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# 8103/x is a non-terminating decimal. Which of the following

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Director
Joined: 25 Oct 2008
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Location: Kolkata,India
8103/x is a non-terminating decimal. Which of the following  [#permalink]

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17 Jul 2009, 23:21
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84% (01:06) correct 16% (01:33) wrong based on 146 sessions

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8103/x is a non-terminating decimal. Which of the following could be a value of x?

A. 2
B. 5
C. 9
D. 12
E. 15

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Re: 8103/x is a non-terminating decimal. Which of the following  [#permalink]

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18 Jul 2009, 01:28
tejal777 wrote:
8103/x is a non-terminating decimal.Which of the following could be a value of x?
a. 2
b. 5
c. 9
d. 12
e. 15

[spoiler]Ans:E[/spoiler]

Elimainated A and B straightaway because we know that 2 or 5 gives us a teminating decimal.Then what??

Then:
c. 9=3*3
d. 12=3*2*2
e. 15=3*5
The sum of digits in 8103 is 12, it means that 8103 is divisible by 3 (i.e. 3 is one of the factors of 8103), which will eliminate one "3" from x, leaving us with only 2's or 5's in options d. and e. Only c is left.
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Re: 8103/x is a non-terminating decimal. Which of the following  [#permalink]

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18 Jul 2009, 08:47
Should be C. 15=3x5. 3 is divisible and 5 will always have a terminating decimal.
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Joined: 27 Nov 2013
Posts: 12
Re: 8103/x is a non-terminating decimal. Which of the following  [#permalink]

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08 Aug 2014, 01:49
Sunchaser20 wrote:
tejal777 wrote:
8103/x is a non-terminating decimal.Which of the following could be a value of x?
a. 2
b. 5
c. 9
d. 12
e. 15

[spoiler]Ans:E[/spoiler]

Elimainated A and B straightaway because we know that 2 or 5 gives us a teminating decimal.Then what??

Then:
c. 9=3*3
d. 12=3*2*2
e. 15=3*5
The sum of digits in 8103 is 12, it means that 8103 is divisible by 3 (i.e. 3 is one of the factors of 8103), which will eliminate one "3" from x, leaving us with only 2's or 5's in options d. and e. Only c is left.

Yes, you are correct. Since when you divide 8103 by 9, after reducing the fraction, you are left with 2701 (2700 + 1) by 3. In this, 2100 can be perfectly divided by 3, by when you divide 1 by 3, you end up with an infinite chain of 0.33333333333333333......
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Re: 8103/x is a non-terminating decimal. Which of the following  [#permalink]

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09 Dec 2015, 12:18
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Hi All,

This question is based heavily on Number Properties involved in division. If you recognize those Number Properties, then you can solve this question in under 30 seconds without performing any lengthy calculations.

We're told that 8103/X is a NON-terminating decimal, meaning that the decimal will NOT end. We're asked which of the following COULD be a value of X?

When dividing an integer by 2 or by 5, the result will either be another integer or a number that has just one decimal point, so neither of these can be the value of X.

Dividing an integer by 9 almost always leads to a repeating decimal, unless the larger number is a multiple of 9. When dividing by 9, there is a great shortcut called 'the rule of 9': if the DIGITS of the larger number sum to a total that is divisible by 9, then the larger number is evenly divisible by 9.

For example:
279 is divisible by 9 because 2+7+9 = 18. Since 18 is divisible by 9, 279 is evenly divisible by 9
17 is NOT divisible by 9 because 1+7 = 8. Since 8 is NOT divisible by 9, 17 is NOT evenly divisible by 9.

Here, we're dealing with 8103. 8+1+0+3 = 12. since 12 is NOT divisible by 9, 8103 is NOT evenly divisible by 9 and thus is a non-terminating decimal.

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8103/x is a non-terminating decimal. Which of the following  [#permalink]

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17 Jul 2017, 18:32
EMPOWERgmatRichC wrote:
Hi All,

This question is based heavily on Number Properties involved in division. If you recognize those Number Properties, then you can solve this question in under 30 seconds without performing any lengthy calculations ...

EMPOWERgmatRichC - What is the logic behind 12 and 15 behind ignored? I see there is a 2 in 12 and 5 in 15 (along with some 3s). So, just because there is 2 and/or 5, we would assume that the division terminates? Please advise!
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Re: 8103/x is a non-terminating decimal. Which of the following  [#permalink]

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17 Jul 2017, 18:44
Blackbox wrote:
EMPOWERgmatRichC wrote:
Hi All,

This question is based heavily on Number Properties involved in division. If you recognize those Number Properties, then you can solve this question in under 30 seconds without performing any lengthy calculations ...

EMPOWERgmatRichC - What is the logic behind 12 and 15 behind ignored? I see there is a 2 in 12 and 5 in 15 (along with some 3s). So, just because there is 2 and/or 5, we would assume that the division terminates? Please advise!

I guess this answers my question? https://gmatclub.com/forum/which-of-the ... l#p1280872
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Re: 8103/x is a non-terminating decimal. Which of the following  [#permalink]

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17 Jul 2017, 18:47
Blackbox wrote:
EMPOWERgmatRichC wrote:
Hi All,

This question is based heavily on Number Properties involved in division. If you recognize those Number Properties, then you can solve this question in under 30 seconds without performing any lengthy calculations ...

EMPOWERgmatRichC - What is the logic behind 12 and 15 behind ignored? I see there is a 2 in 12 and 5 in 15 (along with some 3s). So, just because there is 2 and/or 5, we would assume that the division terminates? Please advise!

OK, I get it now. The 3 in 15 gets cancelled out because 8103 is a multiple of 3. Similarly, the 3 in 12 also cancels out as 3 goes into 8103 2701 times
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Re: 8103/x is a non-terminating decimal. Which of the following  [#permalink]

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25 Apr 2019, 01:47
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Re: 8103/x is a non-terminating decimal. Which of the following   [#permalink] 25 Apr 2019, 01:47
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