Is the average of ten integers greater than 10?
(1) Half of the integers are greater than 10.
(2) Half of the integers are less than 10.
What's the best way to determine whether statement 1 is sufficient? Can any experts help?
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Is the average of ten integers greater than 10?
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If the average of 10 integers = 10, then the SUM of the 10 integers = (number of integers)(average of the integers) = 10*10 = 100.ardz24 wrote:Is the average of ten integers greater than 10?
(1) Half of the integers are greater than 10.
(2) Half of the integers are less than 10
Implication:
For the average of the 10 integers to be GREATER THAN 10, the sum of the 10 integers must be GREATER THAN 100.
Question stem, rephrased:
Is the sum of the 10 integers greater than 100?
Both statements are satisfied by the following cases:
Case 1: 0, 0, 0, 0, 0, 11, 11, 11, 11, 11
Case 2: 0, 0, 0, 0, 0, 100, 100, 100, 100, 100
In Case 1, the sum of the 10 integers is less than 100, so the answer to the rephrased question stem is NO.
In Case 2, the sum of the 10 integers is greater than 100, so the answer to the rephrased question stem is YES.
Since the answer is NO in Case 1 but YES in Case 2, the two statements combined are INSUFFICIENT.
The correct answer is E.
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Statement One Alone:ardz24 wrote:Is the average of ten integers greater than 10?
(1) Half of the integers are greater than 10.
(2) Half of the integers are less than 10.
Half of the integers are greater than 10.
Although we know that 5 of the 10 integers are greater than 10, we do not know anything regarding the 5 other integers. Therefore we cannot determine whether the average is greater or less than 10. Statement one alone is not sufficient to answer the question.
Statement Two Alone:
Although we know that 5 of the 10 integers are less than 10, we do not know anything regarding the 5 other integers. Therefore, we cannot determine whether the average is greater or less than 10. Statement two alone is not sufficient to answer the question.
Statements One and Two Together:
Logically using the information from both statements, we see that we still cannot determine whether the average is greater or less than 10. We do not know how far above 10 the 5 integers are or how far below 10 the other 5 integers are. Thus, it's possible to get an average that is greater than 10, equal to 10, or less than 10.
Answer: E
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