Is t odd ?

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by Anurag@Gurome » Fri Jan 07, 2011 9:44 pm
nehatandon wrote:If t is an integer, is t odd?
(1)t/3 is not an integer.
(2)t-1/3 is not an integer.
Statement 1: (t/3) is not an integer.
Implies t is not divisible by 3. This doesn't help us to conclude whether t is even or odd. Consider,
  • 1. t = 5 => Odd
    2. t = 8 => Even
Not sufficient.

Statement 2: (t - 1)/3 is not an integer.
Implies (t - 1) is not divisible by 3. This also doesn't help us to conclude whether t is even or odd. Consider the same examples as above.


Not sufficient.

1 & 2 Together: t and (t - 1) both are not divisible by 3. Hence (t + 1) must be divisible by 3. But this also does not help us to conclude whether t is even or odd. Consider the same examples as above.

Not sufficient.

The correct answer is E.
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by nehatandon » Fri Jan 07, 2011 10:08 pm
Anurag@Gurome wrote:
nehatandon wrote:If t is an integer, is t odd?
(1)t/3 is not an integer.
(2)t-1/3 is not an integer.
Statement 1: (t/3) is not an integer.
Implies t is not divisible by 3. This doesn't help us to conclude whether t is even or odd. Consider,
  • 1. t = 5 => Odd
    2. t = 8 => Even
Not sufficient.

Statement 2: (t - 1)/3 is not an integer.
Implies (t - 1) is not divisible by 3. This also doesn't help us to conclude whether t is even or odd. Consider the same examples as above.


Not sufficient.

1 & 2 Together: t and (t - 1) both are not divisible by 3. Hence (t + 1) must be divisible by 3. But this also does not help us to conclude whether t is even or odd. Consider the same examples as above.

Not sufficient.

The correct answer is E.
Thanks Anurag. I think for this type of problem plugging in number is the best choice. Your examples made it clear.
Thanks for the solution.

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by bblast » Wed Jan 12, 2011 12:46 am
hey Anurag,
Just tried this problem.

I think I went wrong somewhere, you will be the best person to tell me.

1> insuff-agreed
2>insufficient-agreed


1+2

if i start picking numbers from 24,25,26,27,28

cant take 24,27 as both are divisible by 3 hence contradicts statement 1.
cant take 25 or 28 as this value of t contradicts statement 2.
So the only value which remains in this range is 26


additinally if we take (t-1)(t)(t+1) as a set of 3 consequetive integers, for t-1 and t to be non mumtiples of 3 they must be the pair of numbers (7,8)(13,14)(25,26). so t is always even here (8,14,26)

which satisfies both statements.

Hence T is not Odd.

answer C.

please let me know where I erred.
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by Anurag@Gurome » Wed Jan 12, 2011 1:00 am
bblast wrote:if i start picking numbers from 24,25,26,27,28

cant take 24,27 as both are divisible by 3 hence contradicts statement 1.
cant take 25 or 28 as this value of t contradicts statement 2.
So the only value which remains in this range is 26
First of all, you cannot really fix a range for t!
The problem says t is an integer. You have to find a general solution not a solution which is only applicable in a particular range. Just extend your list to 29 or start picking numbers from 23, see what happens.
bblast wrote:additinally if we take (t-1)(t)(t+1) as a set of 3 consequetive integers, for t-1 and t to be non mumtiples of 3 they must be the pair of numbers (7,8)(13,14)(25,26). so t is always even here (8,14,26)
What about, (4, 5), (10, 11), (16, 17) etc?
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by bblast » Wed Jan 12, 2011 1:35 am
Got it, thank you Anurag
Cheers !!

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