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What is the rationale for the above? I'm not understanding the idea of subtracting .0002, and then adding it back to the other factor.

While solving, I just noticed that the second digit from the right, in each of the answer choices was different, so we only need to multiply the "9" and "8" terms across .9998, add the resulting lines, and see which choice matched the second digit in the answer we just found.

Thanks

Last edited by JackSparr0w on 23 Oct 2014, 07:50, edited 1 time in total.

I think this is quickest to work out using good old long mulptiplication- We only need to work out the second last digit as these are all different 9998*9998 = 79984 89982

So this will sum to a number ending with 04 which is option C

EDIT * Not able to get the allignments right on the long multiplication so this is really hard to understand for anyone who do not understand long multiplication. Anyone able to fix it?

I see. But I was refering to Bunuel's explanation. I also ended up in moltiplying the last two terms but I got D instead of C. Can anyone explain Bunuel's method? It might be useful for the next time I face such a question.

The easiest way is to rewrite the decimal as a binomial and then apply the rule for the square of a binomial \((a+b)^2\) = \(a^2+b^2+2ab\) therefore \((0.9998)^2\) = \((1-2*10^-4)^2\) do the math and find the answer.

Just take last 2 digits, which are 9 and 8. So 98 * 98. The answer is 9604. We dnt need to even complete this 98*98 calculation. Look at last 2 digits of the end result, 04. There is only one option providing 04.
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