Three Digits, sum and product
Pro Problems > Math > Number and Quantity > Number Theory > DigitsThree Digits, sum and product
I'm a three digit number. My first two digits multiply to 12, and my last two digits add to 14. What number am I?
Solution
In order to make it feasible for teachers to use these problems in their classwork, no solutions are publicly visible, so students cannot simply look up the answers. If you would like to view the solutions to these problems, you must have a Virtual Classroom subscription.
Similar Problems
Three Digit Number
I am thinking of a three-digit number. The sum of my digits is 17. Two of my digits add to 10, and two of my digits are the same. Find all possible values for my number.
Happy New Year
Happy New Year! I am a four-digit year, and my last two digits are a perfect square. The sum of my first and third digits is a perfect square. My second digit is a perfect square. All my digits add to a perfect square.
If you subtract my first, second, and third digit from my last digit, you get a perfect square.
If you subtract my third digit from my first digit, you get a perfect square.
Oh, by the way, I'm a perfect square.
What year am I?
Reverse Me
I'm a three digit number. Reverse my digits and subtract, and the result is 198. Reverse my digits and add, and the result is 1272.
What number am I?
Grapes on the Vine
The number of grapes on my grape vine is a three digit number. It is 7 times as much as the number of grapes on the vine last year, and 11 times the number of grapes on the vine the previous year. Next year, if I have twice as many grapes as I do this year, the number of grapes will still be a three digit number, but if I have three times as many grapes, the number of grapes will be a four digit number. If I have 21 times as many grapes, the number of grapes will be a five digit number.
If each jar of grape juice requires 20 grapes, how many full jars of grape juice can I make this year?
Five Digit Number
The sum of the digits of a three digit number is eighteen. The first digit is three more than the last digit. There is a repeated digit in the number. What are all possible values of the number?
Sum of Digits
Find the sum of all the integers between one and 100 which have 14 as the sum of their digits.
Two Digit Pattern Matching
How many two-digit numbers are there such that the digits match at least one of the following patterns:
- The digits are both multiples of three.
- Neither of the digits are multiples of two.
- The digits add to 8.
- The digits are perfect squares.
I Have Three Digits
I am a three digit number, and the following things are true about me:
- The product of two of my digits is 8.
- The sum of my digits is 13.
- My first digit is four times my second digit.
What number am I?
Find the Number
My digits are all odd, and they add to 18. My first digit is four more than my last digit, the product of my digits is between 300 and 315, and I am less than 100,000. If my digits are not in descending order, what numbers could I be?
Three Digit Difference
Two positive integers, A and B, both have 3 digits. A is bigger than B. A – B is between 300 and 400. What is the value of A - B?
Blogs on This Site
Like us on Facebook to get updates about new resources