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Remainder 1 - Must be true

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Junior | Next Rank: 30 Posts
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by lamhe » Thu May 21, 2009 5:54 pm
For any positive integer x, (x) is defined to be the remainder when 3x is divided by 2, which of the following must be equal to 1?

I. (2x+1)
II. (2x)+1
III. 2(x+1)

(A) I only
(B) II only
(C) III only
(D) I and II
(E) I, II, and III
Vishal
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by cramya » Thu May 21, 2009 8:28 pm
Would go with [spoiler]D)[/spoiler]

I can substitute any x since its true for all x or do it algebrically

I. (2x+1)

3(2x+1) / 2 = 6x/2+3/2 = 0+1 remainder 1

II. (2x)+1

3(2x)/2 + 1 = 0+1 = remainder 1

III. 2(x+1)

Remainder cannot be 1

2 3(x+1) /2 = remainder cannot be 1 so not part of must be true


Hope I dint misinterpret something here(Stmt iii).

Regards,
CR
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by lamhe » Thu May 21, 2009 10:59 pm
You got it...its D
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