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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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New post 07 Jan 2015, 04:54
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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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New post 07 Jan 2015, 05:48
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1
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.

Answer: D.

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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New post 07 Jan 2015, 05:51
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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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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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

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New post 07 Jan 2015, 05:59
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.

Answer: D.

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

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New post 07 Jan 2015, 11:00
Hi solitaryreaper,

Can you provide the source for this DS question?

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

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New post 07 Jan 2015, 11:35
EMPOWERgmatRichC wrote:
Hi solitaryreaper,

Can you provide the source for this DS question?

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Hi Rich,
I have already mentioned the source - It's from 800score.com .
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Re: For a positive number x, {x} is the fractional part of x.  [#permalink]

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New post 07 Jan 2015, 11:56
Hi solitaryreaper,

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

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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] 04 Oct 2018, 05:41
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