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If the average (arithmetic mean) of 13, 17, x, 12 and 16 is greater than 15, which of the following must be true?

I. x is the median of the numbers

II. x is equal to 15

III. x is greater than the average of the numbers

Paleontologists in 1947 found a large group of fossilized skeletons of the carnivorous dinosaur Coelophysis. In the space where one Coelophysis's stomach had been, there were bones from another individual of the same species. The paleontologists concluded from this that Coelophysis was cannibalistic.

In order to evaluate the strength of the paleontologists’s argument, it would be most helpful to know which of the following?

The table lists 12-pack prices for Aquaphino Water sold in 39 US UDS Stores ("Up and Down the Street" stores) across 5 major cities on May 25, 2012. Store types are categorized as Grocers, Gas Stations, or C-Store (convenience store).

For each of the following statements, select Yes if the statement is true based solely on the information reported for the Accounts on this day. Otherwise, select No.

The average (arithmetic mean) of 5 distinct, single digit integers is 5. If two of the integers are discarded, the new average is 4. What is the greatest of these integers?

(1) Exactly 3 of the integers are consecutive primes.

(2) The least integer is 3.

 ­If the value of is positive, which of the following ranges represents the value of k?