So, the other day I asked ChatCPT 4 to solve the following question:
If x and y are the tens digit and the units digit, respectively, of the product 725,278 * 67,066, what is the value of x + y. Can you explain the easiest solution without calculating the whole number?
Chat GPT gave this answer:
To find the tens digit of the product, we only need to consider the multiplication
of the tens digit of the first number (7) with the units digit of the second number (6)
and add it to the multiplication of the units digit of the first number (8) with
the tens digit of the second number (6), and then consider the tens digit of the result.
7×6=42
8×6=48
42+48=90
The tens digit of 90 is 9.
x+y=9+8=17
The value of x+y is 17.
The answer to this question is 12 and despite the answer being wrong, logic is correct until a certain point. I gave ChatGPT another shot with different numbers but it couldn’t solve any of them.
To find the tens and units digits of the product ( 725,278 \times 67,066 ) without calculating the entire product, you can focus only on the last two digits of each number. This is because only the last two digits of each number will affect the tens and units digits of the product.
Let’s break it down:
Consider the Last Two Digits of Each Number:
The last two digits of ( 725,278 ) are ( 78 ).
The last two digits of ( 67,066 ) are ( 66 ).
Multiply These Digits:
Multiply ( 78 \times 66 ).
Calculate the Last Two Digits of the Result:
( 78 \times 66 = 5148 ).
The last two digits are ( 48 ).
So, the tens digit (( x )) is ( 4 ) and the units digit (( y )) is ( 8 ).