How many odd integers are greater than the integer x and less than the : GMAT Data Sufficiency (DS)
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# How many odd integers are greater than the integer x and less than the

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

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22 Feb 2009, 11:21
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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

OPEN DISCUSSION OF THIS QUESTION IS HERE: how-many-odd-integers-are-greater-than-the-integer-x-and-100521.html
[Reveal] Spoiler: OA
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Re: How many odd integers are greater than the integer x and less than the [#permalink]

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22 Feb 2009, 18:04
look this is B..

cause if there are 24 integers btw x and y..then we know 12 are even and 12 odd..

1) is insuff cause it doesnt tell us whats in between..it just tells us there are 12 even integers...well if x is even then you will have one possibility if x=odd then you have another possibility..
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Re: How many odd integers are greater than the integer x and less than the [#permalink]

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22 Feb 2009, 19:34
stmt 1:

There are 12 even integers b/w x and Y.

For example i took 2 even integers b/w x and Y.

1,2,3,4,5,6 - 2 odd and 2 even
1,2,3,4,5 - still 2 even but 1 odd.
insufficient.
stmt 2:
there 24 integers >x and < y.
clearly there are 12 odd and 12 even in between them.
Hence B.
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Re: How many odd integers are greater than the integer x and less than the [#permalink]

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22 Feb 2009, 19:41
From stmt1, there are 12 even numbers between x and y. ==> number of odd numbers can be either 11 / 12 /13 since it depends on the combination of x and y being even / odd. Hence insufficient.

From stmt2 - there are 24 integers between x and y. From this we know that exactly half of them are odd and half are even. Hence we know that the number of odd numbers are 12. Hence sufficent.

IMO B
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Re: How many odd integers are greater than the integer x and less than the [#permalink]

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23 Feb 2009, 10:00
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The OA is B but why are we concluding that there equal number of odd and even integers in 24 integers? in question, there is no hint about this.

in 24 integers, there can be 20 even numbers and 4 can be odd integers, right?

this is gmatprep test #1 questio though.
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Re: How many odd integers are greater than the integer x and less than the [#permalink]

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23 Feb 2009, 11:58
ugimba wrote:
The OA is B but why are we concluding that there equal number of odd and even integers in 24 integers? in question, there is no hint about this.

in 24 integers, there can be 20 even numbers and 4 can be odd integers, right?

this is gmatprep test #1 questio though.

I think this is a good queston. I have treated them as the consecutive integers between x and y. If the integers between the x and y are not consecutive, then the question stem should say that a SET of integers where do not know what the integers are.

Probably lets see if any others respond to this question.
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Re: How many odd integers are greater than the integer x and less than the [#permalink]

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23 Feb 2009, 18:35
mrsmarthi wrote:
ugimba wrote:
The OA is B but why are we concluding that there equal number of odd and even integers in 24 integers? in question, there is no hint about this.

in 24 integers, there can be 20 even numbers and 4 can be odd integers, right?

this is gmatprep test #1 questio though.

I think this is a good queston. I have treated them as the consecutive integers between x and y. If the integers between the x and y are not consecutive, then the question stem should say that a SET of integers where do not know what the integers are.

Probably lets see if any others respond to this question.

I got E. I did not really understand why everyone treated these integers as consecutive integers. Nowhere in the question stem it is mentioned that they are consecutive integers.
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Re: How many odd integers are greater than the integer x and less than the [#permalink]

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23 Feb 2009, 19:30
ugimba wrote:
The OA is B but why are we concluding that there equal number of odd and even integers in 24 integers? in question, there is no hint about this.

in 24 integers, there can be 20 even numbers and 4 can be odd integers, right?

this is gmatprep test #1 questio though.

wow, great catch.. reinforces how we can make assumptions too easily. Interesting to see that gmatprep writers made the same assumption.
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Re: How many odd integers are greater than the integer x and less than the [#permalink]

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23 Feb 2009, 19:31
kukulkan wrote:
mrsmarthi wrote:
ugimba wrote:
The OA is B but why are we concluding that there equal number of odd and even integers in 24 integers? in question, there is no hint about this.

in 24 integers, there can be 20 even numbers and 4 can be odd integers, right?

this is gmatprep test #1 questio though.

