Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation
Already signed up?
New to KöMaL?
I want the old design back!!! :-)

Problem C. 1095. (November 2011)

C. 1095. Which product is greater: 555\; 555\; 555\; {553 \cdot 666}\; 666\; 666\; 669 or 555\; 555\; 555\; {557 \cdot 666}\; 666\; 666\; 664?

(5 pont)

Deadline expired on December 12, 2011.


Sorry, the solution is available only in Hungarian. Google translation

Megoldás. Legyen \(\displaystyle a=111\ 111\ 111\ 111\). Ekkor az összehasonlítandó szorzatok \(\displaystyle B=(5a-2)(6a+3)\) és \(\displaystyle J=(5a+2)(6a-2)\), azaz \(\displaystyle B=30a^2 +3a -6\) és \(\displaystyle J=30a^2 -4\). Mivel \(\displaystyle B-J=3a-2>0\), ezért a bal oldali szorzat nagyobb, mint a jobb oldali.


Statistics:

464 students sent a solution.
5 points:339 students.
4 points:40 students.
3 points:29 students.
2 points:15 students.
1 point:8 students.
0 point:21 students.
Unfair, not evaluated:12 solutions.

Problems in Mathematics of KöMaL, November 2011