Greg Assembles Units of a Certain Product at a Factory. GMAT Problem Solving

Question: Greg assembles units of a certain product at a factory. Each day he is paid $2.00 per unit for the first 40 units that he assembles and $2.50 for each additional unit that he assembles that day. If Greg assembled at least 30 units on each of two days and was paid a total of $180.00 for assembling units on the two days, what is the greatest possible number of units that he could have assembled on one of the two days?

1. 48
2. 52
3. 56
4. 60
5. 64

“Greg Assembles Units of a Certain Product at a Factory”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book "GMAT Official Guide Quantitative Review". To solve GMAT Problem Solving questions a student must have knowledge about a good number of qualitative skills. GMAT Quant section consists of 31 questions in total. The GMAT quant topics in the problem-solving part require calculative mathematical problems that should be solved with proper mathematical knowledge. 

Solution and Explanation:

Approach Solution 1:

The given condition states that the total pay for 2 days is $180.

We have to maximise the number of units assembled on one of the days to find the greatest possible units assembled by him. This can be done by minimising the number of units on day 2 is important.

It is given that Greg assembles 30 units each day so the minimum units is basically 30 on Day 1. This implies that, Payment for Day 1 is equal to

(30)($2) = $60

If Greg is paid $60 for Day 1, then he must have received $120 on Day 2 so that the total becomes $180.

If Greg was paid $120 on Day 2, we need to find the total number of units he assembled in Day 2.

However, it is given that Greg is paid $2.00 per unit for the first 40 units that he assembles and $2.50 for each additional unit

So, for the first 40 units, Greg is paid $80
This is implied from- 40 x $2 = 80

$120 - $80 = $40

So, the remaining $40 was paid to Greg for the additional units he assembled at a rate of $2.50/unit. This implies-

$40/$2.50 = 16 units

So, the TOTAL number of units assembled = 40 + 16 = 56

Correct Answer: C

Approach Solution 2:

A minimum of 30 units are assembled in 1 day.

Total earnings of Greg in 2 days = $180

Day 1, Gregg assembled- 30 units * 2 = $60 (it is Assumed since we need to find the maximum number of units assembled in a day.)

Day 2 of assembling for Greg is 40 units *2 = $80 Total $140

Remaining Balance is equal to $40
This implies- 180-140

For every additional unit, Greg earns $2.5 per unit. That means he earned $40 in the enhanced rate.

Therefore, additional units = 40 / 2.5 = 16 units.

These are assumed to be assembled on Day 2 since we need to find the maximum number of units assembled in a day.

Therefore, the total number of units assembled in Day 2 is 40 + 16 = 56 units.

Correct Answer: C

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