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Decimal Representation Problem

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Decimal Representation Problem

by gmat009 » Tue Oct 07, 2008 4:18 pm
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.
A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is
sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.

OA is B, IMO E
Can someone plz. explain
Last edited by gmat009 on Tue Oct 07, 2008 6:34 pm, edited 1 time in total.
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by cubicle_bound_misfit » Tue Oct 07, 2008 6:12 pm
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.

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by mbaquest » Tue Oct 07, 2008 7:24 pm
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?
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by mental » Sun Oct 12, 2008 7:22 am
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?
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Re: Decimal Representation Problem

by parallel_chase » Sun Oct 12, 2008 10:07 am
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.
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by mental » Mon Oct 13, 2008 9:21 am
thanks Parallel for clearing the question

ans B indeed
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by Rashmi1804 » Mon Mar 23, 2009 11:56 am
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
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Re: Decimal Representation Problem

by Stuart@KaplanGMAT » Mon Mar 30, 2009 11:15 am
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).
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Re: Decimal Representation Problem

by Stuart@KaplanGMAT » Mon Mar 30, 2009 11:17 am
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!
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