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gmattest001 Junior | Next Rank: 30 Posts
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Thu Dec 20, 2012 6:58 am
hmgp22 wrote:
I keep running out of time for those questions that usually require testing out values and seeing whether expressions is correct.

For example:

a, b, and c are integers in the set { a, b , c, 51, 85 ,72 } Is the median of the set greater than 80?

1. b > c> 69
2. a< c< 71

Is there a more efficient way to solve these types of problems besides just testing different values?
In my opinion because in these type of question we need to think of those number those make then false as soon as possible....
say i want to test
By using 1.
let me take c=70 and b=71

then place it in order for median 51,70,71,72,85,a
here a can be anything because any information is not provide for that.

so its assume it max then all the number so our median is (71+72)/2 =71.5

so ouranswer is no...

Go for second option.....

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ceilidh.erickson GMAT Instructor
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Fri Jan 25, 2013 10:41 am
Maybe this will help - whenever you're testing values on DS, have this goal in mind: "let me pick some values that will give me a YES answer, then some that will give me a NO answer." This way, you're thinking about extremes, and not just testing randomly.

(1) b > c > 69

So let's think about extremes - what are the smallest possible values of b and c? 71 and 70. If that's the case, our set is (rearranged in order except for a): [a, 51, 70, 71, 72, 85]. Here, it doesn't matter what a is; the median has to be between 70 and 72. This would give us a NO answer.

So can we come up with a YES answer? What would the opposite extreme be? We just know that b and c are greater than 69, so there's no limit to how big they could be! We could say c = 1000, b = 1001, and a = 1002. In that case, our set would be: [51, 72, 85, 1000, 1001, 1002]. Clearly the median is way bigger than 80, so we get a YES answer.

If we have a YES and a NO, it's insufficient.

(2) a < c < 71

Let's think of extremes again. What are the smallest possible values? Let's say a = 1, b = 2, and c = 3. Our set is [1, 2, 3, 51, 72, 85]. Clearly the median is less than 80, so we get a NO.

What are the largest possible values? The largest that c can be is 70, and the largest 1 can be is 69. There are no restrictions on b, so we can say b = 1000. Our set is [51, 69, 70, 72, 85, 1000]. Here, even with a and c at their highest, the median is still only 71. We can't find any values where the median is greater than 80. This is SUFFICIENT.

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HerrGrau Senior | Next Rank: 100 Posts
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Wed Jan 30, 2013 9:31 am
Hi,

With many data sufficiency questions there are an infinite amount of possibilities for testing numbers. But, just as everyone else said: Test the extremes

The concept of Limits/Extremes/Max/Min is all over the GMAT in PS and DS. Learning how to think in terms of the extremes of the question is an invaluable skill.

HG.

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