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

Question

In 2009, an individual placed a total of $26,000 in 23 different investments. In 2010, that individual placed further funds in two new investments. Is the average (arithmetic mean) number of dollars of the amount placed in investments per investment for all 25 investments less than $1,200?

(1) Each investment added in 2010 contained more than $1,000.

(2) Each investment added in 2010 contained less than $1,500.

(1) Each investment added in 2010 contained more than $1,000.

(2) Each investment added in 2010 contained less than $1,500.

himani2093 · Answer

Total Investment before- $26,000/23 
Now 2 new investments increased or decreased, depends on the new investment values.
1. Each investment added in 2010 contained more than $1,000
If it contained more than 1000 then, at least 2000/25 is added to original average. Sufficient
2. Less than 1500 can be anything. It could have brought down avg to less than 1200. So NS
Answer is B

lacktutor · Answer

\frac{(26000+x)}{25} <1200???

Statement1:  
Let's say that at least each investment contained $1500 
-->  \frac{(26000+3000)}{25} = \frac{29000}{25} =1160 (yes)

-->if each investment contained $2000, then  \frac{(26000+4000)}{25} = \frac{30000}{25} =1200 (no)

Insufficient

Statement2 : If we consider $1500 the maximum amount of investment in 2010, then 
-->  \frac{(26000+3000)}{25} = \frac{29000}{25} =1160 (YES)
Also, any amount of investment less than $1500 satisfies the question and Always will be YES
 Sufficient

The answer is B.

Archit3110 · Answer

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

Bunuel · Answer

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).

Bunuel · Answer

Video Explanation

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

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