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is the mean even

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Source: — Data Sufficiency |

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by Brent@GMATPrepNow » Thu Jul 23, 2015 8:05 am
j_shreyans wrote:For a set X containing n integers, is the mean even?

(1) n is even.
(2) All of the integers in set X are even.
Target question: Is the mean even?

Statement 1: n is even.
This statement doesn't FEEL sufficient, so I'm going to TEST some values.
There are several sets that satisfy statement 1. Here are two:
Case a: the numbers are {12, 12}. Here, n is even, and the mean = 12, which is EVEN
Case b: the numbers are {10, 12}. Here, n is even, and the mean = 11, which is ODD
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Aside: For more on this idea of plugging in values when a statement doesn't feel sufficient, you can read my article: https://www.gmatprepnow.com/articles/dat ... lug-values

Statement 2: All of the integers in set X are even.
This statement doesn't FEEL sufficient either, so I'm going to TEST some values.
There are several sets that satisfy statement 1. Here are two:
Case a: the numbers are {12, 12}. Here, all of the integers are even and the mean = 12, which is EVEN
Case b: the numbers are {10, 12}. Here, all of the integers are even and the mean = 11, which is ODD
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Combined, we still get the same two cases:
Case a: the numbers are {12, 12}. Here n is even AND all of the integers are even. In this case, the mean = 12, which is EVEN
Case b: the numbers are {10, 12}. Here n is even AND all of the integers are even. In this case, the mean = 11, which is ODD
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer = E

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Brent
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by DavidG@VeritasPrep » Thu Jul 23, 2015 8:06 am
For a set X containing n integers, is the mean even?

(1) n is even.

(2) All of the integers in set X are even.
Let's pick some simple numbers. For statement 1, we know n is even, so let's say n = 2, and we have two numbers in the set.
Set 1: {2, 4} mean = 3. Mean is not even, so the answer is NO
Set 2: {2, 10} mean = 6. Mean is even, so answer is YES
Not Sufficient.

Statement 2. Well, if all the integers are even, we can reuse both sets above. Not sufficient.

Together: we've already proven that we can get a YES and a NO if there are an even number of elements and every element in the set is even. So together they are not sufficient. Answer is E
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by Max@Math Revolution » Fri Jul 31, 2015 11:35 am
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 equations ensures a solution.

In original condition, we have many variables (n integers) because it is hard to match the number of equations so E is likely to be the answer. Let me prove. In (1) and (2), if 2,2, (2+2)/2=2 Yes, but if 2,4, (2+4)/2=3 No. Not sufficient. E is the answer.

Why E? If you know our own innovative logics to find the answer, you don't need to actually solve the problem.

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by nikhilgmat31 » Wed Aug 05, 2015 1:05 am
it is a great question. misleaded to get answer B earlier.

Great numbers picks by Brent.
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by GMATGuruNY » Wed Aug 05, 2015 2:12 am
j_shreyans wrote:For a set X containing n integers, is the mean even?

(1) n is even.

(2) All of the integers in set X are even.
Statements combined:
If n=2 -- implying that X contains 2 even integers -- then the integers in X can be represented as n and n + 2a, where n is an even integer and a is an integer.
Average of the 2 integers = sum/number = (n + n + 2a)/2 = (2n + 2a)/2 = n + a.
Implication:
If a is EVEN, then the average = n + a = EVEN + EVEN = EVEN, in which case the answer to the question stem is YES.
If a is ODD, then the average = n + a = EVEN + ODD = ODD, in which case the answer to the question stem is NO.
INSUFFICIENT.

The correct answer is E.
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by Max@Math Revolution » Thu Aug 20, 2015 9:06 am
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 equations ensures a solution.



In original condition, we have many variables (n integers) so E is likely to be the answer. Let me prove.


In (1) and (2), if 2,2, (2+2)/2=2 Yes, but if 2,4, (2+4)/2=3 No. Not sufficient. E is the answer.


If you know our own innovative logics to find the answer, you don't need to actually solve the problem.

www.mathrevolution.com

- The one-and-only World's First Variable Approach for DS and IVY Approach for PS that allow anyone to easily solve GMAT math questions.

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