BTGmoderatorDC wrote: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?

A. 48

B. 52

C. 56

D. 60

E. 64

GIVEN: Total pay for 2 days is $180
In order to MAXIMIZE the number of units assembled on one of the days, we must MINIMIZE the number of units assembled on the other day

We're told that Greg assembled at least 30 units each day.
So, the MINIMUM is 30 units
Let's say that Greg assembled 30 units on DAY 1

Payment for Day 1 = (30)($2) = $60
If Greg is paid $60 for Day 1, then he must have received $120 on Day 2.

If Greg was paid $120 on Day 2, how many units did he assemble?

GIVEN: 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 (since 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
$40/$2.50 = 16 units
So, the TOTAL number of units assembled = 40 + 16 = 56

Answer: C

Cheers,
Brent

Hi All,

We're told that 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.

While this question is 'wordy', the math behind it isn't too difficult - so you have to be careful about organizing all of the given information and labeling your work. To start, we know that Greg was paid a TOTAL of $180 for the two days of work - and we want to find the situation in which he would be paid the most for one particular day. This is essentially a "limit" question; to make one day the highest possible, we have to make the other day the lowest possible. To make Day 1 as low as possible, Greg would assemble just 30 units...

Day 1: 30 units @ $2/unit = $60

This means that Greg would earn the remaining $180 - $60 = $120 on Day 2... He'd start by producing 40 units at the standard rate...

Day 2 40 units @2/unit = $80

This would leave him $120 - $80 = $40 that he would earn at the $2.50/unit rate.

$40/$2.50 =
$80/$5 =
16 units

Thus, for Day 2, he would assemble 40 + 16 = 56 units.

Final Answer: C

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