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

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06 Sep 2010, 12:09
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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
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06 Sep 2010, 12:32
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Orange08 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 x and less than y
2) There are 24 integers greater than x and less than y

Sorry, I tried to search the forum for previous explanations. But since the search was too generic, it didn't fetch any results.

(1) 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) 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).

Orange08 wrote:
why are the integers assumed consecutive over here?

Are you talking about (2)? If we are told that there are 4 integers more than X=1 and less than Y=6, then these integers are 2, 3, 4, and 5 - 4 consecutive integers, how else? Note that half are odd and half are even. Or if X=2 and Y=7 then these integers would be 3, 4, 5 and 6 - 4 consecutive integers: half are odd and half are even.

Hope it's clear.
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Re: odd integers greater than integer x and less than integer y [#permalink]

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06 Sep 2010, 12:35
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Statement (1) : 12 even integers between x and y ... As an example let x be 20 and y be 46. There are 12 even integers and 13 odd integers; if x is 20 and y is 45, there are 12 even and 12 odd integers ... So clearly (1) alone is not sufficient

Statement (2) : 24 integers between x and y .... if you consider them in order they have to be even, odd, even, odd .... OR odd,even, odd, even ..... : Either case 12 even and 12 odd ... So (2) alone is sufficient
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Re: odd integers greater than integer x and less than integer y [#permalink]

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07 Sep 2010, 13:07
Quote:
Hope it's clear.

You are genius. Many thanks Bunuel
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Re: odd integers greater than integer x and less than integer y [#permalink]

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29 Oct 2010, 13:34
Bunuel wrote:
Orange08 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 x and less than y
2) There are 24 integers greater than x and less than y

Sorry, I tried to search the forum for previous explanations. But since the search was too generic, it didn't fetch any results.

(1) 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) 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).

Orange08 wrote:
why are the integers assumed consecutive over here?

Are you talking about (2)? If we are told that there are 4 integers more than X=1 and less than Y=6, then these integers are 2, 3, 4, and 5 - 4 consecutive integers, how else? Note that half are odd and half are even. Or if X=2 and Y=7 then these integers would be 3, 4, 5 and 6 - 4 consecutive integers: half are odd and half are even.

Hope it's clear.

hey bunnel, when you say "4 integers more than X=1 and less than Y=6" why cant it be 1,2,2,2,2,6, or, 1,2,5,5,5,6 this satisfies the statement rather than consecutive integers, right, the question did not say only consecutive or different numbers,,,, ,,iam i missing somethi here,,,,could you explain
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Re: odd integers greater than integer x and less than integer y [#permalink]

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29 Oct 2010, 13:45
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satishreddy wrote:
Bunuel wrote:
Orange08 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 x and less than y
2) There are 24 integers greater than x and less than y

Sorry, I tried to search the forum for previous explanations. But since the search was too generic, it didn't fetch any results.

(1) 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) 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).

Orange08 wrote:
why are the integers assumed consecutive over here?

Are you talking about (2)? If we are told that there are 4 integers more than X=1 and less than Y=6, then these integers are 2, 3, 4, and 5 - 4 consecutive integers, how else? Note that half are odd and half are even. Or if X=2 and Y=7 then these integers would be 3, 4, 5 and 6 - 4 consecutive integers: half are odd and half are even.

Hope it's clear.

hey bunnel, when you say "4 integers more than X=1 and less than Y=6" why cant it be 1,2,2,2,2,6, or, 1,2,5,5,5,6 this satisfies the statement rather than consecutive integers, right, the question did not say only consecutive or different numbers,,,, ,,iam i missing somethi here,,,,could you explain

What is "1,2,2,2,2,6, or, 1,2,5,5,5,6"?

Let me ask you a question: how many integers are more than 1 and less than 6? Can the answer be other than 4 (2, 3, 4 and 5)?

Or another way: if 1<n<6 then how many integer values n can take?
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Re: How many odd integers... [#permalink]

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18 Dec 2010, 21:24
Statement (1) : 12 even integers between x and y
let x be 2 and y be 28. There are 12 even integers and 13 odd integers.
if x is 2 and y is 27, there are 12 even and 12 odd integers -- Insufficient

Statement (2) : 24 integers between x and y
if you consider them in order they have to be
even, odd, even, odd
OR
odd,even, odd, even
So, always 12 even and 12 odd - Sufficient

B.
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Re: How many odd integers... [#permalink]

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19 Dec 2010, 00:27
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Werewolf 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 x and less than y

2. There are 24 integers greater than x and less than y

The first statement says there are 12 even integers. There are two cases for this:

1. x is an odd integer, in which case there will be 12 even integers but only 11 odd integers.
2. x is an even integer, in which case there will be 12 each of even and odd integers.

Hence this is insufficient.

Statement 2 says there are 24 integers greater than x and lesser than y.

Two cases:

1. x is an odd integers, which means there will be 12 even integers and 12 odd integers.
2. x is an even integer, in which case there will be 12 each of even and odd integers.

In both cases, the answer is the same and hence answer is B. I got tripped up by this question, good one.
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22 Mar 2012, 02:30
How many odd integers are greater than integer X and less than 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.

