It is currently 23 Sep 2017, 09:42

# Happening Now:

Alleviate MBA app anxiety! Come to Chat Room #2

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

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

Author Message
TAGS:

### Hide Tags

Manager
Joined: 25 Jul 2010
Posts: 140

Kudos [?]: 548 [2], given: 29

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

### Show Tags

06 Sep 2010, 13:09
2
KUDOS
28
This post was
BOOKMARKED
00:00

Difficulty:

75% (hard)

Question Stats:

49% (00:54) correct 51% (00:56) wrong based on 762 sessions

### HideShow timer Statistics

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
[Reveal] Spoiler: OA

Kudos [?]: 548 [2], given: 29

Math Expert
Joined: 02 Sep 2009
Posts: 41698

Kudos [?]: 124613 [7], given: 12079

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

### Show Tags

06 Sep 2010, 13:32
7
KUDOS
Expert's post
15
This post was
BOOKMARKED
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.
_________________

Kudos [?]: 124613 [7], given: 12079

Retired Moderator
Joined: 02 Sep 2010
Posts: 794

Kudos [?]: 1155 [2], given: 25

Location: London
Re: odd integers greater than integer x and less than integer y [#permalink]

### Show Tags

06 Sep 2010, 13:35
2
KUDOS
2
This post was
BOOKMARKED
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
_________________

Kudos [?]: 1155 [2], given: 25

Math Expert
Joined: 02 Sep 2009
Posts: 41698

Kudos [?]: 124613 [2], given: 12079

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

### Show Tags

29 Oct 2010, 14:45
2
KUDOS
Expert's post
1
This post was
BOOKMARKED
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?
_________________

Kudos [?]: 124613 [2], given: 12079

Ms. Big Fat Panda
Status: Three Down.
Joined: 09 Jun 2010
Posts: 1916

Kudos [?]: 2181 [2], given: 210

Concentration: General Management, Nonprofit
Re: How many odd integers... [#permalink]

### Show Tags

19 Dec 2010, 01:27
2
KUDOS
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.

Kudos [?]: 2181 [2], given: 210

Current Student
Joined: 27 Jun 2012
Posts: 407

Kudos [?]: 902 [1], given: 184

Concentration: Strategy, Finance
Re: odd integers greater than integer x and less than integer y [#permalink]

### Show Tags

24 Jan 2013, 22:24
1
KUDOS
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).
_________________

Thanks,
Prashant Ponde

Tough 700+ Level RCs: Passage1 | Passage2 | Passage3 | Passage4 | Passage5 | Passage6 | Passage7
VOTE GMAT Practice Tests: Vote Here
PowerScore CR Bible - Official Guide 13 Questions Set Mapped: Click here

Kudos [?]: 902 [1], given: 184

Manager
Joined: 25 Jul 2010
Posts: 140

Kudos [?]: 548 [0], given: 29

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

### Show Tags

07 Sep 2010, 14:07
Quote:
Hope it's clear.

You are genius. Many thanks Bunuel

Kudos [?]: 548 [0], given: 29

Intern
Joined: 25 Sep 2010
Posts: 20

Kudos [?]: 43 [0], given: 7

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

### Show Tags

29 Oct 2010, 14:34
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

Kudos [?]: 43 [0], given: 7

Manager
Joined: 25 Jun 2010
Posts: 91

Kudos [?]: 44 [0], given: 0

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

### Show Tags

18 Dec 2010, 22:24
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.

Kudos [?]: 44 [0], given: 0

Senior Manager
Joined: 13 Mar 2012
Posts: 354

Kudos [?]: 191 [0], given: 31

Concentration: Operations, Strategy

### Show Tags

22 Mar 2012, 03:30
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
_________________

Practice Practice and practice...!!

If there's a loophole in my analysis--> suggest measures to make it airtight.

