Tricky Word Problems

Question

a two-digit number is a positive integer greater than 10 but is not a prime number. when its digits are reversed, the result is 45 less than the original number, and is a perfect square. Give the units digit of the original two-digit number.

 

This is so tricky!

Answer 1

x = 10s digit

 

y = units digit

 

10x + y = the number

 

10x + y > 10

 

10y + x = 10x + y - 45

 

9y = 9x - 45

 

y = x - 5

 

10y + x is a perfect square: 25, 36, 49

49 => y = 4, x = 9, y = 9 - 5.

 

Original number is 94.

 

94 > 10 √

49 = 94 - 45 √

√(49) = 7 √

 

The units digit of the original number is 4.

Answer 2

Hi Addie;

10<x

The result is 45 less than the original number...

The original number is...

55<x

Because it is two digits...

x<100

The reverse (r)...

r<55

Let's find all such perfect squares...

25---no

36---no

49+45=***94***

√49=7