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Example 6. Is the sum of six consecutive integers even?

1. The first integer is odd
2. The average of six integers is odd
Watch out for Yes/No data sufficiency questions; they are the hardest and the most misleading.
Example 6: The answer to this one is D. (1) Statement says that the sum of the integers is odd, which gives a NO answer to our question, but is SUFFICIENT to give an answer, therefore sufficient. (2) Says that the sum is odd, which is sufficient to give a Yes answer. In both cases it was sufficient to answer the question, except in the first case, the answer was NO and in the other, it was YES. Make sure you don't confuse No with insufficient because they are not related here.

(1) appears to be sufficient; however, I can't find an example of (2 -The average of six integers is odd) even existing. Thoughts? Also do people know if in general with DS questions if (1) and (2) can both have distinct answers and still be sufficient? Thanks

Example 6. Is the sum of six consecutive integers even?

1. The first integer is odd 2. The average of six integers is odd Watch out for Yes/No data sufficiency questions; they are the hardest and the most misleading. Example 6: The answer to this one is D. (1) Statement says that the sum of the integers is odd, which gives a NO answer to our question, but is SUFFICIENT to give an answer, therefore sufficient. (2) Says that the sum is odd, which is sufficient to give a Yes answer. In both cases it was sufficient to answer the question, except in the first case, the answer was NO and in the other, it was YES. Make sure you don't confuse No with insufficient because they are not related here.

(1) appears to be sufficient; however, I can't find an example of (2 -The average of six integers is odd) even existing. Thoughts? Also do people know if in general with DS questions if (1) and (2) can both have distinct answers and still be sufficient? Thanks

Let me start this one off.

My answer is A. However,

Just from the question stem, by definition we know that the sum of 6 consecutive integers will always be odd

So I am not sure how to use the 2 statements since the question stem itself tells us the sum will never be Even

St: 1
First integer is Odd. So,

O+E+O+E+O+E --->O+E is always Odd so the sum is Always Odd.

So I guess it is suff.

We can also try pluggin in value -2, -1, 0, 1, 2, 3 etc.

St.2

Average of 6 consecutive integers is Odd.

We know,

Sum/6 = Odd----> which means Sum = 6*Odd---> Even,

However,

The sum can never be Even. Try plugging in values.

Also the average will never be a integer will be a fraction which when rounded up will be either Odd or Even

For some reason I believe that there is something wrong with the question at least with St.2

B/c we determine from the stem itself that the sum will always be Odd.

Re: Question on DS help page, Example 6 [#permalink]
14 Jun 2006, 08:44

Alanjackson wrote:

Example 6. Is the sum of six consecutive integers even?

1. The first integer is odd 2. The average of six integers is odd

Example 6: The answer to this one is D.

(1) Statement says that the sum of the integers is odd, which gives a NO answer to our question, but is SUFFICIENT to give an answer, therefore sufficient. (2) Says that the sum is odd, which is sufficient to give a Yes answer. In both cases it was sufficient to answer the question, except in the first case, the answer was NO and in the other, it was YES. Make sure you don't confuse No with insufficient because they are not related here.

It appears that (2) is not possible; however if it were some how possible, it would be sufficient. Is that what you all are thinking? Thanks

st 2 alone is perfectly ok, nothing wrong, and is possible. . but if we combine 1 and 2 with the information given in the question, 1 and 2 donot go togather.

st 2 means, sum of 6 consecutive integers is 6 times the average (the avg. could be 1 or 3 or 5 or 7 or so on). from 2, the total is even where as from 1 the total is odd.