Test: Mean - GMAT MCQ

A 200% increase over 2,000 products per month would be 6,000 products per month.  (Recall that 100% = 2,000, 200% = 4,000, and "200% over" means 4,000 + 2,000 = 6,000.) In order to average 6,000 products per month over the 4 year period from 2005 through 2008, the company would need to produce 6,000 products per month × 12 months × 4 years = 288,000 total products during that period. We are told that during 2005 the company averaged 2,000 products per month. Thus, it produced 2,000 × 12 = 24,000 products during 2005. This means that from 2006 to 2008, the company will need to produce an additional 264,000 products (288,000 – 24,000). The correct answer is D.

We can simplify this problem by using variables instead of numbers. x = 54,820, 
    x + 2 = 54,822. The average of (54,820)² and (54,822)² = 


= x²+2x+2

Now, factor x² + 2x +2. This equals x² + 2x +1 + 1, which equals (x + 1)² + 1.
Substitute our original number back in for x as follows:
(x + 1)² + 1 = (54,820 + 1)² + 1 = (54,821)² + 1.

  The correct answer is D.
 

First, let’s use the average formula to find the current mean of set S: Current mean of set S = (sum of the terms)/(number of terms): (sum of the terms) = (7 + 8 + 10 + 12 + 13) = 50    (number of terms) = 5    50/5 = 10     
Mean of set S after integer n is added = 10 × 1.2 = 12         Next, we can use the new average to find the sum of the elements in the new set and compute the value of integer n. Just make sure that you remember that after integer n is added to the set, it will contain 6 rather than 5 elements.     Sum of all elements in the new set = (average) × (number of terms) = 12 × 6 = 72     Value of integer n = sum of all elements in the new set – sum of all elements in the original set = 72 – 50 = 22     The correct answer is D. 

Let x = the number of 20 oz. bottles     48 – x = the number of 40 oz. bottles     The average volume of the 48 bottles in stock can be calculated as a weighted average: 

Therefore there are 12 twenty oz. bottles and 48 – 12 = 36 forty oz. bottles in stock. If no twenty oz. bottles are to be sold, we can calculate the number of forty oz. bottles it would take to yield an average volume of 25 oz: 
Let n = number of 40 oz. bottles 

(12)(20) + 40n = 25n + (12)(25) 
15n = (12)(25) – (12)(20)
 15n = (12)(25 – 20) 
15n = (12)(5) 
15n = 60 
n = 4 
Since it would take 4  forty oz. bottles along with 12 twenty oz. bottles to yield an average volume of 25 oz, 36 – 4 = 32 forty oz. bottles must be sold. The correct answer is D.