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

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

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07 Jan 2015, 04:54
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68% (01:27) correct 32% (01:49) wrong based on 226 sessions

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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
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Re: For a positive number x, {x} is the fractional part of x. [#permalink]

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07 Jan 2015, 05:48
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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.
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Re: For a positive number x, {x} is the fractional part of x. [#permalink]

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07 Jan 2015, 05:51
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Expert's post
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.
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Kudos [?]: 139338 [1], given: 12786

Manager
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Re: For a positive number x, {x} is the fractional part of x. [#permalink]

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07 Jan 2015, 05:59
1
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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.

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Re: For a positive number x, {x} is the fractional part of x. [#permalink]

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07 Jan 2015, 11:00
Hi solitaryreaper,

Can you provide the source for this DS question?

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

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Special Offer: Save $75 + GMAT Club Tests Free Official GMAT Exam Packs + 70 Pt. Improvement Guarantee www.empowergmat.com/ ***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*********************** Kudos [?]: 3774 [0], given: 173 Manager Joined: 23 Sep 2013 Posts: 124 Kudos [?]: 30 [0], given: 87 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, 11:35 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 Kudos [?]: 30 [0], given: 87 EMPOWERgmat Instructor Status: GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 10696 Kudos [?]: 3774 [0], given: 173 Location: United States (CA) GMAT 1: 800 Q51 V49 GRE 1: 340 Q170 V170 Re: For a positive number x, {x} is the fractional part of x. [#permalink] ### Show Tags 07 Jan 2015, 11:56 Hi solitaryreaper, Thanks for pointing that out - I didn't catch it in the Tags. GMAT assassins aren't born, they're made, Rich _________________ 760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com # Rich Cohen Co-Founder & GMAT Assassin Special Offer: Save$75 + GMAT Club Tests Free
Official GMAT Exam Packs + 70 Pt. Improvement Guarantee
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Re: For a positive number x, {x} is the fractional part of x. [#permalink]

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21 Jul 2016, 12:00
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Re: For a positive number x, {x} is the fractional part of x. [#permalink]

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09 Sep 2017, 09:51
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Re: For a positive number x, {x} is the fractional part of x.   [#permalink] 09 Sep 2017, 09:51
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