Q: How many odd integers are greater than integer x and less than integer y?
st1: there are 12 even integers between x and y.
st2: there are 24 integers between x and y.
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DS: ODD integers
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Statement 1: There are 12 even integers greater than x and less than y.How many odd integers are greater than 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
Let the 12 consecutive even integers greater than x and less than y be the following:
0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22.
Here, x<0 and y>22.
If x=-1 and y=23, then every odd integer between 1 and 21, inclusive, will be greater than x and less than y, for a total of 11 odd integers.
If x=-1 and y=24, then every odd integer between 1 and 23, inclusive, will be greater than x and less than y, for a total of 12 odd integers.
INSUFFICIENT.
Statement 2: There are 24 integers greater than x and less than y.
EXACTLY HALF of these 24 consecutive integers must be odd.
Thus, the number of odd integers greater than x and less than y = 12.
SUFFICIENT.
The correct answer is B.
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Statement 1: There are 12 even integers greater than x and less than y.romitrock wrote:yes Mitch i agree with this solution, but in the actual question they havent anything about the integers being consecutive.
that is why i posted this.
this is a question from the Gmat prep practice test 1.
If we select 12 NON-consecutive even integers to place between x and y, then there will be MORE THAN 12 even integers greater than x and less then y.
Consider the following case:
0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 24.
Here, the 12 even integers are consecutive except for the last two.
If x=-1 and y=25, then the following even integers will be greater than x and less than y:
0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24.
The result is 13 even integers between x and y.
Implication:
For statement 1 to be satisfied, the 12 even integers selected MUST be consecutive.
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THANKS Mitch,
i had the impression that if we have to choose 12 even integers between x and y, we can choose infinite no. of integers depending on the values of x and y , if the nos. are not to be consecutive.
so in a way it is implied that the integers should be consecutive.
so it was a trick kind of thing in the question which needs to be identified.
I thought it isn't mentioned in the question so i should not consider it on my own.
i had the impression that if we have to choose 12 even integers between x and y, we can choose infinite no. of integers depending on the values of x and y , if the nos. are not to be consecutive.
so in a way it is implied that the integers should be consecutive.
so it was a trick kind of thing in the question which needs to be identified.
I thought it isn't mentioned in the question so i should not consider it on my own.
