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In the decimal notation of number (2/23)^3. What is the thir

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In the decimal notation of number (2/23)^3. What is the thir [#permalink] New post 30 Jun 2007, 08:49
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In the decimal notation of number (2/23)^3. What is the third digit to the right of the decimal point?

A. 0
B. 1
C. 2
D. 4
E. 8
[Reveal] Spoiler: OA

Last edited by Bunuel on 31 Dec 2012, 04:31, edited 1 time in total.
Renamed the topic and edited the question.
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Re: In the decimal notation of number (2/23)^3. What is the thir [#permalink] New post 31 Dec 2012, 04:35
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vshaunak@gmail.com wrote:
In the decimal notation of number (2/23)^3. What is the third digit to the right of the decimal point?

A. 0
B. 1
C. 2
D. 4
E. 8


Notice that (\frac{2}{23})^3<(\frac{2}{20})^3.

Now, (\frac{2}{20})^3=(\frac{1}{10})^3=0.001.

Finally, since (\frac{2}{23})^3<0.001, then the third digit to the right of the decimal point of (\frac{2}{23})^3 is 0.

Answer: A.
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Re: PS Decimal digits [#permalink] New post 30 Jun 2007, 08:56
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vshaunak@gmail.com wrote:
In the decimal notation of number (2/23)^3. What is the third digit to the right of the decimal point?

a. 0
b. 1
c. 2
d. 4
e. 8

Is there any quick approach without solving it completely?


The first digit after the decimal point in (2/23) is 0. That is something like 0.0x, which is equal to 0.x * (10^-1). Therefore, the third power will be (0.x)^3 * (10^-3). And, hence, the third digit to the right of the decimal point is 0. Choice A.
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Re: PS Decimal digits [#permalink] New post 30 Jun 2007, 12:17
vshaunak@gmail.com wrote:
In the decimal notation of number (2/23)^3. What is the third digit to the right of the decimal point?

a. 0
b. 1
c. 2
d. 4
e. 8

Is there any quick approach without solving it completely?


i believe in such cases, we need to identify the answer quickly because such questions have obvious answer.

for ex: if it is 5:20 now, what was the time 367,210 minuets earlier?

in this case, if the answers are: 2:05, 2:10, 2:26, 2:31 and 2:45.

2:10 is obvious answer because we need to deduct 10 minuets from 20 minuets.

even if the answers are: 2:00, 2:10, 2:20, 2:30 and 2:40, the correct one is 2:10 because deducting 10 from 20 can never be other than 10.

therefore, i think we need find whether the question asks calculation or some quick tricks.
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Re: PS Decimal digits [#permalink] New post 30 Dec 2012, 21:54
Himalayan wrote:
In the decimal notation of number (2/23)^3. What is the third digit to the right of the decimal point?

a. 0
b. 1
c. 2
d. 4
e. 8

Is there any quick approach without solving it completely?


i believe in such cases, we need to identify the answer quickly because such questions have obvious answer.

for ex: if it is 5:20 now, what was the time 367,210 minuets earlier?

in this case, if the answers are: 2:05, 2:10, 2:26, 2:31 and 2:45.

2:10 is obvious answer because we need to deduct 10 minuets from 20 minuets.

even if the answers are: 2:00, 2:10, 2:20, 2:30 and 2:40, the correct one is 2:10 because deducting 10 from 20 can never be other than 10.

therefore, i think we need find whether the question asks calculation or some quick tricks.[/quote]





Dear Club members

I didn't understand why we deducted 10 minutes from 20. Can someone please elaborate.

Thank you
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Re: In the decimal notation of number (2/23)^3. What is the [#permalink] New post 30 Dec 2012, 23:04
vshaunak@gmail.com wrote:
In the decimal notation of number (2/23)^3. What is the third digit to the right of the decimal point?

a. 0
b. 1
c. 2
d. 4
e. 8

Is there any quick approach without solving it completely?

quicker way:

(2/23)^3 can be written as (25-23/23)^3 and hence (25/23-1)^3>>(1.08XYZ-1)^3>>>0 should be third digit
Re: In the decimal notation of number (2/23)^3. What is the   [#permalink] 30 Dec 2012, 23:04
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