Math Is Fun Forum

Jan3

Member

Registered: 2008-07-19

Posts: 1

Urgent: need help

Dear all,
I need help for this qns. Please kindly lend me a helping hand. thanks alot!         

                 ABC
                 XBC
                _____
                16BC

Each number represent a number. What number does BC represent?

Identity

Member

Registered: 2007-04-18

Posts: 934

Re: Urgent: need help

Are the numbers distinct? Can 0 be a number? This is what I've got so far:

Let's think of all the possible C such that they multiply to give another number with unit digit C.
0 × 0 = 0
1 × 1 = 1
5 × 5 = 25
6 × 6 = 36
So C can be 0 or 1 or 5 or 6.

Now think of all numbers BC such that when squared, end in BC.
We could test all numbers BC such that C = 0, but in that case you have 10B × 10B = 100B², but 100B² is a number ending in 2 zeroes, so this cannot work.
Next, test all numbers BC such that C = 1, in this case, (10B+1)(10B+1) = 100B² +20B + 1. It will end in 1, but 20B will only have B as its tens digit if B = 0. Going back to the original equation however, A01 × 01 will always be 3-digit, so this case cannot work either.
Next, if C = 5, (10B+5)(10B+5) = 100B²+100B+25. It will hence always end in 25. The only way this works is if BC = 25. But, 025 × 25 = 625 (too low) and 125 × 25 = 3125 (already too high) so this can't work either.
Lastly, if C = 6, if you test the cases (there aren't many), we find that none work.

Hence, there is NO SOLUTION. NOOOOOOOOOOOOOOOOOOOOOOOOOOOOoooooooooooooooooooooooooooooo

Jan3

Member

Registered: 2008-07-19

Posts: 1

Re: Urgent: need help

thanks for your prompt reply!
i'll take note.

Dragonshade

Member

Registered: 2008-01-16

Posts: 147

Re: Urgent: need help

Here's my work

Last edited by Dragonshade (2008-07-20 13:57:40)