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Manager  B
Joined: 23 Sep 2013
Posts: 128
Concentration: Strategy, Marketing
WE: Engineering (Computer Software)
For a positive number x, {x} is the fractional part of x.  [#permalink]

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27 00:00

Difficulty:   65% (hard)

Question Stats: 58% (02:06) correct 42% (02:18) wrong based on 278 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
Math Expert V
Joined: 02 Sep 2009
Posts: 60555
Re: For a positive number x, {x} is the fractional part of x.  [#permalink]

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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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Math Expert V
Joined: 02 Sep 2009
Posts: 60555
Re: For a positive number x, {x} is the fractional part of x.  [#permalink]

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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.
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Joined: 23 Sep 2013
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Re: For a positive number x, {x} is the fractional part of x.  [#permalink]

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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 V
Status: GMAT Assassin/Co-Founder
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Re: For a positive number x, {x} is the fractional part of x.  [#permalink]

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Hi solitaryreaper,

Can you provide the source for this DS question?

GMAT assassins aren't born, they're made,
Rich
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Manager  B
Joined: 23 Sep 2013
Posts: 128
Concentration: Strategy, Marketing
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Re: For a positive number x, {x} is the fractional part of x.  [#permalink]

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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 V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 15958
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]

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Hi solitaryreaper,

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

GMAT assassins aren't born, they're made,
Rich
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Re: For a positive number x, {x} is the fractional part of x.  [#permalink]

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_________________ Re: For a positive number x, {x} is the fractional part of x.   [#permalink] 27 Oct 2019, 00:57
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