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Problem Solving 3

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Source: — Data Sufficiency |

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by Brent@GMATPrepNow » Tue Apr 12, 2016 6:55 am
What is the 25th digit to the right of the decimal point in the decimal form of 6/11?

A) 3
B) 4
C) 5
D) 6
E) 7
If we use LONG DIVISION and divide 6 by 11, we see a pattern emerge.
We get: 6/11 = 0.5454....
So, the 1st digit to the right of the decimal point is 5
The 2nd digit to the right of the decimal point is 4
The 3rd digit to the right of the decimal point is 5
The 4th digit to the right of the decimal point is 4
and so on...

Every ODD digit (1st, 3rd, 5th, etc) is 5
Every EVEN digit (2nd, 4th, 6th etc) is 4

So, the 25th digit will be 5

Answer: C

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by [email protected] » Tue Apr 12, 2016 10:28 am
Hi ezzeldin.khaled79,

The GMAT Quant section will include a number of questions that will require that you convert one form of data into another. You might be asked for "unit conversions", which include minutes to seconds, dollars to cents, etc. You might also be asked to convert fractions to decimals to percents.

Here, knowing the value of 1/11 makes this question fairly straightforward.

1/11 is a "repeater"; 1/11 = .09090909etc

So 6/11 is 6 times that + .54545454etc.

Since we're asked for the 25th digit, we're asked for which digit appears in odd "spots"

Final Answer: C

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by OptimusPrep » Thu Apr 14, 2016 7:29 pm
[email protected] wrote:Can someone explain the right answer for this Question?

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Question such as these are fairly easy to solve and we just need to find a pattern in the result.
6/11 = 0.545454...
Here since the first digit is 5, therefore all the odd digits will be 5
Hence the 25th digit = 5
Correct Option: C
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by Matt@VeritasPrep » Fri Apr 15, 2016 1:25 pm
This seems like a good time to bring up a very cool property of decimals that the GMAT likes to test now and then:

(xy)/99 = .xyxyxyxy...

Since 6/11 = 54/99, we'd have .54545454... and could count it from there.
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