GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 16 Oct 2019, 23:40

### GMAT Club Daily Prep

#### 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

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

# For a positive number x, {x} is the fractional part of x.

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

### Hide Tags

Manager
Joined: 23 Sep 2013
Posts: 130
Concentration: Strategy, Marketing
WE: Engineering (Computer Software)
For a positive number x, {x} is the fractional part of x.  [#permalink]

### Show Tags

07 Jan 2015, 05:54
5
22
00:00

Difficulty:

55% (hard)

Question Stats:

59% (02:05) correct 41% (02:22) wrong based on 312 sessions

### HideShow timer Statistics

For a positive number x, {x} is the fractional part of x. {x} = x-[x] , where [x] is the greatest integer less than or equal to x. The fractional part of 12.8, for example is 0.8. What is the value of {z}, if z is positive and has exactly 4 digits after the decimal?

(1) {z/3} = 0.4175
(2) {3z} = 0.7575
Math Expert
Joined: 02 Sep 2009
Posts: 58403
Re: For a positive number x, {x} is the fractional part of x.  [#permalink]

### Show Tags

07 Jan 2015, 06:48
7
3
For a positive number x, {x} is the fractional part of x. {x} = x-[x] , where [x] is the greatest integer less than or equal to x. The fractional part of 12.8, for example is 0.8. What is the value of {z}, if z is positive and has exactly 4 digits after the decimal?

(1) {z/3} = 0.4175. This implies that the fractional part of z/3 is 0.4175, thus:

$$\frac{z}{3} = integer + 0.4175$$;

$$z= 3*integer + 3*0.4175$$;

$$z= 3*integer + 1.2525$$;

$$z=(3*integer+1)+0.2525$$;

$$z=integer+0.2525$$.

Therefore, {z}, the fractional part of z is 0.2525. Sufficient.

(2) {3z} = 0.7575. This implies that the fractional part of 3z is 0.7575, thus:

$$3z = integer + 0.7575$$;

$$z = \frac{integer}{3} + 0.2525$$;

Here comes in play the part of the stem which says that z is positive and has exactly 4 digits after the decimal. If integer above is NOT a multiple of 3, then integer/3 would be a recurring decimal (non-terminating), and z itself would also be a recurring decimal, which would contradict the fact that it should have exactly 4 digits after the decimal. Therefore z must be a multiple of 3.

$$z =\frac{(multiple \ of \ 3)}{3} + 0.2525$$;

$$z = integer + 0.2525$$.

Therefore, {z}, the fractional part of z is 0.2525. Sufficient.

Hope it's clear.
_________________
##### General Discussion
Math Expert
Joined: 02 Sep 2009
Posts: 58403
Re: For a positive number x, {x} is the fractional part of x.  [#permalink]

### Show Tags

07 Jan 2015, 06:51
1
solitaryreaper wrote:
For a positive number x, {x} is the fractional part of x. {x} = x-[x] , where [x] is the greatest integer less than or equal to x. The fractional part of 12.8, for example is 0.8. What is the value of {z}, if z is positive and has exactly 4 digits after the decimal?

(1) {z/3} = 0.4175
(2) {3z} = 0.7575

Check other function questions in our Special Questions Directory:

Operations/functions defining algebraic/arithmetic expressions
Symbols Representing Arithmetic Operation
Rounding Functions
Various Functions

Also check Terminating and Recurring Decimals questions there.

Hope it helps.
_________________
Manager
Joined: 23 Sep 2013
Posts: 130
Concentration: Strategy, Marketing
WE: Engineering (Computer Software)
Re: For a positive number x, {x} is the fractional part of x.  [#permalink]

### Show Tags

07 Jan 2015, 06:59
1
Bunuel wrote:
For a positive number x, {x} is the fractional part of x. {x} = x-[x] , where [x] is the greatest integer less than or equal to x. The fractional part of 12.8, for example is 0.8. What is the value of {z}, if z is positive and has exactly 4 digits after the decimal?

(1) {z/3} = 0.4175. This implies that the fractional part of z/3 is 0.4175, thus:

$$\frac{z}{3} = integer + 0.4175$$;

$$z= 3*integer + 3*0.4175$$;

$$z= 3*integer + 1.2525$$;

$$z=(3*integer+1)+0.2525$$;

$$z=integer+0.2525$$.

Therefore, {z}, the fractional part of z is 0.2525. Sufficient.

(2) {3z} = 0.7575. This implies that the fractional part of 3z is 0.7575, thus:

$$3z = integer + 0.7575$$;

$$z = \frac{integer}{3} + 0.2525$$;

Here comes in play the part of the stem which says that z is positive and has exactly 4 digits after the decimal. If integer above is NOT a multiple of 3, then integer/3 would be a recurring decimal (non-terminating), and z itself would also be a recurring decimal, which would contradict the fact that it should have exactly 4 digits after the decimal. Therefore z must be a multiple of 3.

$$z =\frac{(multiple \ of \ 3)}{3} + 0.2525$$;

$$z = integer + 0.2525$$.

Therefore, {z}, the fractional part of z is 0.2525. Sufficient.

Hope it's clear.

I was particularly confused with B. This is the explanation I was looking for.
Again, great explanation Bunuel !!
Thanks a lot.
EMPOWERgmat Instructor
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 15263
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: For a positive number x, {x} is the fractional part of x.  [#permalink]

### Show Tags

07 Jan 2015, 12:00
Hi solitaryreaper,

Can you provide the source for this DS question?

GMAT assassins aren't born, they're made,
Rich
_________________
Contact Rich at: Rich.C@empowergmat.com

The Course Used By GMAT Club Moderators To Earn 750+

souvik101990 Score: 760 Q50 V42 ★★★★★
ENGRTOMBA2018 Score: 750 Q49 V44 ★★★★★
Manager
Joined: 23 Sep 2013
Posts: 130
Concentration: Strategy, Marketing
WE: Engineering (Computer Software)
Re: For a positive number x, {x} is the fractional part of x.  [#permalink]

### Show Tags

07 Jan 2015, 12:35
EMPOWERgmatRichC wrote:
Hi solitaryreaper,

Can you provide the source for this DS question?

GMAT assassins aren't born, they're made,
Rich

Hi Rich,
I have already mentioned the source - It's from 800score.com .
Regards,
SR
EMPOWERgmat Instructor
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 15263
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: For a positive number x, {x} is the fractional part of x.  [#permalink]

### Show Tags

07 Jan 2015, 12:56
Hi solitaryreaper,

Thanks for pointing that out - I didn't catch it in the Tags.

GMAT assassins aren't born, they're made,
Rich
_________________
Contact Rich at: Rich.C@empowergmat.com

The Course Used By GMAT Club Moderators To Earn 750+

souvik101990 Score: 760 Q50 V42 ★★★★★
ENGRTOMBA2018 Score: 750 Q49 V44 ★★★★★
Non-Human User
Joined: 09 Sep 2013
Posts: 13204
Re: For a positive number x, {x} is the fractional part of x.  [#permalink]

### Show Tags

04 Oct 2018, 06:41
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Re: For a positive number x, {x} is the fractional part of x.   [#permalink] 04 Oct 2018, 06:41
Display posts from previous: Sort by

# For a positive number x, {x} is the fractional part of x.

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne