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

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07 Jan 2015, 05:54

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67% (01:29) correct
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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?

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.

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?

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

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07 Jan 2015, 06:59

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This post received KUDOS

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.

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

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21 Jul 2016, 13:00

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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, 10:51

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).

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