We have students that are preparing for the Pythagoras Contest which is a nation wide Grade 6 math challenge.

In the preparatory tests we have run into several questions that we can not understand.

Is there anyone who can help us?

1. If 1 * 9 = 0, 9 * 8 = 72, 2 * 8 = 9, then 9 * 9 = ?

   A)81   B)19   C)0   D)61   E)80

2. To multiply a number by 25 we can

   A) multiply it five times by 5
   B) multiply it by 5 and then add 5
   C) multiply it by 2 and then by 5
   D) multiply it by 2 and then add 5
   E) multiply it by 100 and then divide it by 4

Thank you in advance for your assistance.

Hi Bruce,

1. The rule for problem 1 seems to be:

   Subtract one from the first number, add one to the second number and then multiply, so

   1*9=(1-1)(9+1)=0x10=0
   9*8=(9-1)(8+1)=8x9=72
   2*8=(2-1)x(8+1)=1x9=9

   Thus
   9*9=(9-1)(9+1)=8x10=80

2. When checking whether the proposed procedure gives the same answer as the traditional one, you really only need ONE bad answer to eliminate a proposal. So take a SIMPLE number (e.g. 1) and test each of the proposals:

   (A) Is 25x1 equal to 5x5x5x5x5x1? NO

   (B) Is 25x1 equal to 5x1+5? NO

   (C) Is 25x1 equal to 1x2x5? NO

   (D) Is 25x1 equal to 1x2+5? NO

   (E) Is 25x1 equal to 1x100/4? YES

   Thus only option (E) could possibly be correct. Given it is multiple choice, you are done.

   If you really want to 'understand' then look at what the formula suggests as an alternative and see if you can see WHY it ALWAYS gives the same answer!