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![For all positive integers x, functions [x] represents the remainder wh](/forum/styles/gmatclub_light/imageset/icon_post_target_unread.svg "For all positive integers x, functions [x] represents the remainder wh"){kind=icon}
18 Jan 2021, 06:41
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B
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For all positive integers x, functions [x] represents the remainder when 3x is divided by 2. If n is a positive integer, then which of the following expression must equal to 1?
A. [2n]
B. [2n] + 1
C. [3n] - 1
D. [3n] + 1
E. [6n] - 1
A. [2n]
B. [2n] + 1
C. [3n] - 1
D. [3n] + 1
E. [6n] - 1
[x] represents the remainder of 3x/2, which of the following
expression is equal to 1:
a. [2x] b. [3x]+1 c. [2x] +1
expression is equal to 1:
a. [2x] b. [3x]+1 c. [2x] +1
18 Jan 2021, 07:12
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Bunuel
3x would leave 1 as remainder if x is odd, otherwise 0.
A. [2n] ........ x=2n....3*2n will be divisible by 2. Hence R=0, and [2n]=0...NO
B. [2n] + 1 ........ x=2n....3*2n will be divisible by 2. Hence R=0, and [2n] + 1=0+1=1...YES
C. [3n] - 1........ x=3n....3*3n will be divisible by 2 if n is even. Hence R=0 and [3n] - 1=0-1=-1. But if n is odd, 3*3n will leave 1 as remainder. Hence R=1-1=0...NO
D. [3n] + 1........ x=3n....3*3n will be divisible by 2 if n is even. Hence R=0+1=1. But if n is odd, 3*3n will leave 1 as remainder. Hence [3n] + 1=1+1=2...NO
E. [6n] - 1........ x=6n....3*6n will be divisible by 2. Hence R=0, and [6n] - 1=0-1=-1...NO
B
18 Jan 2021, 13:25
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For all positive integers x, functions [x] represents the remainder when 3x is divided by 2. If n is a positive integer, then which of the following expression must equal to 1?
A. [2n] -> 3*2n/2 will have remainder Zero. Expression is not equal to 1. Incorrect
B. [2n] + 1 -> 3*2n/2 will have remainder Zero. Further, 1 is added. So, expression is equal to 1. Correct
C. [3n] - 1 -> 3*3n/2 will have remainder 1. Further, 1 is substracted. So, expression is equal to 0. Incorrect
D. [3n] + 1 -> 3*3n/2 will have remainder 1. Further, 1 is added. So, expression is equal to 2. Incorrect
E. [6n] - 1 -> 3*6n/2 will have remainder 0. Further, 1 is substracted. So, expression is equal to -1. Incorrect
So, I think B.
A. [2n] -> 3*2n/2 will have remainder Zero. Expression is not equal to 1. Incorrect
B. [2n] + 1 -> 3*2n/2 will have remainder Zero. Further, 1 is added. So, expression is equal to 1. Correct
C. [3n] - 1 -> 3*3n/2 will have remainder 1. Further, 1 is substracted. So, expression is equal to 0. Incorrect
D. [3n] + 1 -> 3*3n/2 will have remainder 1. Further, 1 is added. So, expression is equal to 2. Incorrect
E. [6n] - 1 -> 3*6n/2 will have remainder 0. Further, 1 is substracted. So, expression is equal to -1. Incorrect
So, I think B.
