APPROACH #1: Testing the answer choices
STRATEGY: As with all GRE Problem Solving questions, we should immediately ask ourselves, Can I use the answer choices to my advantage?
In this case, it's possible to test the answer choices, AND I can see how we might eliminate some answer choices first (more on this later).
Now we should give ourselves about 20 seconds to identify a faster approach.
Well, we can also solve the question algebraically, but that approach could take a while for this tricky question.
Since I feel like I can eliminate 2 or 3 answer choices first, I'm going to test the given values.

Given: The merchant sells EACH of the remaining calculators for $5 more than the average cost of the x calculators
So, for example, if the correct answer is C (x = 26) , then the average cost of each of the 26 calculators will be a complete mess, since 26 doesn't divide nicely into $300
We get: average cost per calculator = $300/26 = $11.538461...
This means the merchant would have to sell each of the remaining 24 calculators at a price of $16.538461..., which makes no sense.

Since answer choices A, C and D don't divide nicely into $300, I'm not going to test these values.
Aside: If the merchant bought 24 calculators (answer choice A), the average price per calculator would be $12.50, which isn't a bad to work with. So if answer choices B and E don't work out, I'll know the correct answer must be A.

Let's test answer choice B (x = 25)
If it costs $300 to purchase 25 calculators, then the average cost per calculator = $300/25 = $12
This means the merchant will sell each of the remaining 23 calculators at a price of $17
So, the total revenue = (23)($17)
I already know this answer is incorrect, because the question tells us that the total revenue was $120 more than the cost of the shipment. In other words, the total revenue must be $420, and since (23)($17) definitely does not equal $420, we can eliminate answer choice B.

Now let's test answer choice E (x = 30)
If it costs $300 to purchase 30 calculators, then the average cost per calculator = $300/30 = $10
This means the merchant will sell each of the remaining 28 calculators at a price of $15
So, the total revenue = (28)($15) = $420
Voila!!
The correct answer is E.



APPROACH #2: Algebra
The merchant originally buys x calculators for $300
So, the average purchase cost = 300/x dollars per calculator

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 dollars per calculator

How many were sold?
Well, the merchant began with x calculators, but used 2 as demonstrators, which means the merchant sold x - 2 calculators.

Finally, the merchant's profit was $120 (after the $300 investment). So, the total 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 as follows:
Start with: [(300/x) + 5](x - 2) = 420
Expand: 300 - (600/x) + 5x - 10 = 420
Multiply both sides by x to get: 300x - 600 + 5x² - 10x = 420x
Simplify: 5x² - 130x - 600 = 0
Divide both sides by 5 to get: x² - 26x - 120 = 0
Factor: (x - 30)(x + 4) = 0
So, x = 30 or x = -4

Since x can't be negative, we know that x = 30

Answer: E