Problem Solving

Question 1

The numbers of cars sold at a certain dealership on six of the last seven business days were 4, 7, 2, 8, 3, and 6, respectively. If the number of cars sold on the seventh business day was either 2, 4, or 5, for which of the three values does the average (arithmetic mean) number of cars sold per business day for the seven business days equal the median number of cars sold per day for the seven days?

I. 2
II. 4
III. 5

(A) II only 
(B) III only 
(C) I and II only 
(D) II and III only 
(E) I, II, and III

Answer 1

The correct answer is B.

Listed in numerical order, the given numbers are 2, 3, 4, 6, 7, and 8.

If the seventh number were 2 or 4, then the numbers in numerical order would be 2, 2, 3, 4, 6, 7, and 8 or 2, 3, 4, 4, 6, 7, and 8. In either case the median would be 4 and the average would be 32/7 or 34/7, neither of which equals 4. So, for neither of the values in I or II does the average equal the median.

If the seventh number were 5, then the numbers in numerical order would be 2, 3, 4, 5, 6, 7, and 8. The median would be 5 and the average would be . Thus, for the value in III, the average equals the median.

Question 2

On Monday, a person mailed 8 packages weighing an average (arithmetic mean) of (12+3/8) pounds, and on Tuesday, 4 packages weighing an average of (15+1/4) pounds. What was the average weight, in pounds, of all the packages the person mailed on both days?

(A) 13+1/3
(B) 13+13/16
(C) 15+1/2
(D) 15+15/16
(E) 16+1/2

Answer 2

The correct answer is A.

Since Average = Sum / No., the information about the two shipments of packages can be expressed as average:

{8(12+3/8) + 4(15+1/4)} / 12 = 13+1/3

Question 3

A student’s average (arithmetic mean) test score on 4 tests is 78. What must be the student’s score on a 5th test for the student’s average score on the 5 tests to be 80?

(A) 80 
(B) 82 
(C) 84 
(D) 86 
(E) 88

Answer 3

The correct answer is E.

The average of the student’s first 4 test scores is 78, so the sum of the first 4 test scores is 312.

If x represents the fifth test score, then the sum of all 5 test scores is and the average of all 5 test scores is (312+x). But the average of all 5 test scores is 80, so:

(312+x)/5 = 80

Solving this, we get x = 88