Which of the following is equal to 0.9998^2 ? : GMAT Problem Solving (PS)
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# Which of the following is equal to 0.9998^2 ?

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Which of the following is equal to 0.9998^2 ? [#permalink]

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02 Jan 2013, 17:58
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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

M15-07
[Reveal] Spoiler: OA

Last edited by Bunuel on 16 Jul 2013, 21:22, edited 4 times in total.
OA
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Re: can some one suggest an easy way to solve this. [#permalink]

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02 Jan 2013, 18:58
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Below is the easier way to solve:
Remember: $$(a-b)^2 = a^2 - 2ab + b^2$$

$$(0.9998) ^2 = (1 -0.0002)^2 = 1^2 - 2 (1) (0.0002) + (0.0002)^2 = 1 - 0.0004 + (0.0002)^2 = 0.9996 + 0.0000004 = 0.99960004$$

Hence choice (C) is the correct answer. (OA - choice (D) is incorrect. Verify using your calculator.)
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Re: can some one suggest an easy way to solve this. [#permalink]

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02 Jan 2013, 19:53
HiteshPunjabi wrote:
Which of the following is equal to (0.9998) 2 ?

0.99950014

0.99950234

0.99960004

0.99960064

0.99961024

Dear Hitesh,

You see the difference between the numbers starts from the last but one digit. So it is enough to multiply and get the last two digits only. Here in the case of 0.9998 x 0.9998, multiply only 98 and 98, you get 9604. The last but one digit is 0 which is only in choice C.
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Re: What is the value of the following (0.9998)^2 ? [#permalink]

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17 Apr 2013, 13:39
Archit143 wrote:
What is the value of the following (0.9998)^2 ?

A 0.99950014
B 0.99950234
C 0.99960004
D 0.99960064
E 0.99961024

I began to multiply .9998 x .9998. I knew the units digit would be 4 (8 x 8 = 64) and then I figured out the hundreds digit by multiplying 9 x 8 + 6 (from the 64) = 84. Rather than doing the rest of the math, I skipped to the tens digit in the second figure. That gave me 9 x 8 = 72 or 2 in the tens column plus the 8 gave me 04 for the first two digits. Figured out it was C.
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Re: What is the value of the following (0.9998)^2 ? [#permalink]

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17 Apr 2013, 13:41
$$(0.9998)^2=(1-0.0002)^2=(1-2*10^-^4)^2=1+2^2*10^-^8-2*2*10^-^4$$ it's the old formula $$(a+b)^2=a^2+b^2+2ab$$

$$1+4*10^-^8-4*10^-^4=1+0.00000004-0.0004$$

$$(1-0.0004)+0.00000004$$
$$0.9996+0.00000004=0.99960004$$
C
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Re: What is the value of the following (0.9998)^2 ? [#permalink]

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17 Apr 2013, 14:47
thnks Zarrolu
i followed the same method....bt i missed ...thnks maan

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Re: Which of the following is equal to 0.9998^2 ? [#permalink]

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18 Apr 2013, 02:23
It just faster to do criss cross multiplication in this question and you can get the answer in less than 30 secs.

9 9 9 8

9 9 9 8

Units place : 8 x 8 = 64 => Units place is 4 with carry over of 4

Tens place : 9x8 + 9x8 + 6 = 150 => Tens place is 0 with carry over of 15

You can stop here since you have already found answer by checking options

This is criss cross multiplication technique from vedic mathematics (http://www.brighthubeducation.com/homew ... thematics/) and i would highly recommend looking it up.

Elaborating 100's place : 9x8 + 9x9 + 9x8 +15 = 240 => 100s place is 0 with carry over 24

1000 place : 9x8 +9x9 + 9x9 + 9x8 + 24 = 330 => 1000 place is 0 with carry over 33 and so on....
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Re: Which of the following is equal to 0.9998^2 ? [#permalink]

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29 Apr 2013, 04:46
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HiteshPunjabi wrote:
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

For the sake of convenience, let us assume it to be= 9998*9998 = 9998*(10000-2) = 99980000-19996 --> the units digit is 4 and the tens a 0. Only C satisfies.

C.
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08 Dec 2014, 07:48
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Re: Which of the following is equal to 0.9998^2 ? [#permalink]

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09 Dec 2014, 00:28
0.9998
0.9998
______
84
82
______
04 in the end

only C
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Re: Which of the following is equal to 0.9998^2 ? [#permalink]

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09 Dec 2014, 00:31
Multiplying

0.9998
0.9998
______
------84
----82
______
------04 in the end

only C
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Which of the following is equal to 0.9998^2 ? [#permalink]

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09 Dec 2014, 02:03
Just for sake of convenience, remove decimal from the question as well from the answer

$$9998^2 = (10^4 - 2)^2 = 100000000 + 4 - 40000 = 100000004 - 40000$$

Last 2 digits are 04

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16 Jan 2016, 15:42
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Re: Which of the following is equal to 0.9998^2 ?   [#permalink] 16 Jan 2016, 15:42
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