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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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How many two-digit numbers, with a non-zero digit in the units place,...
Let 'ab' be the two digit number. Where b ≠ 0.
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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 thereare a total of 6 such numbers.
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How many two-digit numbers, with a non-zero digit in the units place,...
Solution:
To count the number of two-digit numbers satisfying the given conditions, let's break down the problem into smaller steps.
Step 1: Identifying the two-digit numbers
We need to find two-digit numbers with a non-zero digit in the units place. So, the range of numbers we need to consider is from 10 to 99.
Step 2: Forming the number by interchanging digits
To find the number formed by interchanging the positions of the digits, we need to consider the tens digit as the units digit and the units digit as the tens digit. For example, if the original number is 23, the number formed by interchanging the positions of the digits would be 32.
Step 3: Finding the condition
The condition given states that the two-digit number should be more than thrice the number formed by interchanging its digits. Mathematically, this can be expressed as:
Number > 3 * (Number formed by interchanging digits)
Step 4: Evaluating the condition
Let's evaluate the condition for each possible two-digit number and check if it satisfies the given condition.
- For the number 10, the number formed by interchanging the digits is 1. But 10 is not more than thrice 1, so it doesn't satisfy the condition.
- For the number 11, the number formed by interchanging the digits is 11. But 11 is not more than thrice 11, so it doesn't satisfy the condition.
- For the number 12, the number formed by interchanging the digits is 21. But 12 is more than thrice 21, so it satisfies the condition.
- For the number 13, the number formed by interchanging the digits is 31. But 13 is more than thrice 31, so it satisfies the condition.
- For the number 14, the number formed by interchanging the digits is 41. But 14 is more than thrice 41, so it satisfies the condition.
- For the number 15, the number formed by interchanging the digits is 51. But 15 is more than thrice 51, so it satisfies the condition.
We can continue this process for all two-digit numbers up to 99 and count the numbers that satisfy the condition.
Step 5: Counting the numbers satisfying the condition
From the evaluation, we can see that there are 6 two-digit numbers that satisfy the given condition.
Therefore, the correct answer is '6'.
To count the number of two-digit numbers satisfying the given conditions, let's break down the problem into smaller steps.
Step 1: Identifying the two-digit numbers
We need to find two-digit numbers with a non-zero digit in the units place. So, the range of numbers we need to consider is from 10 to 99.
Step 2: Forming the number by interchanging digits
To find the number formed by interchanging the positions of the digits, we need to consider the tens digit as the units digit and the units digit as the tens digit. For example, if the original number is 23, the number formed by interchanging the positions of the digits would be 32.
Step 3: Finding the condition
The condition given states that the two-digit number should be more than thrice the number formed by interchanging its digits. Mathematically, this can be expressed as:
Number > 3 * (Number formed by interchanging digits)
Step 4: Evaluating the condition
Let's evaluate the condition for each possible two-digit number and check if it satisfies the given condition.
- For the number 10, the number formed by interchanging the digits is 1. But 10 is not more than thrice 1, so it doesn't satisfy the condition.
- For the number 11, the number formed by interchanging the digits is 11. But 11 is not more than thrice 11, so it doesn't satisfy the condition.
- For the number 12, the number formed by interchanging the digits is 21. But 12 is more than thrice 21, so it satisfies the condition.
- For the number 13, the number formed by interchanging the digits is 31. But 13 is more than thrice 31, so it satisfies the condition.
- For the number 14, the number formed by interchanging the digits is 41. But 14 is more than thrice 41, so it satisfies the condition.
- For the number 15, the number formed by interchanging the digits is 51. But 15 is more than thrice 51, so it satisfies the condition.
We can continue this process for all two-digit numbers up to 99 and count the numbers that satisfy the condition.
Step 5: Counting the numbers satisfying the condition
From the evaluation, we can see that there are 6 two-digit numbers that satisfy the given condition.
Therefore, the correct answer is '6'.
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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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