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# In the decimal representation of d, where 0 < d < 1, is the tenths’ di

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Math Expert
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In the decimal representation of d, where 0 < d < 1, is the tenths’ di  [#permalink]

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09 Oct 2018, 03:05
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85% (hard)

Question Stats:

39% (02:13) correct 61% (02:03) wrong based on 27 sessions

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In the decimal representation of d, where 0 < d < 1, is the tenths’ digit of d greater than 0?

(1) 12d is an integer.
(2) 6d is an integer.

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Re: In the decimal representation of d, where 0 < d < 1, is the tenths’ di  [#permalink]

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09 Oct 2018, 03:41
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1
Bunuel wrote:
In the decimal representation of d, where 0 < d < 1, is the tenths’ digit of d greater than 0?

(1) 12d is an integer.
(2) 6d is an integer.

(1) Since we are checking if d is greater than something, we'll start by checking the minimum: Let's say 12d=1 ==> d=1/12 ==> d<0.1 - the tenth's digit will be zero. the answer is no.
But now let's try a larger integer: say 12d=6 ==> d=0.5 - tenth's digit is 5 - the answer is yes.
we've used the data to produce two contradictory solutions - insufficient! eliminate answers A & D

2) similarly, let's start with the minimum: 6d=1 ==> d = 1/6 = ~0.16 - the tenths digit is 1 - the answer is yes. and since this is the minimum, any other integer will only give us a larger value for d. therefore, the answer is definitely yes - sufficient! eliminate C & E - B is our answer!
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Re: In the decimal representation of d, where 0 < d < 1, is the tenths’ di  [#permalink]

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09 Oct 2018, 21:57
Bunuel wrote:
In the decimal representation of d, where 0 < d < 1, is the tenths’ digit of d greater than 0?

(1) 12d is an integer.
(2) 6d is an integer.

Math Expert
Joined: 02 Aug 2009
Posts: 7940
Re: In the decimal representation of d, where 0 < d < 1, is the tenths’ di  [#permalink]

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09 Oct 2018, 22:55
2
saurabh9gupta wrote:
Bunuel wrote:
In the decimal representation of d, where 0 < d < 1, is the tenths’ digit of d greater than 0?

(1) 12d is an integer.
(2) 6d is an integer.

what is tenths digit
0.xy here x is tenths digit

(1) 12d is an integer.
so $$12d=x.....d=\frac{x}{12}$$
case I :- x is 1
$$d=\frac{1}{12}$$ Now $$\frac{1}{10}>\frac{1}{12}$$.......$$0.1>\frac{1}{12}$$ there fore d = 0.0rst
yes, tenths digit is 0
case I :- x is 6
$$d=\frac{6}{12}=\frac{1}{2}=0.5$$
no, tenths digit is not 0 but 5
insuff

(2) 6d is an integer.
so $$6d=x.....d=\frac{x}{6}$$
Min value of d when :- x is 1
$$d=\frac{1}{6}$$ Now $$\frac{1}{10}<\frac{1}{6}$$.......$$0.1<\frac{1}{6}$$ therefore d = 0.rst
yes, tenths digit is always>0
suff

B
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Re: In the decimal representation of d, where 0 < d < 1, is the tenths’ di  [#permalink]

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10 Oct 2018, 02:35
Bunuel wrote:
In the decimal representation of d, where 0 < d < 1, is the tenths’ digit of d greater than 0?

(1) 12d is an integer.
(2) 6d is an integer.

1) 12d is an integer that means d is in the form of 1/2, 1/3, 1/4, 1/6, 1/12

The tenths digit in $$\frac{1}{2}$$, $$\frac{1}{3}$$, $$\frac{1}{4}$$ and $$\frac{1}{6}$$ is >0

1/12 units digit = 0

Insufficient.

2)
6d is an integer means d is in the form of $$\frac{1}{2}$$, $$\frac{1}{3}$$, $$\frac{1}{4}$$ and $$\frac{1}{6}$$

each of which the units digit is >0

Sufficient

B
Re: In the decimal representation of d, where 0 < d < 1, is the tenths’ di   [#permalink] 10 Oct 2018, 02:35
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