Kudos [?]: 191 [0], given: 31

Intern
Joined: 30 Nov 2011
Posts: 30

Kudos [?]: 64 [0], given: 23

Location: United States
GMAT 1: 700 Q47 V38
GPA: 3.54
Re: How many odd integers are greater than the integer x and [#permalink]

### Show Tags

22 Mar 2012, 07:16
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

Kudos [?]: 64 [0], given: 23

Math Expert
Joined: 02 Sep 2009
Posts: 41698

Kudos [?]: 124613 [0], given: 12079

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

### Show Tags

22 Mar 2012, 07:43
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.
_________________

Kudos [?]: 124613 [0], given: 12079

Intern
Joined: 30 Nov 2011
Posts: 30

Kudos [?]: 64 [0], given: 23

Location: United States
GMAT 1: 700 Q47 V38
GPA: 3.54
Re: How many odd integers are greater than the integer x and [#permalink]

### Show Tags

22 Mar 2012, 07:55
You are great bunuel, I got it, thanks.

Kudos [?]: 64 [0], given: 23

Senior Manager
Joined: 21 Mar 2010
Posts: 307

Kudos [?]: 31 [0], given: 33

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

### Show Tags

01 May 2012, 11:12
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

Kudos [?]: 31 [0], given: 33

Manager
Status: I will not stop until i realise my goal which is my dream too
Joined: 25 Feb 2010
Posts: 225

Kudos [?]: 60 [0], given: 16

Schools: Johnson '15
Re: odd integers greater than integer x and less than integer y [#permalink]

### Show Tags

18 Jun 2012, 08:47
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...
_________________

Regards,
Harsha

Note: Give me kudos if my approach is right , else help me understand where i am missing.. I want to bell the GMAT Cat

Satyameva Jayate - Truth alone triumphs

Kudos [?]: 60 [0], given: 16

Director
Status: Gonna rock this time!!!
Joined: 22 Jul 2012
Posts: 511

Kudos [?]: 71 [0], given: 562

Location: India
GMAT 1: 640 Q43 V34
GMAT 2: 630 Q47 V29
WE: Information Technology (Computer Software)
Re: odd integers greater than integer x and less than integer y [#permalink]

### Show Tags

24 Jan 2013, 22:03
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?
_________________

hope is a good thing, maybe the best of things. And no good thing ever dies.

Who says you need a 700 ?Check this out : http://gmatclub.com/forum/who-says-you-need-a-149706.html#p1201595

My GMAT Journey : http://gmatclub.com/forum/end-of-my-gmat-journey-149328.html#p1197992

Kudos [?]: 71 [0], given: 562

Math Expert
Joined: 02 Sep 2009
Posts: 41698

Kudos [?]: 124613 [0], given: 12079

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

### Show Tags

25 Jan 2013, 05:16
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)."
_________________

Kudos [?]: 124613 [0], given: 12079

Director
Status: Gonna rock this time!!!
Joined: 22 Jul 2012
Posts: 511

Kudos [?]: 71 [0], given: 562

Location: India
GMAT 1: 640 Q43 V34
GMAT 2: 630 Q47 V29
WE: Information Technology (Computer Software)
Re: How many odd integers are greater than the integer x and [#permalink]

### Show Tags

25 Jan 2013, 05:26
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..
_________________

hope is a good thing, maybe the best of things. And no good thing ever dies.

Who says you need a 700 ?Check this out : http://gmatclub.com/forum/who-says-you-need-a-149706.html#p1201595

My GMAT Journey : http://gmatclub.com/forum/end-of-my-gmat-journey-149328.html#p1197992

Kudos [?]: 71 [0], given: 562

Math Expert
Joined: 02 Sep 2009
Posts: 41698

Kudos [?]: 124613 [0], given: 12079

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

### Show Tags

25 Jan 2013, 05:33
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..

_________________

Kudos [?]: 124613 [0], given: 12079

Intern
Joined: 26 Jan 2013
Posts: 1

Kudos [?]: [0], given: 0

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

### Show Tags

26 Jan 2013, 01:00
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?

Kudos [?]: [0], given: 0

How many odd integers are greater than the integer x and   [#permalink] 26 Jan 2013, 01:00

Go to page    1   2   3    Next  [ 44 posts ]

Similar topics Replies Last post
Similar
Topics:
5 Is x an integer greater than 1? 24 31 Jan 2017, 01:01
The integer x is how much greater than 4? 2 29 Aug 2016, 12:17
1 If X is greater than two, is X the square of an odd prime integer? 3 23 Sep 2017, 01:41
5 How many integers are greater than x, but less than y? 7 26 Nov 2014, 07:27
16 How many odd integers are greater than the integer x and less than the 17 21 Oct 2014, 16:53
Display posts from previous: Sort by