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The average wages of a worker during a fortnight...

This topic has 2 expert replies and 0 member replies

The average wages of a worker during a fortnight...

Post Fri Nov 10, 2017 9:48 am
The average wages of a worker during a fortnight comprising 15 consecutives working days was $90 per day. During the first 7 days, his average wages was $87 per day and the average wages during the last 7 days was $92 per day. What was his wage on the 8th day?

A. $83
B. $90
C. $92
D. $97
E. $104

The OA is D.

Please, can any expert explain this PS question for me? I have many difficulties to understand why that is the correct answer. Thanks.

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GMAT/MBA Expert

Post Fri Nov 10, 2017 11:18 am
Hi swerve,

We're told that the average pay a worker received for 15 consecutives working days was $90 per day. During the first 7 days, his average wages was $87 per day and the average wages during the last 7 days was $92 per day. We're asked for his wage on the 8th day.

There are a number of different ways to approach the 'math' in this question. Here's an approach that allows you to avoid a lot of 'step-heavy' math and focus on the 'relationships' between the numbers.

Since the average pay was $90/day, we can track how much 'below average' or 'above average' the individual days are...
-For the first 7 days, the average pay was $87/day, thus each of those days was $3 BELOW the average... meaning that we're (7)($3) = $21 'below' in total here.
-For the last 7 days, the average pay was $92/day, thus each of those days was $2 ABOVE the average... meaning that we're (7)($2) = $14 'above' in total here.

With those 14 days, we're a total of '$7 below' what the average is supposed to be, so that final day (the 8th day) has to make up for that difference...

8th day = $90 + $7 = $97

Final Answer: D

GMAT assassins aren't born, they're made,
Rich

_________________
Contact Rich at Rich.C@empowergmat.com

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GMAT/MBA Expert

Post Fri Nov 10, 2017 1:01 pm
Quote:
The average wages of a worker during a fortnight comprising 15 consecutives working days was $90 per day. During the first 7 days, his average wages was $87 per day and the average wages during the last 7 days was $92 per day. What was his wage on the 8th day?

A. $83
B. $90
C. $92
D. $97
E. $104

The OA is D.

Please, can any expert explain this PS question for me? I have many difficulties to understand why that is the correct answer. Thanks.
Hi Swerve,
Let's take a look at your question.

The wages of a worker during a fortnight comprising 15 consecutive working days = $90 per day
We know that,
$$Average\ \ =\ \frac{Sum}{Days}$$
$$Sum\ =\ Average\ \times\ Days$$
$$Sum\ =\ 90\ \times15\ =\ 1350$$
Therefore,
Sum of wages of 15 days = $1350

Next the question states that During the first 7 days, his average wages was $87 per day.
Again using the average formula, we will find the sum of wages of first 7 days.
$$Average\ \ =\ \frac{Sum}{Days}$$
$$Sum\ =\ Average\ \times\ Days$$
$$Sum\ =\ 87\ \times7\ =\ 609$$
Therefore,
Sum of wages of first 7 days = $609

Next the question states that he average wages during the last 7 days was $92 per day.
Again using the average formula, we will find the sum of wages of last 7 days.
$$Average\ \ =\ \frac{Sum}{Days}$$
$$Sum\ =\ Average\ \times\ Days$$
$$Sum\ =\ 92\ \times7\ =\ 644$$
Therefore,
Sum of wages of last 7 days = $644

We need to find the wage on 8th day.
We know that,
Sum of wages of first 7 days + Wage on 8th day + Sum of wages of last 7 days = Sum of wages of 15 days
Plugin in all the known wages we calculated above,
609 + Wage on 8th day + 644 = 1350
Wage on 8th day + 609 + 644 = 1350
Wage on 8th day + 1253 = 1350
Wage on 8th day = 1350 - 1253
Wage on 8th day = 97
The wage on 8th day is $97.

Therefore, Option D is true.

Hope it helps.
I am available if you'd like any follow up.

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