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Concentration: Entrepreneurship, International Business

GMAT 1: 730 Q50 V39

GPA: 3.2

WE: Education (Education)

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

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23 Feb 2013, 12:58

You can consider x to be a negative number say -10 and y to be a positive number. Now statement 2 states that there are 24 numbers greater than x and lesser than y. Hence, the value of y is 15. Now, calculate the number of odd numbers between these numbers. It will be 12 -9,-7,-5,-3,-1,1,3,5,7,9,11,13.

Even if x is a negative odd number and y a positive even numbers with 24 numbers between them, the result would be same. I am unsure of how you found statement 2 to be INSUFFICIENT.

It would be great if you could let me know about your understanding of this statement.

nothingman wrote:

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?

Concentration: Entrepreneurship, International Business

GMAT 1: 730 Q50 V39

GPA: 3.2

WE: Education (Education)

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

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25 Feb 2013, 11:54

Statement 2 states that There are 24 integers greater than x and less than y. There are totally 24 integers between these two numbers excluding these two numbers. The statement does not mention anything about the sign or values of this number. There is no other way for 24 integers to exist between 2 integers without being consecutive.

Consider the number of integers between 1 and 10 exclusive. The answer has to be 8(2,3,4,5,6,7,8,9). Is there any other possible answer?

Hope this helps!

jbisht 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

in case (2) Is it good to assume that these are 24 consecutive integers ??

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

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26 Apr 2014, 09:01

Statement (ii) is really tricky one.

At first I thought If X= 1 I can take any number for Y say y= 50 and I can put any 24 numbers between them.

These numbers can all be even. But The sentence " There are 24 integers greater than x and less than y " is not what I am thinking.

If x=1, y=50 , how can it be 24 integers in between them? Actually, without writing I thought it wrongly but when I wrote example, I realized that the numbers are consecutive.

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

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05 May 2014, 00:10

hi bunnel

st 1 can still be written and tried... but st 2 will be time consuming... how do we know for sure that when there r 24 even I between x & y then there will be 24 odd I, without manually doing this? as doing it manually time consuming...

as you suggest we should take smaller number to try but how to decide which numbers will gave same result as 12 & 24.. any double? like i can take 4 for case 1 and 8 for case 2?
_________________

Hope to clear it this time!! GMAT 1: 540 Preparing again

st 1 can still be written and tried... but st 2 will be time consuming... how do we know for sure that when there r 24 even I between x & y then there will be 24 odd I, without manually doing this? as doing it manually time consuming...

as you suggest we should take smaller number to try but how to decide which numbers will gave same result as 12 & 24.. any double? like i can take 4 for case 1 and 8 for case 2?

(2) says that there are 24 (even) integers greater than integer x and less than integer y. The important part is that the number of integers between x and y is even. In this case half of them must be odd and another half must be even. How else? Can there be 11 odd integers and 13 odd integer greater than x and less than y?

If we were told that there are 3 (odd) integers greater than integer x and less than integer y, then this would be insufficient, because there could be 1 odd and 2 evens or 2 odds and 1 even.
_________________

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

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22 Oct 2014, 03:14

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.

Answer: B.

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.

Hi Bunuel If in statement-2, there is odd number ..like 5 integers between x and y then it will be insuff ? Thanks.

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.

Answer: B.

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.

Hi Bunuel If in statement-2, there is odd number ..like 5 integers between x and y then it will be insuff ? Thanks.

Yes, in that case the statement would be insufficient. We could have 2 odd, 3 even or 2 even, 3 odd.
_________________

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

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24 Oct 2014, 05:05

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

B.

1) There are 12 even integers greater than x and less than y let the list of even integers be = 2,4,6,...,24 => x < (2,4,...,24) < y including odd integers: x < (1,2,3,...,25) < y now we cannot be sure if 1 or 25 (or both) would exist in this list or not. so insufficient.