1) can be 11 or 12
insufficient

2) only possibility is 12

sufficient

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

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22 Mar 2012, 06:16
Bunuel, I chose E instead of B, since it is not stated that the integers are consecutive, so do you have any explanation on this matter ?
thank you
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Re: How many odd integers are greater than the integer x and [#permalink]

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22 Mar 2012, 06:43
Bunuel, I chose E instead of B, since it is not stated that the integers are consecutive, so do you have any explanation on this matter ?
thank you

(2) says that: there are 24 integers greater than x and less than y. Naturally those 24 integers between x and y are consecutive, how else? Consider x=1 and y=26: there are following 24 integers between them: 2, 3, 4, ..., 25.

Also check this post about the same issue: how-many-odd-integers-are-greater-than-the-integer-x-and-100521.html#p809821

Hope it's clear.
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22 Mar 2012, 06:55
You are great bunuel, I got it, thanks.
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How many odd integers are greater than the integer x and [#permalink]

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01 May 2012, 10:12
Given 24 numbers, equal number will be odd and even.- second statement.

First statement- given 12 even numbers- you cannot guess the number of odd nos

example- 0-26 then you have 12 even and 12 odd. x= 0 and y =26
1, 26 12 even and 13 odd

1,25 and 0,25 are also options. therefore b is conclusive
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Re: odd integers greater than integer x and less than integer y [#permalink]

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18 Jun 2012, 07:47
Bunuel wrote:
Orange08 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 x and less than y
2) There are 24 integers greater than x and less than y

Sorry, I tried to search the forum for previous explanations. But since the search was too generic, it didn't fetch any results.

(1) 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) 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).

Orange08 wrote:
why are the integers assumed consecutive over here?

Are you talking about (2)? If we are told that there are 4 integers more than X=1 and less than Y=6, then these integers are 2, 3, 4, and 5 - 4 consecutive integers, how else? Note that half are odd and half are even. Or if X=2 and Y=7 then these integers would be 3, 4, 5 and 6 - 4 consecutive integers: half are odd and half are even.

Hope it's clear.

so here we are assuming the consecutive integers?

I missed it, and i failed to answer this in PREP test...

Kudos Bunuel...ur explanations are always the best...
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Re: odd integers greater than integer x and less than integer y [#permalink]

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24 Jan 2013, 21:03
Bunuel wrote:
Orange08 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 x and less than y
2) There are 24 integers greater than x and less than y

Sorry, I tried to search the forum for previous explanations. But since the search was too generic, it didn't fetch any results.

(1) 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) 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).

Orange08 wrote:
why are the integers assumed consecutive over here?

Are you talking about (2)? If we are told that there are 4 integers more than X=1 and less than Y=6, then these integers are 2, 3, 4, and 5 - 4 consecutive integers, how else? Note that half are odd and half are even. Or if X=2 and Y=7 then these integers would be 3, 4, 5 and 6 - 4 consecutive integers: half are odd and half are even.

Hope it's clear.

I think the best way to cehck 2 would be to reduce the number to 4 from 24 and try out.. eoeoeo.. the result would be in sync with 24 numbers .. same applies to 1 as well.

what say?
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Re: odd integers greater than integer x and less than integer y [#permalink]

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24 Jan 2013, 21:24
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Sachin9 wrote:
I think the best way to cehck 2 would be to reduce the number to 4 from 24 and try out.. eoeoeo.. the result would be in sync with 24 numbers .. same applies to 1 as well.

what say?

Yes that should work for this problem. Even I would have solved this way (reduce the sample size from 12 to 2 and 24 to 4)
1) There are 2 even integers greater than x and less than y
INSUFFICIENT: XeoeY or XoeoeY - gives 1 or 2 odds
2) There are 4 integers greater than x and less than y
SUFFICIENT: XoeoeY or XeoeoY - both give same number of odds, 2. If it works for 4 then it will work for 24.

Hence choice(B).
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Re: odd integers greater than integer x and less than integer y [#permalink]

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25 Jan 2013, 04:16
Sachin9 wrote:
Bunuel wrote:
Orange08 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 x and less than y
2) There are 24 integers greater than x and less than y

Sorry, I tried to search the forum for previous explanations. But since the search was too generic, it didn't fetch any results.

(1) 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) 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).

Orange08 wrote:
why are the integers assumed consecutive over here?

Are you talking about (2)? If we are told that there are 4 integers more than X=1 and less than Y=6, then these integers are 2, 3, 4, and 5 - 4 consecutive integers, how else? Note that half are odd and half are even. Or if X=2 and Y=7 then these integers would be 3, 4, 5 and 6 - 4 consecutive integers: half are odd and half are even.

Hope it's clear.

I think the best way to cehck 2 would be to reduce the number to 4 from 24 and try out.. eoeoeo.. the result would be in sync with 24 numbers .. same applies to 1 as well.

what say?

Sachin, please read the solution you are quoting: "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)."
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Re: How many odd integers are greater than the integer x and [#permalink]

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25 Jan 2013, 04:26
Sachin, please read the solution you are quoting: "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)."

I didn't get this bunuel..
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Re: How many odd integers are greater than the integer x and [#permalink]

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25 Jan 2013, 04:33
Sachin9 wrote:
Sachin, please read the solution you are quoting: "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)."

I didn't get this bunuel..

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

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26 Jan 2013, 00:00
Hi! why is it that nobody (and I mean on any forum) has considered X to be a negative integer? If that's the case then the option E would be the clear answer, wouldn't it?
How many odd integers are greater than the integer x and   [#permalink] 26 Jan 2013, 00:00

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