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M15-07

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Joined: 02 Sep 2009
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16 Sep 2014, 00:55
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Difficulty:

35% (medium)

Question Stats:

68% (00:50) correct 32% (00:48) wrong based on 73 sessions

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Which of the following is equal to $$(0.9998)^2$$?

A. 0.99950014
B. 0.99950234
C. 0.99960004
D. 0.99960064
E. 0.99961024

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16 Sep 2014, 00:55
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Official Solution:

Which of the following is equal to $$(0.9998)^2$$?

A. 0.99950014
B. 0.99950234
C. 0.99960004
D. 0.99960064
E. 0.99961024

$$0.9998^2 = (0.9998 - 0.0002)(0.9998 + 0.0002) + (0.0002)^2 =$$

$$=0.9996*1 + 0.00000004 = 0.99960004$$.

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Updated on: 23 Oct 2014, 07:50
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

Originally posted by JackSparr0w on 20 Oct 2014, 18:34.
Last edited by JackSparr0w on 23 Oct 2014, 07:50, edited 1 time in total.
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Joined: 16 Oct 2014
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20 Oct 2014, 23:16
1
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?
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Joined: 22 Nov 2012
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28 Dec 2015, 12:29
I think this the explanation isn't clear enough, please elaborate.
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28 Dec 2015, 12:43
Yup, I just multiplied the last two digits as well. Takes like 30 seconds!
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28 Dec 2015, 14:39
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.

Thanks!
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11 Jul 2016, 02:56
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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.
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Joined: 14 Oct 2012
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30 Mar 2017, 20:56
My 2 cents:
(0.9998)^2 = (1.0000 - 0.0002)^2 = (1.0000)^2 - 2*(1.0000)*(0.0002) + (0.0002)^2 = 1 - 0.0004 + 0.00000004
= 0.9996 + 0.00000004 = 0.99960004 | C
(a-b)^2 = a^2 - 2*a*b + b^2
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Joined: 21 Jul 2015
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17 Sep 2017, 11:19
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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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Re: M15-07   [#permalink] 17 Sep 2017, 11:19
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