A merchant paid $300 for a shipment of x identical

BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

This topic has expert replies

Post new topic Post Reply

Previous Topic Next Topic

AAPL: Moderator; Posts: 2599; Joined: Sun Oct 29, 2017 2:08 pm; Followed by:2 members

A merchant paid $300 for a shipment of x identical

by AAPL » Fri Dec 28, 2018 5:43 am

Timer

00:00

Your Answer

Global Stats

GMAT Paper Tests

A merchant paid $300 for a shipment of x identical calculators. The merchant used 2 of the calculators as demonstrators and sold each of the others for $5 more than the average (arithmetic mean) cost of the x calculators. If the total revenue from the sale of the calculators was $120 more than the cost of the shipment, how many calculators were in the shipment?

A. 24
B. 25
C. 26
D. 28
E. 30

OA E.

Quote

Source: Beat The GMAT — Problem Solving | Fri Dec 28, 2018 5:43 am

Manasa3190: Junior | Next Rank: 30 Posts; Posts: 22; Joined: Sat Oct 07, 2017 7:45 am

answer

by Manasa3190 » Fri Dec 28, 2018 8:17 pm

Cost of each calculator = (300/x)
selling price of each calculator is = 420/(x-2)
Since, Selling price = Cost Price + Profit

Selling Price - Cost Price = 5 (per unit)

(420/(x-2)) - (300/x) = 5
(84/(x-2) ) - (60/x) = 1
Solving the above equation,
x^2 - 26x - 120 = 0
x^2 - 30x + 6 - 120 = 0
x = 30,-6

Number of calculators can't be negative = 30

Quote

GMAT/MBA Expert

[email protected]: Elite Legendary Member; Posts: 10392; Joined: Sun Jun 23, 2013 6:38 pm; Location: Palo Alto, CA; Thanked: 2867 times; Followed by:511 members; GMAT Score:800

by [email protected] » Sat Dec 29, 2018 10:51 am

Hi All,

The information in the prompt include a variety of nice 'round' numbers, so it's likely that the number of calculators in the shipment is also a round number AND divides evenly into 300. Only two of the answers 'fit' that idea - 25 and 30, so let's TEST THE ANSWERS and see if either of those values fits all of the information given in the prompt.

IF.... X = 30 and there are 30 calculators in the shipment....
The merchant paid $300/30 = $10 per calculator
2 calculators were used for demonstrations, so 30 - 2 = 28 calculators were sold
Each of the 'sold' calculators brought in $10+$5 = $15
The total revenue was ($15)(28) = $420
The total profit was $420 - $300 = $120

This is an exact match for what we were told, so this MUST be the answer.

Final Answer: E

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

Contact Rich at [email protected]

Quote

GMAT/MBA Expert

Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Sun Feb 10, 2019 7:27 am

AAPL wrote:GMAT Paper Tests

A merchant paid $300 for a shipment of x identical calculators. The merchant used 2 of the calculators as demonstrators and sold each of the others for $5 more than the average (arithmetic mean) cost of the x calculators. If the total revenue from the sale of the calculators was $120 more than the cost of the shipment, how many calculators were in the shipment?

A. 24
B. 25
C. 26
D. 28
E. 30

OA E.