psm12se wrote:Set A consist of 10 terms, each of which is a reciprocal of a prime number, is the median of the set less than 1/5?
(1) Reciprocal of the median is a prime number.
(2) The product of any two terms of the set is a terminating decimal.
Target question: Is the median of the set less than 1/5
Statement 1: The median of the numbers is 30
There are several possible sets that satisfy this condition. Here are two:
Case a: set A = {1/7, 1/7, 1/7,...1/7} in which case the median = 1/7,
so the median IS less than 1/5
Case b: set A = {1/2, 1/2, 1/2,...1/2} in which case the median = 1/2,
so the median is NOT less than 1/5
Since we cannot answer the
target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: The product of any two terms of the set is a terminating decimal
There's a nice rule that says something like this:
If a/b results in a terminating decimal, then the denominator, b, MUST be the product of 2's and 5's only!
So, for example, if b = 20, the fraction a/b will result in a terminating decimal. The same holds true for other values of b such as 4, 5, 25, 40, 2, 8, and so on.
So, statement 1 tells us that set A must consist of 1/2's and 1/5's ONLY.
Since set A has an EVEN number of terms, the median will be the AVERAGE of the two middlemost terms.
Since the terms must be 1/2's and 1/5's ONLY, there are only three possible cases.
case a: the two middlemost terms are 1/2 and 1/2, in which case the median is 1/2, which means
the median is NOT less than 1/5
case b: the two middlemost terms are 1/5 and 1/5, in which case the median is 1/5, which means
the median is NOT less than 1/5
case c: the two middlemost terms are 1/5 and 1/2, in which case the median is 7/20, which means
the median is NOT less than 1/5
In all three cases,
the median is NOT less than 1/5
Since we can answer the
target question with certainty, statement 2 is SUFFICIENT
Answer =
B
Cheers,
Brent
