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# Is d a decimal with exactly 10 digits?

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Is d a decimal with exactly 10 digits?  [#permalink]

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02 Dec 2017, 01:22
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Difficulty:

45% (medium)

Question Stats:

57% (01:21) correct 43% (01:35) wrong based on 79 sessions

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$$d = \frac{x}{y}$$
In the expression above, x is an 8-digit integer and y is a 9-digit integer. Is d a decimal with exactly ten digits?
(1) The sum of all the digits in the numerator is not a multiple of 3.
(2) 33 is a factor of the denominator.

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Is d a decimal with exactly 10 digits?  [#permalink]

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02 Dec 2017, 07:14
1
helloksin wrote:
$$d = \frac{x}{y}$$
In the expression above, x is an 8-digit integer and y is a 9-digit integer. Is d a decimal with exactly ten digits?
(1) The sum of all the digits in the numerator is not a multiple of 3.
(2) 33 is a factor of the denominator.

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Statement 1: implies $$x$$ is not a multiple of $$3$$. but nothing mentioned about $$y$$. Insufficient

Statement 2: implies $$y$$ is a multiple of $$3$$. but nothing mentioned about $$x$$. Insufficient

Combining 1 & 2, we know $$x$$ is not a multiple of $$3$$ & $$y$$ is a multiple of $$3$$, hence $$d$$ will be a recurring decimal number.

so $$d$$ will not have exactly ten digits after decimal point. Sufficient

Option C
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Re: Is d a decimal with exactly 10 digits?  [#permalink]

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02 Dec 2017, 08:03
1
helloksin wrote:
$$d = \frac{x}{y}$$
In the expression above, x is an 8-digit integer and y is a 9-digit integer. Is d a decimal with exactly ten digits?
(1) The sum of all the digits in the numerator is not a multiple of 3.
(2) 33 is a factor of the denominator.

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1) Numerator is not a multiple of 3, but nothing is given for y. So insufficient.
2) Denominator is a multiple of 33, Hence a multiple of 3 and 11. No info for numerator. So insufficient.

Combining 1 & 2, the denominator is bound to have 3 since numerator is not a multiple of 3. So recurring decimal(1/3=.3333333333.., 2/3=0.6666666....) hence decimal with not exactly 10 digits. Hence C.
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Re: Is d a decimal with exactly 10 digits?  [#permalink]

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21 Feb 2019, 07:24
Stat1 provides information on the numerator only -> insufficient
Stat2 provides information on the denominator only -> insufficient

Stat2: Denominator is divisible by 33= 3*11

1/3 and 1/11 are both result recurring decimal fractions
1/3=0.33333333.... 1/11=0.09090909090...

Stat1: numerator isn't divisible by 3 -> the decimal will surely be a recurring decimal -> (C)

I found this link very useful in describing terminating and recurring decimals. Please see: 1 Changing a Fraction into a Decimal number: http://www.maths.surrey.ac.uk/hosted-si ... l#section1
Re: Is d a decimal with exactly 10 digits?   [#permalink] 21 Feb 2019, 07:24
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