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tagged by: Brent@GMATPrepNow

This topic has 2 expert replies and 0 member replies

### Top Member

ardz24 Master | Next Rank: 500 Posts
Joined
22 Aug 2017
Posted:
302 messages

#### A merchant paid $300 for a shipment of x identical calculato Sat Sep 16, 2017 4:53 am 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

Is there a strategic approach to this question?

OA: E

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### GMAT/MBA Expert

Rich.C@EMPOWERgmat.com Elite Legendary Member
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Tue Sep 19, 2017 2:53 pm
Hi ardz24,

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.

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

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Contact Rich at Rich.C@empowergmat.com

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### GMAT/MBA Expert

Brent@GMATPrepNow GMAT Instructor
Joined
08 Dec 2008
Posted:
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GMAT Score:
770
Sat Sep 16, 2017 6:18 am
ardz24 wrote:
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 Here's one approach: If it costs$300 to purchase x calculators, then the average cost per calculator is 300/x

Later, the calculators are sold for $5 more than the average purchase cost of 300/x dollars So, the resell price is 300/x + 5 How many were sold? Well, the merchant began with x calculators, but used 2 as demonstrators, so the merchant sold x - 2 calculators. Finally, the merchant's profit was$120 (after a $300 investment). So, the revenue was$420

We can now write an equation: (300/x + 5)(x - 2) = 420

IMPORTANT: This is an awful equation to solve. At this point, it may be faster to try plugging in the answer choices.

Or we can solve the equation.
(300/x + 5)(x - 2) = 420
Expand: 300 - (600/x) + 5x - 10 = 420
Multiply both sides by x: 300x - 600 + 5x^2 - 10x = 420x
Simplify: 5x^2 - 130x - 600 = 0
Divide both sides by 5: x^2 - 26x - 120 = 0
Factor: (x - 30)(x + 4) = 0
So, x = 30 or x = -4

Since x can't be negative, x = 30 = E

Cheers,
Brent

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