2) There are 24 integers greater than x and less than y considering the aforementioned list again even if we consider 1-24 or 2-25 we will have the same number of odd integers. so sufficient.
_________________

Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

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

There are 2 variables (x,y) and 2 equations from the question and the 2 conditions, so there is high chance (C) will be our answer. Looking at the conditions together, if there are 12 even numbers out of the 24 integers, there are of course 12 odd integers, so the answer becomes (C). But this is an integer question which is one the the key questions, if we apply 4(A) mistake types, Looking at condition 1, the number of odd integers becomes (35-11)/2+1=13 when x=10, y=36, and (33-13)/2+1=11 when x=11, y=35; this does not give unique answer, so this is insufficient. From condition 2, if there are 24 integers, there has to be 12 even and 12 odd. This is sufficient, making the answer (B).

For cases where we need 2 more equation, such as original conditions with “2 variables”, or “3 variables and 1 equation”, or “4 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 70% chance that C is the answer, while E has 25% chance. These two are the majority. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since C is most likely to be the answer using 1) and 2) separately according to DS definition (It saves us time). Obviously there may be cases where the answer is A, B, D or E.
_________________

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

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02 Nov 2015, 00:28

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.

Answer: B.

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 might sound dumb but the fact that consecutive is confusing. we're only told 24 integers are greater than x :/ I was confused between B and E

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.

Answer: B.

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 might sound dumb but the fact that consecutive is confusing. we're only told 24 integers are greater than x :/ I was confused between B and E

(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.

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

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10 Aug 2016, 12:50

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.

Answer: B.

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.

Something further to this: This question could have been a lot tedious if the 2nd stmt read there are 23 numbers between x and y.

Odd number of consecutive integer would have thrown the count of evens and odds off balance.

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

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20 Aug 2016, 22:34

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.

Answer: B.

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.

Great explanation as always Buunel! Happy to see the consecutive integers doubt clarified as well.

A little off topic, but first look at eoeoeoeoeoeoeoeoeoeoeoe reminded me of the minion from Despicable Me

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

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29 Aug 2016, 00:40

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.

Answer: B.

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.

In statement 2- If the number of integers between X and Y was odd, say 23 or 21. Would the statement be sufficient? What would have been the answer in that case?

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

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30 Aug 2016, 01:20

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

1. let just say there are 3 even integers greater than x and less than y

if x =even x odd e odd e odd e odd => so 4 odd. if X =odd o e o e o e o => 2 odd

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

let just say there are 4 integers greater than x and less than y

e o e o e 0 => 2 odd o e o e 0 o => 2 odd

THis is working only if There are 24 integers greater than x and less than y, the value in red is even. if it is odd. will not work. (untill unless we know what x is even /odd)

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

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29 Dec 2016, 06:09

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.

Answer: B.

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.

Hi Bunuel !! Thanks for the explanation.

So trying to explore the concept further, if statement 2 had said that there are (say) 3 instead of 4 i.e odd no of integers between x & y, we would not be able to answer the question because i would again depend on the values of X & Y.

Also in statement 1 if they had said that there are 12 consecutive odd nos, the result would be not sufficient again.

So from this, what I understand is that for counting nos, if we are referring to odd only or even only nos in b/w we need to know the first two numbers. But when we have consecutive no of even integers, it doesnt matter what the 2 encapsulating numbers are.

Is there a rule or generalisation that can be made for counting ?? (especially for such tricky questions or is this to be solved by actually considering a few cases as you have done ?? )

My counting concepts are poor, so would appreciate if you can direct me towards some counting theory.

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

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29 Dec 2016, 06:17

sudhirgupta93 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.

Answer: B.

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.

In statement 2- If the number of integers between X and Y was odd, say 23 or 21. Would the statement be sufficient? What would have been the answer in that case?

Answer would be insufficient - eg. take smaller nos. if x=1 & y=5, so we have 1 <2,3,4<5 so only 1 odd no if x=2 & y=6, so we have 2<3,4,5<6 , so now we have 2 odd nos.

I have posted a similar query to bunuel for clarification regarding generalization of this counting principle.But from what I can gather, when we have an even no of consecutive integers, we will have have an equal no of odd & equal no of even nos between them. & when we have even no or odd number of integers to count, then it will depend on the 2 numbers encapsulating them.