I am 4-digit number divisibleby 3.My tens digit is three times as great as my thousands digit, and sum of my digit is 15 .if you reverse my digit , I am divisible by 2 as well as by6.what am I?
To find the 4-digit number that meets the given conditions, we will break down the question step by step.
Step 1: The number is divisible by 3.
A number is divisible by 3 if the sum of its digits is also divisible by 3. In this case, the sum of the digits is 15, so the number is divisible by 3.
Step 2: The tens digit is three times as great as the thousands digit.
Let's assume the thousands digit is x. According to the given condition, the tens digit will be 3x.
Step 3: Finding the possible values.
We know the sum of the digits is 15, so we can establish the equation: x + 3x + (x + 3x) + (3x + x) = 15.
Simplifying the equation: 15x + 6x = 15.
Combining like terms: 21x = 15.
Dividing both sides by 21: x = 15 / 21.
Solving for x: x = 5/7.
Since the thousands digit cannot be a fraction, there is no valid solution for this step. Therefore, we can conclude that the given conditions do not lead to a valid 4-digit number.
Apologies, but there is no possible value for the given conditions.
To find the 4-digit number that meets the given conditions, let's break down the information step-by-step:
1. The number is divisible by 3: This means that the sum of its digits must be divisible by 3.
2. The tens digit is three times as great as the thousands digit: Let's call the thousands digit "A" and the tens digit "B." According to the given information, B = 3A.
3. The sum of the digits is 15: The sum of all four digits must equal 15. We can write this as: A + B + C + D = 15.
4. Reversing the digits makes the number divisible by 2 and 6: For a number to be divisible by 2, the units digit must be even. For a number to be divisible by 6, it must also be divisible by both 2 and 3. Therefore, the units digit must be both even and divisible by 3.
Let's use these conditions to solve for the number step-by-step:
Step 1: Since the number is divisible by 3, we can determine that the sum of its digits must also be divisible by 3. In this case, that means the sum of A + B + C + D = 15 must be divisible by 3.
Step 2: Looking at the given information that B = 3A, we can substitute B with 3A in the equation from Step 1. This gives us: A + 3A + C + D = 15.
Step 3: Simplifying the equation further, we have 4A + C + D = 15.
Step 4: Given that the number is divisible by 2, the units digit must be even. The possible options for the units digit are 0, 2, 4, 6, or 8.
Step 5: Since the number is divisible by 6, the units digit must be both even and divisible by 3. From the possible options in Step 4, the only viable choice is 6.
Step 6: Next, we substitute D with 6 in the equation from Step 3: 4A + C + 6 = 15.
Step 7: Simplifying further, we get 4A + C = 9.
Step 8: The only possible values for A and C that satisfy the equation in Step 7 are A = 1 and C = 5.
Step 9: Therefore, the thousands digit (A) is 1, the tens digit (B) is 3 times that value, so B = 3, and the units digit (D) is 6. Reversing the digits for the number gives us 1636.
Therefore, the 4-digit number that meets all the given conditions is 1636.