Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

Given: x is a fraction in the range 0<x<1 --> x=0,abcd... Question: is a=0?

(1) 16x is an integer --> x=\frac{integer}{16}, where 0<integer<16 (as 0<x<1). Now, the least value of x is x=\frac{1}{16}=0.0625 and the tenth digit is zero BUT the highest value of x is x=\frac{15}{16}=0.9375 and the tenth digit is nonzero (9). Not sufficient.

(2) 8x is an integer --> x=\frac{integer}{8}, where 0<integer<8 (as 0<x<1). Now, the least value of x is x=\frac{1}{8}={0.125} and the tenth digit is already nonzero thus all other values of x will be more than 0.125 and therefore will have nonzero tenth digit. Sufficient.

Re: In the decimal representation of x, where 0 < x < 1, is the [#permalink]
20 Sep 2012, 04:28

3

This post received KUDOS

An alternate & probably easy solution for this problem

1) x can be 1/2,1/4,1/8,1/16 & all will give integer when multiplied by 16. X can be = .5, .25, .125 or .0625 –Tenth digit can be zero but its not sure - Not Sufficient 2) x can be 1/2,1/4,1/8, & all will give integer when multiplied by 16. X can be = .5, .25, .125 –Tenth digit is always non zero – Sufficient Answer B

Hope it will help
_________________

If you like my Question/Explanation or the contribution, Kindly appreciate by pressing KUDOS. Kudos always maximizes GMATCLUB worth-Game Theory

If you have any question regarding my post, kindly pm me or else I won't be able to reply

Re: In the decimal representation of x, where 0 < x < 1, is the [#permalink]
24 Jun 2013, 13:09

1

This post received KUDOS

Statement 1: For tenth digit to to be zero the fraction multiplied by 16 must be less than 1/10. For 16x to be an integer, x could be 1/16 or 1/8. Not Sufficient

Statement 2: Same logic as above except for 8 to be an integer it can only be multiplied by 1/8 (which is more than 1/10) Sufficient.

Re: In the decimal representation of x, where 0 < x < 1, is the [#permalink]
25 Jun 2013, 09:11

1

This post received KUDOS

udaymathapati wrote:

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.

From the given statement we can conclude that x is terminating decimal. Let x = .abc where we need to find whether a equal to 0 or not

From St 1 : 16x is an Integer ------->x can be 0.125 or 0.0625 as when multiplied by 16 both the values of x give us Integer values 2 and 1 respectively

From St 2: 8x is integer. Knowing that 8X is an integer we can safely conclude that "a" not equal to 0. The least possible value of x will be 0.125 and other possible values of x can be multiple of 0.125 only i.e 0.250, 0.375, 0.500 and hence "a" will never be zero.

Ans is B
_________________

“Many of life's failures are people who did not realize how close they were to success when they gave up.”

“If you can't fly then run, if you can't run then walk, if you can't walk then crawl, but whatever you do you have to keep moving forward.”

“Renew, release, let go. Yesterday’s gone. There’s nothing you can do to bring it back. You can’t “should’ve” done something. You can only DO something. Renew yourself. Release that attachment. Today is a new day!”

gmatclubot

Re: In the decimal representation of x, where 0 < x < 1, is the
[#permalink]
25 Jun 2013, 09:11