How to solve this Olympiad Maths question ?

[Corinthia]

Question : Find the value of 20042005 × 20052004 − 20042004 × 20052005

Answer is 10000

Anyone know the logical steps / explanation to the answer ?

Thanks

[tan_r]

In maths, multiplication is done before addition or subtraction. It has always been the rule. Why? I dunno!

(20042005 x 20052004) - (20042004 x 20052005)

[Corinthia]

Thanks.

(20042005 x 20052004) - (20042004 x 20052005) is correct but in order to find the answer, calculator is required. Calculator is not allowed in solving the question..

I have tried a few methods and I think I have found a solution using algebra.

Would like to know if there are better ways or more logical steps to find the answer.

[tesdniMa]

(a+1)(b-1) - a.b

= a.b + b - a - 1 - a.b

= b - a - 1 = 10000

since b - a = 10001

was that your algebraic solution ?


how long are you normally given for such a question?

do you have links for such papers?

[Corinthia]

Yes, this is the algebraic solution I used.

For the benefit of others, here is the solution.

20042005*20052004-20042004*20052005

= [(20042004+1)*(20052005-1)]-20042004*20052005
= [20042004*20052005-20042004+20052005-1]-20042004*20052005
= [20042004*20052005-20042004*20052005] -20042004+20052005-1
= 0-20042004+20052005-1
= 0+10001-1
= 10000

This is one of the Olympiad maths questions for upper primary in Singapore (primary 5 & 6). I doubt the algebra way is within the scope of this age group. I am looking for “easier” solution" (if any) that match this age group..

The link to these questions was sent by my kid's school to me. I am not sure whether I can post here..

[AltV]

Question : Find the value of 20042005 × 20052004 − 20042004 × 20052005

Answer is 10000

Anyone know the logical steps / explanation to the answer ?

Thanks

20042005 x 20052004 - 20042004 x 20052005
= (20042004 +1) x 20052004 - 20042004 x (20052004 +1)
= (20042004 x 20052004 + 20052004) - (20042004 x 20052004 + 20042004) ** use (a + b) x c = ac + bc
let X = 20042004 x 20052004, then
= X + 20052004 - X - 20042004
= 20052004 - 20042004
= 10000

[Corinthia]

20042005 x 20052004 - 20042004 x 20052005
= (20042004 +1) x 20052004 - 20042004 x (20052004 +1)
= (20042004 x 20052004 + 20052004) - (20042004 x 20052004 + 20042004) ** use (a + b) x c = ac + bc
let X = 20042004 x 20052004, then
= X + 20052004 - X - 20042004
= 20052004 - 20042004
= 10000

Thanks, the application of your algebraic solution (a + b) x c = ac + bc is a better one..

It is "easier" to understand compares to what I used earlier, (a+1)(b-1) = ab-a+b-1..

Both are using the same principle - to get rid of unwanted unknowns in an equation..

[AltV]

Still, it is out of the scope of primary student math.

[Corinthia]

Still, it is out of the scope of primary student math.

You are right... but this is Singapore !!

If you are aware of ICAS (The International Competitions and Assessments for Schools), you will know Singapore is one year ahead in the same age group.

For example, the exam papers for Year 5 (public school in Australia, International school in Malaysia), Standard 5 (public school in Malaysia), Grade 5 (South Africa) are NOT the exam papers for Primary 5 students in Singapore, but for Primary 4 students.. !!

You can find the above info at the last page of the exam papers.