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GMAT Prep No. of Odd Integers

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by shovan85 » Fri Oct 22, 2010 12:16 pm
IMO C

1: 12 Even.
But we do not know how many total integers are there between x and y
so we cannot say how many are Odd.
Insufficient.

2: 24 integers between x and y (excluding both)
This is also Insufficient.

Combine both, there are x< 24 integers < y and 12 Even so rest of the integers are bound to be Odd.

PS: Zero is even.
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by clock60 » Fri Oct 22, 2010 2:03 pm
not too sure that the answer is C, to me it is B, my reasoning
how many odd numbers between x and y
(1) there are 12 even integers between x and y,
here i apply to simple numbers taking that the number of even numbers is even
x=1, y=5 and set looks like:1 2,3 4 5, here we have two even numbers and 1 odd
x=1, y=6, with set 1,2,3,4,5,6 two even numbers 2, 4 and two odd numbers 3 and 5
i hope the same is true with 12 even numbers as in 1 st
so insufficient
(2) to me suffcient
taking that the number of integers between x and y is even ( here 24 ) the number of odd will be always equals the number of even 24/2=12. to verify
let it be 4 numbers between x and y
1,2,3,4,5,6 x=1, y=6 two even two odd
2,3,4,5,6,7 x=2, y=7 two even two odd
but in case the the number if integers between x and y is odd different cases are possible
the number of integers is 3
1,2,3,4,5-two even 1-odd, 2,3,4,5,6 1even 2 odd
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by Testluv » Fri Oct 22, 2010 2:26 pm
Yeah, the correct answer is definitely choice B, and clock60's approach--that of picking numbers--is REALLY great in odd/even problems.

Looking at (1):

Let x = 0. The 12th even integer greater than 0 is 24. So, y can be 25 or 26 (either way there will be 12 even integers greater than x but less than y). So, there may be 12 or 13 odd integers greater than x but less than y. Thus, (1) is insufficient.

Looking at (2):

Again, let x = 0. Then, y must be 25. Since we have an even number of consecuitve integers separating x and y (ie, 24 integes separating x and y), exactly half are odd, and half are even. So, there are 12 odd integers greater than x but less than y. And the beauty of picking numbers in odd/even problems is that, here for example, we don't need to test other cases. So, (2) is sufficient.

****

(0 is certainly even because it falls between two odd integers on the number line.)
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by shovan85 » Fri Oct 22, 2010 10:13 pm
Testluv wrote: Looking at (2):

Again, let x = 0. Then, y must be 25. Since we have an even number of consecuitve integers separating x and y (ie, 24 integes separating x and y), exactly half are odd, and half are even. So, there are 12 odd integers greater than x but less than y. And the beauty of picking numbers in odd/even problems is that, here for example, we don't need to test other cases. So, (2) is sufficient.

****
(0 is certainly even because it falls between two odd integers on the number line.)
But Option 2 says: 2) There are 24 integers greater than x and less than y
And Question says: How many odd integers are greater than integer x and less than integer y?

So i thought x< 24 integers <y and as no where it is mentioned that the 24 integers are consecutive I can take all as Odd .
This was my thought behind making B insufficient.

Please let me know why my assumption stated in BOLD is wrong?
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by novel » Fri Oct 22, 2010 10:55 pm
I did it in this way.
if x and y are both even or odd then the no of numbers between x and Y (excluding both) is always odd.Futrther th depending on nature of X the nature of number in between varies.
Ex- 5 nos between5 and 11 out of which 3 are even 2 are odd.
5 nos between 2 and 8 out of which 2 are even 3 are odd.


and id x and y are of opposite nature(even/odd) then no of numbers between x and Y (excluding both) is always even.
In this case half the numbers are even and half are odd.
For eg 6 no bet 5 and 12 out of which 3 are even 3 are odd.

accordingly IMO B
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by Testluv » Sat Oct 23, 2010 1:20 pm
shovan85 wrote: So i thought x< 24 integers <y and as no where it is mentioned that the 24 integers are consecutive I can take all as Odd .
This was my thought behind making B insufficient.

Please let me know why my assumption stated in BOLD is wrong?
Hi shovan,

If there are 24 integers greater than x, then they have to be consecutive. If they weren't consecutive, then even the intervening integers are greater than x, and more than 24 integers would be greater than x.

For example, assume x is 0. If there ARE 24 integers greater than x but less than y, then y is 25. If y were greater than 25, then there would be more than 24 integers greater than x but less than y. I hope that makes sense!
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by shovan85 » Sat Oct 23, 2010 1:26 pm
Testluv wrote:
shovan85 wrote: So i thought x< 24 integers <y and as no where it is mentioned that the 24 integers are consecutive I can take all as Odd .
This was my thought behind making B insufficient.

Please let me know why my assumption stated in BOLD is wrong?
Hi shovan,

If there are 24 integers greater than x, then they have to be consecutive. If they weren't consecutive, then even the intervening integers are greater than x, and more than 24 integers would be greater than x.

For example, assume x is 0. If there ARE 24 integers greater than x but less than y, then y is 25. If y were greater than 25, then there would be more than 24 integers greater than x but less than y. I hope that makes sense!
Sorry TestLuv but could not understand the underlined part.

Also one more question... Am I thinking too much when the Q is simple :( ? Because it was in front of me I had two solutions either B or C. I chose C because if it is so simple then it would not have appeared. Anyways thanks for the help.
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by Testluv » Sat Oct 23, 2010 9:40 pm
Hey shovan,

yeah, the underlined part was a bit cryptic. If there ARE 24 integers greater than x but less than y, then exactly 24 integers separate x and y on the number line. (If we interpret it as 24, say, even integers separating x and y, then we would have 48 (or 49) integers separating them (not 24).)

Are you overthinking this statement? Perhaps. But I think the english is difficult in this question. If you thought the answer may have been B, then you were very close to interepreting (2) correctly--you just had to trust yourself!
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by shovan85 » Sat Oct 23, 2010 10:21 pm
Testluv wrote:yeah, the underlined part was a bit cryptic. If there ARE 24 integers greater than x but less than y, then exactly 24 integers separate x and y on the number line. (If we interpret it as 24, say, even integers separating x and y, then we would have 48 (or 49) integers separating them (not 24).)
Thanks!! It really helped a lot.
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