Data Sufficiency

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.

Statement 1: a - 3 < a + 2 < a + 5
Hence, median of (a + 2), (a - 3), and (a + 5) is a + 2.
So, a + 2 = 14
--> a = 12

But don't know anything about b.

Not sufficient

Statement 2: Mode of a set of data is the value that appears most often that set.
As the only mode of a, b, and 14 is 14, exactly on of a and b must be 14.

Not sufficient

1 & 2 Together: As a = 12, b must be equal to 14.

Sufficient

The correct answer is C.

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