Decimal Representation Problem

let me try this one

from stmt 1 choose x =1/16

16x is an integer and 1/16 = 0.0blablabla

but for x=1/8

16x is an integer but 1/8 = 0.1blablabla

stmt 2 :

choose x=1/8 this can be the smallest value to make 8x an integer

and 1/8 = 0.125 whatever factor of 8 you choose after that the tenth digit will be non zero and 8x will be an integer.

hence answer is B.

someone please let me know if I am wrong.

regards,

Here is what I think

1) 16x is integer, so x could be 1/2,1/4,1/8 or 1/16 no unique solution
2) 8x is integer, so x could be 1/2, 1/4 or 1/8, no unique solution

3) Taking both together we end up with 1/2, 1/4 & 1/8 so no unique solution.

I think its E?

IMO E
CAN SOMENE PLEASE EXPLAIN THE QUESTION

0<X<1, X is in decimal rep

1> 16x is integar so x can be equivalent of 1/16, 2/16, 3/16, 4/16, 5/16......to 15/16...giving different tenths digits

2> 8x is integar. so X = 1/8, 2/8, 3/8, 4/8, 5/8, 6/8, 7/8 giving different tenths digits

combined they yeild same as 8x.....

WHAT AM I MISSING?

This is the correct question

In the decimal representation of x, where 0< x< 1, is the tenths digit of x nonzero?
1) 16x is an integer
2) 8x is an integer

0 < x < 1

x is a decimal representation of a number greater than 0 and less than 1

Statement I
16x is an integer

x = 1/16, almost minimum value of x, tenths digit = 0
x = 15/16 almost the maximum value of x, tenth digit = 9

Insufficient.

Statement II
8x is an integer
x = 1/8, almost minimum value of x, tenth digit = 1
x=7/8, almost maximum value of x, tenth digit = 8
you can try with any value of x, the tenth digit will always be greater then 0

Sufficient.

Hence B.


"gmat009" kindly check before posting the question.

thanks Parallel for clearing the question

ans B indeed

Answer is not B....

Say x=0.50 => 8*0.50 = 4.0, An integer.....
X=0.25=? 8*0.25= 2.00, An integer....

So...Tenths decimal need not be greater than 0 for 8x to be an integer...hence the answer is E

gmat009 wrote:In the decimal representation of x, where 0 < x < 1, what is the tenths digit if x nonzero?
(1) 16x is an integer.
(2) 8x is an integer.

Can someone plz. explain

The answer is E: not enough information.

First, the tenths digit is the one directly to the right of the decimal. A quick refresher:

In the number 1234.567

1 is the thousands digit
2 is the hundreds digit
3 is the tens digit
4 is the ones or units digit
5 is the tenths digit
6 is the hundredths digit
7 is the thousandths digit

Second, let's make sure we're answering the correct question.

In the decimal representation of x, where 0 < x < 1, what is the tenths digit if x nonzero?

The question is not "is the tenths digit nonzero?". We're told that x is nonzero and we want to find the tenths digit.

Now to the statements:

(1) 16x is an integer.

We could have x = .25 (16*.25 = 4, which is an integer). What's the tenths digit of .25? 2

We could have x = .5 (16*.5 = 8, which is an integer). What's the tenths digit of .5? 5

More than one possible value: insufficient.

(2) 8x is an integer.

We could have x = .25 (8*.25 = 2, which is an integer). What's the tenths digit of .25? 2

We could have x = .5 (8*.5 = 4, which is an integer). What's the tenths digit of .5? 5

More than one possible value: insufficient.

Together: we've already shown that the x could be .25 OR .5 (each value for x worked for both statements). Accordingly, the tenths digit of x could still be either 2 or 5: not enough information, choose (E).

parallel_chase wrote:This is the correct question

In the decimal representation of x, where 0< x< 1, is the tenths digit of x nonzero?
1) 16x is an integer
2) 8x is an integer

However, if this is the correct question, Parallel Chase has done a great job explaining why "b" is correct!