Director
Joined: 26 Oct 2016
Posts: 510
Location: United States
Concentration: Marketing, International Business
GPA: 4
WE:Education (Education)
Re: The average of 6 numbers in a set is equal to 0. What is the
[#permalink]
01 Mar 2017, 17:20
Since the average of the 6 numbers in a set is 0, the sum of the 6 numbers is 0. We also know there could be positive numbers and negative numbers in the set. Zero is not mentioned, but this does not rule it out. In order for the sum of the numbers in the set to be 0, either all the terms are 0, or there are some positives and some negatives.
(1) INSUFFICIENT: Statement 1 tells us that the set has at least one positive number, and that each positive term is 10. We should try to prove insufficiency. For instance, the set could be {–2, –2, –2, –2, –2, 10}, and the number of positive terms minus the number of negative terms would be 1 – 5 = –4. Alternatively, the set could be {–20, –20, 10, 10, 10, 10}, and the answer would be 4 – 2 = 2.
(2) INSUFFICIENT: Statement 2 tells us that the set has at least one negative number, and that each negative term is –5. Again, we should try to prove insufficiency. The set could be {–5, 1, 1, 1, 1, 1}, and the number of positive terms minus the number of negative terms would be 5 – 1 = 4. The set could be {–5, –5, –5, 2, 5, 8}, and the answer would be 3 – 3 = 0.
(1) & (2) INSUFFICIENT: The statements together suggest that the set has twice as many –5 terms as 10 terms, in order to maintain a sum of 0. If every term is negative or positive, then the set would have to be {–5, –5, –5, –5, 10, 10} and the definitive answer would be 2 – 4 = –2. However, zero terms are possible, so the set could be {–5, –5, 0, 0, 0, 10} and an alternative answer would be 1 – 2 = –1.
Hence E.