How many different numbers could Jenny have thought of?

Question

Jenny thinks of a two-digit number. Daniel reverses the digits and when the two numbers are added the total is 143. How many different numbers could Jenny have thought of?

 

a. 2

b. 4

c. 6

d. 8

 

Answer 1

Have you learned algebra yet?

 

To do this using algebra, you'd say the following:

 

Let x be the tens place of Jenny's number, and let y be the ones place.  So her number is 10x + y.

 

Daniel reverses the digits, so his number is 10y + x.

 

Add the two together and you get 11x + 11y.

 

Since that's equal to 143, x + y must be equal to 143 / 11, which is 13.

 

So the two digits have to add up to 13.

 

So list the numbers that Jenny could have used, where the digits add up to 13:

 

49

58

67

76

85

94

 

So the answer is c.

 

To check this, for each one reverse the digits and add the two numbers.  You'll see that in each case, the sum is 143.