it is a 3 digit number
all the digits are different
the first and second digits are multiple of 3
the first digit is greater than the second digit.
the sum of the first two digits is 7 more that the third digit
the number is not a multiple of 5 the third digit is greater than 3
let the number have the form abc
"the first and second digits are multiple of 3
the first digit is greater than the second digit."
---> has to be 63c or 963, would also consider 30c
"the sum of the first two digits is 7 more that the third digit "
--> a+b-7 = c , which rules out the case 30c
for 63c , c = 2, but the third digit has to greater than 3
for 96c , c = 8
so the number is 968
check:
is it a 3 digit number? yes
are all the digits different? yes
are the 1st and 2nd multiples of 3? yes
is the first > the 2nd ? yes
is the sum of the first and second 7 more than the third? yes
the number is NOT a multiple of 5 ? yes
the third digit > 3 ? yes
Note the hint about multiples of 5 was not needed.
Which one is first number from left or right
Let's break down the given information step-by-step to find the desired 3-digit number:
Step 1: All the digits are different.
Step 2: The first and second digits are multiples of 3.
Step 3: The first digit is greater than the second digit.
Step 4: The sum of the first two digits is 7 more than the third digit.
Step 5: The number is not a multiple of 5.
Step 6: The third digit is greater than 3.
Let's start solving these steps one by one:
Step 1: All the digits are different.
Since it's a 3-digit number, we need to find three different digits for the number.
Step 2: The first and second digits are multiples of 3.
We'll list down the multiples of 3: 3, 6, 9.
Step 3: The first digit is greater than the second digit.
Since the first digit is greater, we can eliminate 3 as a possibility for the first digit.
Step 4: The sum of the first two digits is 7 more than the third digit.
We need to find three numbers that satisfy this condition. Let's list them down:
- 6 + 9 = 15 (not 7 more than any single-digit number)
- 9 + 6 = 15 (not 7 more than any single-digit number)
- 9 + 3 = 12 (possible)
Step 5: The number is not a multiple of 5.
Since we haven't found the number yet, we can't confirm if it's a multiple of 5 or not.
Step 6: The third digit is greater than 3.
Since the only possible sum we found in step 4 is 12, and the third digit must be greater than 3, the only remaining possibility is 9.
Putting it all together, the 3-digit number that satisfies all the given conditions is 963.
To find the three-digit number that satisfies these conditions, we can break down the problem step by step:
1. The first and second digits are multiples of 3:
Since the first digit must be greater than the second digit, our options are limited. Possible pairs are (3, 6), (3, 9), and (6, 9).
2. The first and second digits add up to 7 more than the third digit:
We can try adding 7 to the first two-digit options to check if any of them satisfy this condition:
- (3 + 7 = 10) and (6 + 7 = 13)
- (3 + 7 = 10) and (9 + 7 = 16)
- (6 + 7 = 13) and (9 + 7 = 16)
3. The third digit is greater than 3:
Out of the possible combinations, we should check which ones have a third digit greater than 3:
- (3, 6, 1) - The third digit is not greater than 3.
- (3, 9, 6) - The third digit is greater than 3.
- (6, 9, 6) - The third digit is greater than 3.
Finally, we have found our solution:
The three-digit number that satisfies all the given conditions is 396.