Over / Under the Average

Targeted practice (explanations below):  

1. For the past n days, the average (arithmetic mean) daily production at a company was 19 units. If today’s production of 57 units raises the average to 21 units per day, what is the value of n ?

2. For the past 16 days, the average (arithmetic mean) daily production at a company was 24 units. If today’s production raises the average to 27 units per day, how many units were produced today?

3. Jeanie scored 55, 47, and 63 on her first three exams. What’s the minimum score she will need on her fourth exam to obtain an average (arithmetic mean) score of at least 58?

4. The average (arithmetic mean) a, b, c, d is c, and c – a = 12 and c – b = 9, what is d in terms of c?

Official Guide practice (find these in your Official Guide or at www.gmatclub.com) 

PS10002  During a trip that they took together, Carmen,

PS04571 If the average (arithmetic mean) of the four numbers together,

PS07369 Over the past 7 weeks, the Smith family

DS12239 A certain list consists of 3 different numbers

DS02706 If x, y, and z are positive numbers

DS69502.01 Is the average (arithmetic mean) of the numbers x, y, and z

Creative practice

1. Take one of the problems above and change the numbers. Work out the new answer.
2. Write a new problem that uses the concept of over / under the average.

Explanations

1. 18 The average of all the days is 21; today’s production of 57 is 36 higher than that average. The 36 over the average. The initial days are each 2 under the average, meaning that we need 36/2 = 18 days to balance things out.
2. 75 The 16 initial days are each 27-24=3 under the average, meaning that we have a total of 48 under the average. This is balanced out by today’s production, which must be 48 over the average. We need to add this to the average of 27.  Take care not to fall into the trap of answering 48+24 = 72; the 24 was the initial average that doesn’t include today’s production.
3. 67 If the average score is 58, then her initial scores were 58-55 = 3 under the average, 58-47 = 11 under the average, and 63-58 = 5 over the average. That makes a total of 9 under the average. The fourth exam must balance this by being 9 over the average,e. 58+9 = 67
4. c+21 Don’t be fooled by the algebra here. Turn ‘c-a=12’ into words: it’s saying that ‘c is 12 bigger than a’, so that a is 12 under the average. Likewise, b is 9 under the average. Consequently, d must be 21 over the average.