I think this is a good queston. I have treated them as the consecutive integers between x and y. If the integers between the x and y are not consecutive, then the question stem should say that a SET of integers where do not know what the integers are.

Probably lets see if any others respond to this question.

I got E. I did not really understand why everyone treated these integers as consecutive integers. Nowhere in the question stem it is mentioned that they are consecutive integers.

would have been more convincing if you had caught it first
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Re: How many odd integers are greater than the integer x and less than the [#permalink]

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24 Feb 2009, 06:49
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ugimba wrote:
The OA is B but why are we concluding that there equal number of odd and even integers in 24 integers? in question, there is no hint about this.

in 24 integers, there can be 20 even numbers and 4 can be odd integers, right?

this is gmatprep test #1 questio though.

I don't know what everyone is going on about: If there are exactly 24 integers between the two numbers they MUST be consecutive, as otherwise there would be more than 24 integers obviously.

It's B.
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Re: How many odd integers are greater than the integer x and less than the [#permalink]

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13 Apr 2009, 06:56
There is no ambiguity here and answer is B.
It would be E if the number of integers between x and y were odd.
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Re: How many odd integers are greater than the integer x and less than the [#permalink]

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13 Apr 2009, 17:25
Yeah agree should be B.

If we start we A then it could be even and then 12 even or odd + 12 even... not suff

Hence B
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Re: How many odd integers are greater than the integer x and less than the [#permalink]

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22 Oct 2009, 23:10
(1) is insufficient – the number of odd integers could be 11, 12, or 13

(2) is sufficient – because the number of odd and the number of even can not differ more than 1. Thus, the only solution is 12.
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Re: How many odd integers are greater than the integer x and less than the [#permalink]

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12 Nov 2009, 18:55
ugimba wrote:
how many odd integers are greater than the integer x and lessthan 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.

(This is DS question )

1) You can have 11 or 12 odd numbers in between x and y depends on whether x, y are even or odd

2) it has to be 12 - sufficient

B.
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Re: How many odd integers are greater than the integer x and less than the [#permalink]

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13 Nov 2009, 23:20
Agreed. If there is exactly n number between the range x and y, then the numbers will be consecutive.
IMO B.
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Re: How many odd integers are greater than the integer x and less than the [#permalink]

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01 Dec 2009, 18:54
You dont need to list out 24 numbers to see the pattern
4 even, 4 odd- 8 total numbers between them
4 even, 4 odd

B is sufficient
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Re: How many odd integers are greater than the integer x and less than the [#permalink]

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

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21 Oct 2014, 15:53
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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.

Here is the string of 12 even integers and 11 odd integers between them: eoeoeoeoeoeoeoeoeoeoeoe.

4 cases are possible:

If x and y are both odd then XeoeoeoeoeoeoeoeoeoeoeoeY then there will be 11 odd integers between them;
If x and y are both even then XoeoeoeoeoeoeoeoeoeoeoeoeoY then there will be 11+2=13 odd integers between them;
If x is even and y is odd then XoeoeoeoeoeoeoeoeoeoeoeoeY then there will be 11+1=12 odd integers between them;
If x is odd and y is even then XeoeoeoeoeoeoeoeoeoeoeoeoY then again there will be 11+1=12 odd integers between them.

Not sufficient.

(2) There are 24 integers greater than x and less than y. Out of 24 consecutive integers greater than X and less than Y in any case half will be odd and another half will be even, so there are 12 odd integers greater than X and less than Y. Sufficient.

P.S. You can try instead of 12 and 24 some smaller numbers to simplify calculations for example 2 even integers for (1) and 4 integers for (2).

OPEN DISCUSSION OF THIS QUESTION IS HERE: how-many-odd-integers-are-greater-than-the-integer-x-and-100521.html[/quote]
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Re: How many odd integers are greater than the integer x and less than the   [#permalink] 21 Oct 2014, 15:53
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