DS: ODD integers

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romitrock: Junior | Next Rank: 30 Posts; Posts: 12; Joined: Tue Dec 15, 2015 12:35 am

by romitrock » Sun Jan 17, 2016 7:31 am

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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Source: Beat The GMAT — Data Sufficiency | Sun Jan 17, 2016 7:31 am

GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Sun Jan 17, 2016 7:39 am

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

Statement 1: There are 12 even 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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romitrock: Junior | Next Rank: 30 Posts; Posts: 12; Joined: Tue Dec 15, 2015 12:35 am

by romitrock » Sun Jan 17, 2016 8:50 am

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.[/quote]

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Sun Jan 17, 2016 9:51 am

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.

Statement 1: There are 12 even integers greater than x and less than y.
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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romitrock: Junior | Next Rank: 30 Posts; Posts: 12; Joined: Tue Dec 15, 2015 12:35 am

by romitrock » Mon Jan 18, 2016 11:20 am

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.

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