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Integers x and y

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by Ashujain » Wed May 30, 2012 5:35 am
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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by aneesh.kg » Wed May 30, 2012 6:17 am
Ashujain 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
I will try to solve this by plugging-in numbers.

Statement(1):
If the 12 even integers are 2, 4, .. 24 then x = {0,1} and y = {25, 26}.
But the number of odd integers greater than x and less than y are 13, 12, 12, 11 for (0,26), (1,26),(0,25), (1,25) respectively.
INSUFFICIENT

Statement(2):
Let me plug-in a even integer value for x and then an odd integer value for x.
If x = 0, then y = 25 and if x = 1, then y = 26.
In both the cases the number of odd integers greater than x and smaller than y is the same(= 12). This will hold true for all values of x and y because is x is an even integer then y is an odd integer and vice-versa.
SUFFICIENT

[spoiler](B)[/spoiler] is the answer.

P.S.: You should be good at calculating/counting the number of consecutive even/odd integers to solve this problem quickly.
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by shrutib » Wed May 30, 2012 7:27 am
I did not understand the answer. The question stem never mentioned that the integers are consecutive. can we still assume it? Please explain.
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by aneesh.kg » Wed May 30, 2012 7:37 am
shrutib wrote:I did not understand the answer. The question stem never mentioned that the integers are consecutive. can we still assume it? Please explain.
Hi Shruti,

What are the integers are between 1 and 10?
2, 3, 4, 5, 6, 7, 8 and 9.

Do we have to bother about the word 'consecutive' being mentioned or not?
No. If the question is asking us about the integers between two numbers, the question is asking us about ALL THE INTEGERS between those two numbers. We can't leave out any of the integers that are between those numbers, can we? And, since all those integers are consecutive, the question does not have to mention the word 'consecutive'.

Even if the question wants us to consider the even integers or the odd integers between two numbers, the question might just say: How many odd integers are there between 7 and 35? or How many even integers are there between 7 and 35? because we have to consider ALL THE INTEGERS satisfying the criteria.

Does that help?
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by GMAT Kolaveri » Wed May 30, 2012 8:24 am
Ashujain 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
We need to find out how many integers are there between X and Y (The variables are explicitly stated as Integers)
why is this check important?
Case 1(integers):X and Y are integers 3 and 5 respectively, the number of integers between 3 and 5 is 1 (that is only 4 lies btw 3 and 5)
Case 2 (non integers): X =3.5 and y=5.5 , the number of integers btw 3.5 and 5.5 is 2 ( that is 4,5 )

Takeaway: Never assume the variables to be integers unless it is explicitly stated in the question. This is one of the GMAT Traps.

Now returning to the problem,
A good practice in DS question is to gauge both the statements and then deciding which flow ( AD/BCE or BD/ACE ) to use.

Looking at both the options it is pretty clear that B answers the question.
So start with BD/ACE flow,
B is sufficient. It gives us the number of integers btw X and Y. Hence ACE is out.
Now checking S1, pick a small number range.
1,2,3,4,5 - Number of even integers = 2 Number of integers = 3
1,2,3,4,5,6 - Number of even integers = 2 Number of integers = 4
Hence S1 is insufficient. D is out. We are left with B[/list]
Regards and Thanks,
Vinoth@GMAT Kolaveri
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Click the thank you button if you like my reply :)
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by 1947 » Wed May 30, 2012 10:04 am
learning here is that in any even set of consecutive numbers no. of even and odd numbers are same.

and in a set of odd numbers ...the count of even and odd numbers will vary.
If my post helped you- let me know by pushing the thanks button. Thanks
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by karthikgmat » Thu Jun 07, 2012 9:57 pm
How do you all think when "There are 24 integers greater than x and less than y" mean x , x+ 1 , x+2 ... x+22 , y

Why it can't be x x+2 x+4 and so on (24 integers).. Y?

As per me answer should be E
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by Stuart@KaplanGMAT » Thu Jun 07, 2012 10:09 pm
karthikgmat wrote:How do you all think when "There are 24 integers greater than x and less than y" mean x , x+ 1 , x+2 ... x+22 , y

Why it can't be x x+2 x+4 and so on (24 integers).. Y?

As per me answer should be E
Hi!

If x+2 and x+4 are between x and y, won't x+1 and x+3 be between them as well?

You're misinterpreting statement (2) as:
x and y are both integers in a set and there are 24 other integers in the set between x and y.
when in fact statement (2) simply tells us that there ARE 24 integers between x and y... period.

The only way this statement can be be true is if y = x + 25 (since the integers between them are x+1, x+2, ..., x+24).
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by karthikgmat » Sun Jun 10, 2012 10:24 am
Thanks Stuart for your reply.. But, I'm still puzzled as per statement 2 why should we interpret it as : between x and y there are 24 consecutive integers?
Stuart Kovinsky wrote:
karthikgmat wrote:How do you all think when "There are 24 integers greater than x and less than y" mean x , x+ 1 , x+2 ... x+22 , y

Why it can't be x x+2 x+4 and so on (24 integers).. Y?

As per me answer should be E
Hi!

If x+2 and x+4 are between x and y, won't x+1 and x+3 be between them as well?

You're misinterpreting statement (2) as:
x and y are both integers in a set and there are 24 other integers in the set between x and y.
when in fact statement (2) simply tells us that there ARE 24 integers between x and y... period.

The only way this statement can be be true is if y = x + 25 (since the integers between them are x+1, x+2, ..., x+24).
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