if 24y5 is a multiple of 3 where y is the digit what might be the value of y?
2400 is a multiple of 3, so y5 must be a multiple of 3.
Can you think of any 2-digit multiples of 3 ending in 5?
To determine if 24y5 is a multiple of 3, we can examine the sum of its digits.
The sum of the digits in 24y5 can be calculated as:
2 + 4 + y + 5 = 11 + y
For 24y5 to be a multiple of 3, the sum of its digits (11 + y) should be divisible by 3.
Let's check the possible values of y to see if they satisfy that condition:
- If y = 0, then the sum of the digits would be 11 + 0 = 11, which is not divisible by 3.
- If y = 1, then the sum of the digits would be 11 + 1 = 12, which is divisible by 3.
- If y = 2, then the sum of the digits would be 11 + 2 = 13, which is not divisible by 3.
- If y = 3, then the sum of the digits would be 11 + 3 = 14, which is not divisible by 3.
- If y = 4, then the sum of the digits would be 11 + 4 = 15, which is divisible by 3.
- If y = 5, then the sum of the digits would be 11 + 5 = 16, which is not divisible by 3.
- If y = 6, then the sum of the digits would be 11 + 6 = 17, which is not divisible by 3.
- If y = 7, then the sum of the digits would be 11 + 7 = 18, which is divisible by 3.
- If y = 8, then the sum of the digits would be 11 + 8 = 19, which is not divisible by 3.
- If y = 9, then the sum of the digits would be 11 + 9 = 20, which is not divisible by 3.
So, the possible values of y that would make 24y5 a multiple of 3 are 1, 4, and 7.
To determine the value of y, if 24y5 is a multiple of 3, we need to consider the divisibility rule for 3.
The divisibility rule for 3 states that a number is divisible by 3 if the sum of its digits is divisible by 3.
In the given number, 24y5, the sum of the digits is 2 + 4 + y + 5 = 11 + y.
For the number to be divisible by 3, the sum of the digits must also be divisible by 3. So, we need to find the possible values of y that make the sum divisible by 3.
To make the sum 11 + y divisible by 3, y must be a digit so that (11 + y) is divisible by 3.
Let's check the possible values of y to find a suitable answer:
- If y = 0, then (11 + y) = 11, which is not divisible by 3.
- If y = 1, then (11 + y) = 12, which is divisible by 3.
- If y = 2, then (11 + y) = 13, which is not divisible by 3.
- If y = 3, then (11 + y) = 14, which is not divisible by 3.
- If y = 4, then (11 + y) = 15, which is divisible by 3.
- If y = 5, then (11 + y) = 16, which is not divisible by 3.
- If y = 6, then (11 + y) = 17, which is not divisible by 3.
- If y = 7, then (11 + y) = 18, which is divisible by 3.
- If y = 8, then (11 + y) = 19, which is not divisible by 3.
- If y = 9, then (11 + y) = 20, which is not divisible by 3.
Therefore, the possible values for y so that 24y5 is a multiple of 3 are 1, 4, and 7.