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# How many odd integers are greater than the integer x and

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How many odd integers are greater than the integer x and [#permalink]

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28 Jul 2007, 13:07
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How many odd integers are greater than the integer x and less than the integer y?

(1) There are 12 even integers greater than x and less than y
(2) There are 24 integers greater than x and less than y

Can someone provide explanations for the 2 statements.

Last edited by nupurgupt on 28 Jul 2007, 21:21, edited 1 time in total.
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28 Jul 2007, 21:11
How many odd integers are greater than the integer x and less than the integer y?

(1) There are 12 even integers greater than y and less than y
(2) There are 24 integers greater than x and less than y

(1) Take the interval from 2 to 10 -->
even integers in b/w = 4, 6, 8
odd integers in b/w = 3, 5, 7, 9

Take the interval from 3 to 11 -->
even integers in b/w = 4, 6, 8
odd integers in b/w = 5, 7, 9

Therefore, INSUFFICIENT

(2) Take the interval from 2 to 9 -->
6 integers in b/w = 3, 4, 5, 6, 7, 8
odd integers in b/w = 3, 5, 7

Take the interval from 3 to 10 -->
6 integers in b/w = 4, 5, 6, 7, 8, 9
odd integers in b/w = 5, 7, 9

Therefore, SUFFICIENT

Is there a better explanation for the question (not using brute force).
Any inputs would be appreciated =)
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28 Jul 2007, 21:17
nupurgupt wrote:
How many odd integers are greater than the integer x and less than the integer y?

(1) There are 12 even integers greater than y and less than y
(2) There are 24 integers greater than x and less than y

(1) Take the interval from 2 to 10 -->
even integers in b/w = 4, 6, 8
odd integers in b/w = 3, 5, 7, 9

Take the interval from 3 to 11 -->
even integers in b/w = 4, 6, 8
odd integers in b/w = 5, 7, 9

Therefore, INSUFFICIENT

(2) Take the interval from 2 to 9 -->
6 integers in b/w = 3, 4, 5, 6, 7, 8
odd integers in b/w = 3, 5, 7

Take the interval from 3 to 10 -->
6 integers in b/w = 4, 5, 6, 7, 8, 9
odd integers in b/w = 5, 7, 9

Therefore, SUFFICIENT

Is there a better explanation for the question (not using brute force).
Any inputs would be appreciated =)

For statement 2 it would be faster without considering numbers.
We know there are 24 integers between x and y. If we have a set of even number of integers exactly half would be odd and the other half even. So statement 2 is sufficient.

If you have copied down statement 1 correctly (12 greater than y and also less than y), then it is clearly insufficient since we have no knowledge of x!!
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28 Jul 2007, 21:22
Thanks for the expln. Sumande
and also for pointing out the typo in S1, i've fixed it now
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28 Jul 2007, 21:50
nupurgupt wrote:
Thanks for the expln. Sumande
and also for pointing out the typo in S1, i've fixed it now

Statement 1 is still insufficient. There can be 11, 12 or 13 odd integers between x and y.
28 Jul 2007, 21:50
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