6
If the units digit is 6, the tens digit must be greater than 18 for the number to be more than thrice the number formed by interchanging the positions of its digits. There are no such numbers.
Case 7: Units digit is 7
If the units digit is 7, the tens digit must be greater than 21 for the number to be more than thrice the number formed by interchanging the positions of its digits. There are no such numbers.
Case 8: Units digit is 8
If the units digit is 8, the tens digit must be greater than 24 for the number to be more than thrice the number formed by interchanging the positions of its digits. There are no such numbers.
Case 9: Units digit is 9
If the units digit is 9, the tens digit must be greater than 27 for the number to be more than thrice the number formed by interchanging the positions of its digits. There are no such numbers.
Therefore, there are a total of 6 numbers that satisfy the given conditions.
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Community Answer
How many two-digit numbers, with a non-zero digit in the units place, ...
Suppose the original number is ab
which means, 10a+b
According to the question,
10a+b > 3×(10b+a)
which gives,
7a > 29b
using hit and trial gives, 51, 61, 71, 81, 91, 92
which means, 10a+b
According to the question,
10a+b > 3×(10b+a)
which gives,
7a > 29b
using hit and trial gives, 51, 61, 71, 81, 91, 92
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How many two-digit numbers, with a non-zero digit in the units place, are there which are more than thrice the number formed by interchanging the positions of its digits?Correct answer is '6'. Can you explain this answer?
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