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solitaryreaper
Joined: 23 Sep 2013
Last visit: 21 Feb 2023
Posts: 119
Given Kudos: 95
Concentration: Strategy, Marketing
Schools: Boston U '20 (WL)
WE:Engineering (Computer Software)
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07 Jan 2015, 05:54
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D
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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
(1) {z/3} = 0.4175
(2) {3z} = 0.7575
07 Jan 2015, 06:48
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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.
Answer: D.
Hope it's clear.
(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.
General Discussion
07 Jan 2015, 06:51
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solitaryreaper
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.
