himu wrote:What is the average (arithmetic mean) of the numbers a & b ?
1.The median of a+2,a-3 & a+5 is 14.
2.The only mode of a,b & 14 is 14.
Target question:
What is the average of a and b?
Statement 1: The median of a+2,a-3 & a+5 is 14.
If we arrange these three values in ascending order we get a-3, a+2, a+5
So, the median is a+2
If the median is 14, then a+2 = 14, which means a = 12
Since we have no info about b,
we cannot determine the average of a and b
So, statement 1 is NOT SUFFICIENT
Statement 2: The only mode of a,b & 14 is 14
In other words, the 3 numbers are not all different (otherwise there would be 3 modes).
There are several pairs of values that meet this condition. Here are two:
Case a: a = 14 and b = 14, in which case
the average of a and b is 14
Case b: a = 14 and b = 2, in which case
the average of a and b is 8
Since we cannot answer the
target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined:
Statement 2 tells us that either a or b (or both) must equal 14 (so that the mode = 14)
Statement 1 tells us that a = 12
Since a does not equal 14, it must be the case that b = 14
Now that we know that a = 12 and b = 14, we can be
certain that
the average of a and b is 13
Since we can now answer the
target question with certainty, the combined statements are SUFFICIENT
Answer =
C
Cheers,
Brent
