This GMAT quant practice question is a problem solving question in Descriptive Statistics. Concept: Compute the average for a set and parts of the set to determine the value of one element of the set. An easy to medium level difficulty question.

#### Question: The average wages of a worker during a fortnight comprising 15 consecutive working days was $90 per day. During the first 7 days, his average wages was $87/day and the average wages during the last 7 days was $92 /day. What was his wage on the 8^{th} day?

- $83
- $92
- $90
- $97
- $104

#### Explanatory Answer

Video explanation provided for this questionFill in the data given in the question in the standard framework as shown below. Most questions in averages can be solved by completing this standard framework. The sum of wages is computed as the product of the number of days and the average wage earned per day.

Description | Number of days | Average Wages | Sum |
---|---|---|---|

All 15 days | 15 | $90 | $1350 |

First 7 days | 7 | $87 | $609 |

Last 7 days | 7 | $92 | $644 |

14 days excluding 8th day | 609 + 644 = $1253 | ||

8th day wage = Wages for all 15 - wages for 14 days excl 8th day | 1350 - 1253 = $97 |

The total wages earned during the 15 days that the worker worked = 15 * 90 = $ 1350.

The total wages earned during the first 7 days = 7 * 87 = $ 609.

The total wages earned during the last 7 days = 7 * 92 = $ 644.

Total wages earned during the 15 days = wages during first 7 days + wage on 8^{th} day + wages during the last 7 days.

Or 1350 = 609 + wage on 8^{th} day + 644

Wage on 8^{th} day = 1350 - 609 - 644 = $ 97.

Choice D is the correct answer.

#### Video Explanation

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