The sum of a 3-digit number and a 1-digit number is 217. The product of the numbers is 642. If one number is between 200-225,what are the numbers?

Question

the sum of a 3-digit number and a 1-digit number is 217. The product of the numbers is 642. If one number is between 200 and 225, what are the numbers?

Answer 1

This gets pretty easy when you get to middle school math.  4th grade is pretty hard.

 

Let's start at the end:  One number is between 200-225.

 

Now, back up just a bit.  The product of the two numbers is 642.  Product comes from multiplying the two numbers.  So, if we divide 642 by the number that is between 200-225, we will get the other number.

  So, divide 200 into 642 and get 3 with a remainder of 42

      divide 225 into 642 and get 2 with a remainder of 192

 

This means that the other number must be either 2 or 3.  (note: this is because dividing by 200 gives the biggest value it could be and dividing by 225 gives the lowest value it could be -- think about sharing a bag of candy, dividing it between 2 friends gets each person the most candy and dividing it between more friends (3) gives each person less candy).

 

Well. if the other number is either 2 or 3, and the product of the two numbers is 642, the numbers must be either:

     2  and 321

or  3  and 214

 

Ah, ha!  That's why the clue, "the sum ... is 217" is very important.  It tells us which one is the answer.

Answer 2

If you are familiar with prime factorization...

642/2=321

321/3=107

642=2*3*107

2*3*107=3*(2*107)=3*214 and 3+214=217

 

You could also use trial and error.

1+216

2+215

3+214=217 and 3*214=642