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.
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is the mean even
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j_shreyans
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Target question: Is the mean even?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.
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
Cheers,
Brent
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DavidG@VeritasPrep
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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.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.
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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Max@Math Revolution
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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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Regardless of your math skills, our world's first Variable Approach (DS) and IVY Approach (PS) help students dramatically reduce their time spent per question and improve accuracy. You will have 10 min. to spare before the test ends.
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.
www.mathrevolution.com
Regardless of your math skills, our world's first Variable Approach (DS) and IVY Approach (PS) help students dramatically reduce their time spent per question and improve accuracy. You will have 10 min. to spare before the test ends.
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nikhilgmat31
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GMATGuruNY
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Statements combined: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.
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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Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
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Max@Math Revolution
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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.
- The easy-to-use solutions. Math skills are totally irrelevant. Forget conventional ways of solving math questions.
- The most effective time management for GMAT math to date allowing you to solve 37 questions with 10 minutes to spare
- Hitting a score of 45 is very easy and points and 49-51 is also doable.
- Unlimited Access to over 120 free video lessons at https://www.mathrevolution.com/gmat/lesson
- Our advertising video at https://www.youtube.com/watch?v=R_Fki3_2vO8
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.
- The easy-to-use solutions. Math skills are totally irrelevant. Forget conventional ways of solving math questions.
- The most effective time management for GMAT math to date allowing you to solve 37 questions with 10 minutes to spare
- Hitting a score of 45 is very easy and points and 49-51 is also doable.
- Unlimited Access to over 120 free video lessons at https://www.mathrevolution.com/gmat/lesson
- Our advertising video at https://www.youtube.com/watch?v=R_Fki3_2vO8
