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OG11 PS - Q219 poor explanation - can anyone help

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OG11 PS - Q219 poor explanation - can anyone help

by Has » Tue Sep 23, 2008 4:37 pm
Hello folks,

OG PS section question 219 has a really poor explanation to the answer - can anyone do a better job?

Question
What is the 25th digit to the right of the decimal point in the form of 6/11 (6 divided by 11)?

Answer is 5

Explanation 6/11 = 0.54545454… every odd numbered digit is 5 therefore 25th digit is 5.


Can someone please do a better job of explaining this to me, also what technique can I apply generally to work out such questions, in under 2 mins…..


Many Thanks
H
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by VP_Jim » Tue Sep 23, 2008 6:57 pm
I think that's the best explanation that there is. You only have to work on the division to four - at most - decimal places to realize it's going to be a repeating sequence. The GMAT would not test you on a number that doesn't have this sequence, since it would take forever to do long division by hand out to the 25th decimal place.

As far as a general technique, look for patterns and shortcuts. Remember that there is almost always an easier way than doing the entire calculation.
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by jazzcat4u » Tue Sep 23, 2008 7:22 pm
i dunno you can try this...but i could be wrong...

to find a specific number in a list of patterned numbers:
1) count the number of items in the pattern = the 2 items in the pattern are "5" and "4"

2) divide the number of items into the place number you are looking for AND NOTE THE REMAINDER = your place number here is 25

25/2 = 12 with remainder of 1

3) count the remainder from the left
6/11 = 0.54545454
- since you only count 1 spot, you land on the number 5

Here's another example of how you can apply this again...
39713971.....find the 87th number on this list

1) how many items do you see? 4 (3971)
2) what is your place number = 87
3) divide and note remainder 87/4 = 21 with remainder of 3
4) count 3 places from the left = 7

to illustrate further - try looking for the 5th number on this list - its obvious that in 39713971, the fifth number is 3. but even if you apply the same method above, you'll still land on 3.
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by Has » Thu Sep 25, 2008 7:00 am
thanks guys - i agree identifying the pattern here is key. But typically for me it is the simple things i have problems with and not the more complicated one.

Such as what is the best process to divide 6 by 11?

i can 60 by 55 which 5 then 5 remainder and try to play with that, but this takes forever and not always accurate, dividing samller numbers by larger ones always gives me problems..... any techniques are welcome... :oops:
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Re: OG11 PS - Q219 poor explanation - can anyone help

by dally_gmat » Fri Sep 26, 2008 8:02 am
Hey Has..

I think we are over complicating this...You have already done half of job..

Has wrote:Hello folks,

OG PS section question 219 has a really poor explanation to the answer - can anyone do a better job?
6/11 = 0.54545454…

I would do only upto 6/11 = 0.5454....since its gonna be repetitive...

No only question is to find 25th digit...so here pattern is 2 digits are repetiting...so 25/2 gives 1 remainder...that means it is first digit of repetitive cycle...which is 5..

I hope I am clear and correct :)
Question
What is the 25th digit to the right of the decimal point in the form of 6/11 (6 divided by 11)?

Answer is 5

Explanation 6/11 = 0.54545454… every odd numbered digit is 5 therefore 25th digit is 5.


Can someone please do a better job of explaining this to me, also what technique can I apply generally to work out such questions, in under 2 mins…..


Many Thanks
H
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by Has » Sat Sep 27, 2008 6:54 am
cool - i'm sticking to my method, 60 over 11, 5 times (i decimal diff) thus 0.5 reminder 5 (thus 0.05) is 50 over 11 which is 4 times (44) (the 4 is 2 decimal diff thus 0.04 total now 0.54) and remainder 6 which is actuallly 0.006 which again becomes 60 but with 3 decimal difference and the cycle continues.

i will use this pricess until i identify the pattern thus answer. Of course, if anyone has a quiclker method, then, by all mean let me knwo.

Thanks ALL
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by welett » Sun Sep 28, 2008 2:07 am
an easy way to find 6/11 in decimal terms

expand it by 9

(6*9)/(11*9) = 54/99

note that 54/99 is the fractional representation of circulating (recurring) decimal 0,545454...
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by Has » Mon Sep 29, 2008 5:25 am
Thanks
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by Jeff@TargetTestPrep » Wed Apr 15, 2015 4:13 am
Has wrote:Hello folks,

OG PS section question 219 has a really poor explanation to the answer - can anyone do a better job?

Question
What is the 25th digit to the right of the decimal point in the form of 6/11 (6 divided by 11)?

Answer is 5

Explanation 6/11 = 0.54545454� every odd numbered digit is 5 therefore 25th digit is 5.


Can someone please do a better job of explaining this to me, also what technique can I apply generally to work out such questions, in under 2 mins�..


Many Thanks
H
Solution:

To solve this question, we first have to use some long division. This long division allows us to get 6/11 in decimal form, which is 0.545454... where "54" is repeating.

We can see that the 1st, 3rd, 5th (and so on) digit to the right of the decimal point is a 5 and that the 2nd, 4th, 6th (and so on) digit to the right of the decimal point is a 4. In other words, each odd-positioned digit is a 5, and each even-positioned digit is a 4.

Because we are being asked about the 25th digit to the right of the decimal point and we see that 25 is odd, we know that the 25th digit is a 5.

The Answer is C

Jeffrey Miller
Head of GMAT Instruction
[email protected]

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