The average (arithmetic mean) high temperature for x days is 70 degrees. The addition of one day with a high temperature of 75 degrees increases the average to 71 degrees. Quantity A : x Quantity B : 5
This is a Quant Comp question with variables, so Plug In more than once. To easily compare the two quantities, recycle the number in the problems by Plugging In x = 5. This problem involves averages, so draw an Average Pie. If x = 5, and the average high temperature over the course of 5 days is 70 degrees, then the total temperature for the 5 days is 5 × 70 = 350. The problem states that one additional day has a high temperature of 75 degrees, so draw another average pie. There are now six days and the total high temperature is 350 + 75 = 425 and the average high temperature for the six days is = . This is less than the 71 degree average specified in the problem. Because the two quantities cannot both equal 5, eliminate (C). If it is unclear whether the value for x needs to be greater or less than 5 to make the average high temperature at the end of the problem equal to 71 degrees, Plug In again. This time, try a number less than 5, such as x = 4. If x = 4, then the total temperature for 4 days with an average of 70 degrees is 4 × 70 = 280. The addition of one day with a high temperature of 75 degrees means that the total high temperature is 280 + 75 = 355 over the course of 5 days. Therefore, the average is = 71. Therefore, the correct value of x is 4 and so the value of Quantity A is 4. This is less than the value of Quantity B, so the correct answer is (B).