Find the digit represented by ? in the following problem: 37? × 35 = 13090. No calculators, please.
Hello, Sigyn3!
I did it "mentally", but then my brain is cluttered with various trivia . . .Find the digit is represented by $\displaystyle {\color{red}?}$ in the following problem: .$\displaystyle 37{\color{red}?} \times 35 \:=\: 13,\!090.$
No calculators, please.
I saw that: .$\displaystyle 37 \times 35 \:=\:(36+1)(36-1) \:=\:36^1 - 1^2 \:=\:1296 - 1 \:=\:1295$
. . So that: .$\displaystyle 370 \times 35 \:=\:12,\!950$ . . . which is 140 short of 13,090
. . Hence, we need four more 35's.
Therefore: , $\displaystyle 37{\color{red}4} \times 35 \:=\:13,\!090$