In the decimal representation of d, where 0

Question

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.

DavidTutorexamPAL · Answer

The answer is B. 
 
(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!

saurabh9gupta · Answer

chetan2u  - your approach plz

chetan2u · Answer

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

Salsanousi · Answer

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

smmc29 · Answer

(1) 12d is an integer

Solving for d, d = 1/12, 2/12, 3/12, ...

1/12 is 0.0...

INSUFFICIENT

(2) 6d is an integer

d minimum is 1/6 = 0.1...

SUFFICIENT

The answer is B

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

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