A number consists of 3 different digits. The ones and tens place digit...
Understanding the Problem
To determine which number satisfies the given conditions, we need to analyze the criteria:
- The number must consist of 3 different digits.
- The ones and tens place digits must be divisible by 4.
- The hundreds place digit must be a multiple of 7.
Evaluating Each Option
Let's look at each option:
- Option a) 784
- Hundreds place: 7 (multiple of 7)
- Tens place: 8 (divisible by 4)
- Ones place: 4 (divisible by 4)
- Digits: 7, 8, 4 (all different)
This option satisfies all the conditions.
- Option b) 647
- Hundreds place: 6 (not a multiple of 7)
This option fails the hundreds place condition.
- Option c) 864
- Hundreds place: 8 (not a multiple of 7)
This option also fails the hundreds place condition.
- Option d) 282
- Hundreds place: 2 (not a multiple of 7)
This option fails the hundreds place condition as well.
Conclusion
After evaluating all options, only option a) 784 meets all the specified criteria:
- Different Digits: 7, 8, and 4 are all unique.
- Divisibility:
- 8 (tens) is divisible by 4.
- 4 (ones) is divisible by 4.
- Hundreds Place: 7 is a multiple of 7.
Thus, the correct answer is option a) 784.
A number consists of 3 different digits. The ones and tens place digit...
- The digits in the ones and tens places must be divisible by 4, meaning these digits can be 4 or 8.
- The digit in the hundreds place must be a multiple of 7, so the digit must be 7.
So, the possible valid numbers are:
- Hundreds place = 7, Tens place = 8, Ones place = 4 → 784
- Hundreds place = 7, Tens place = 4, Ones place = 8 → 748
However, you are asking for the number 784, which satisfies all the conditions:
- Hundreds digit = 7 (multiple of 7)
- Tens digit = 8 (divisible by 4)
- Ones digit = 4 (divisible by 4)
Thus, the required number is 784.