In 2009, an individual placed a total of $26,000 in 23 different inves

given
total investment 2009 ; 26000 $
are two new investment made avg ; 1200 i.e total 30,000
#1
Each investment added in 2010 contained more than $1,000.
may or may not be possible insufficient
#2
Each investment added in 2010 contained less than $1,500
so definately no answer to Is the average (arithmetic mean) number of dollars of the amount placed in investments per investment for all 25 investments less than $1,200?

IMO B sufficient

Official Explanation

If we call the amount of new investment x (that's for both new investments), then we want to know if $26,000+x is small enough for the average to be less than $1,200. After the addition, there are 25 investments, so the average formula gives us the following as the question we are being asked:

(26,000 + x)/25 <1,200
x < 4,000

In other words, if the total amount of the two new investments is less than $4,000, the answer to the question is "yes," and otherwise it's "no." Let's turn to the data statements, separately first.

Statement (1) tells us that each new investment was more than $1,000. Case I: each investment was $1,500. The total of the two is $3,000, which is less than $4,000, so the answer to the question is "yes." Case II: each investment was $10,000. This is a legal case, by the data statement, and generates an opposite answer, so Statement (1) is insufficient.

Statement (2) tells us that each new investment was less than $1,500. That means their sum is less than $3,000, which means that their sum is less than $4,000. So the answer to the question is definitively "yes," and Statement (2) is sufficient.

The correct answer is (B).

Video Explanation