Problem Solving

RBBmba@2014 wrote:A motorcycle importer is planning on increasing the price of a certain model by $1000. At this new price 5 fewer motorcycles will be sold per month, but the total revenues will increase by $26,000 to $594,000. What is the number of motorcycles the manufacturer will sell at this new price?

(A) 51
(B) 61
(C) 66
(D) 71
(E) 76

GMATGuruNY wrote:

RBBmba@2014 wrote:A motorcycle importer is planning on increasing the price of a certain model by $1000. At this new price 5 fewer motorcycles will be sold per month, but the total revenues will increase by $26,000 to $594,000. What is the number of motorcycles the manufacturer will sell at this new price?

(A) 51
(B) 61
(C) 66
(D) 71
(E) 76

We can PLUG IN THE ANSWERS, which represent the number of motorcycles sold at the higher price.
The correct answer choice is almost certainly to be a factor of the total revenue of $594,000.
Since 594 = 9*66, the correct answer is probably C.
When the correct answer choice is plugged in, new revenue - old revenue = 26000.

Answer choice C: 66
Here, 66 bikes earn a total of $594,000, implying that the price per bike = 549000/66 = 9000.
Thus, the price per bike before the $1000 increase = 9000-1000 = 8000.

Since 5 more bikes were sold before the $1000 increase, the number of bikes sold before the price increase = 66+5 = 71.
Revenue earned by 71 bikes at a price of $8000 each = 71*8000 = 568000.

New revenue - old revenue = 549000 - 568000 = 26000.
Success!

The correct answer is C.

RBBmba@2014 wrote:
Just a quick question - is there no other way we could solve this as in this particular case option C works fine but in cases where option C won't work we'll have to go on testing with other options and this will become time consuming, I think ? (Although I find it NOT suitable to solve by forming equations!)

A motorcycle importer is planning on increasing the price of a certain model by $1000. At this new price 5 fewer motorcycles will be sold per month, but the total revenues will increase by $26,000 to $594,000. What is the number of motorcycles the manufacturer will sell at this new price?

(A) 22
(B) 33
(C) 66
(D) 99
(E) 132

[email protected] wrote:HI RBBmba@2104,

What is the source of this question?

Not every question on Test Day can be solved quickly. Certain questions require more time than others (and some even require 3 minutes of real 'work'). This question was designed without much of any 'shortcuts' (except for the pattern that 594,000 is a multiple of 66).

You could try solving this question with a 'system' of equations, but even that would take a lot of time and effort. TESTing THE ANSWERS is arguably the fastest approach, but it still takes time.

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

GMATGuruNY wrote:

RBBmba@2014 wrote:
Just a quick question - is there no other way we could solve this as in this particular case option C works fine but in cases where option C won't work we'll have to go on testing with other options and this will become time consuming, I think ? (Although I find it NOT suitable to solve by forming equations!)

Even if every answer choice were a factor of 594000, we would have to test at most two answer choices.
To illustrate, let's say the problem read as follows:

A motorcycle importer is planning on increasing the price of a certain model by $1000. At this new price 5 fewer motorcycles will be sold per month, but the total revenues will increase by $26,000 to $594,000. What is the number of motorcycles the manufacturer will sell at this new price?[/b]

(A) 22
(B) 33
(C) 66
(D) 99
(E) 132

D: 99
Here, 99 bikes earn a total of $594,000, implying that the price per bike = 594000/99 = 6000.
Thus, the price per bike before the $1000 increase = 6000-1000 = 5000.

Since 5 more bikes were sold before the $1000 increase, the number of bikes sold before the price increase = 99+5 = 104.
Revenue earned by 104 bikes at a price of $5000 each = 104*5000 = 520000.

New revenue - old revenue = 594000 - 520000 = 74000.
Here, the difference between the revenues is TOO BIG.

B: 33
Here, 33 bikes earn a total of $594,000, implying that the price per bike = 594000/33 = 18000.
Thus, the price per bike before the $1000 increase = 18000-1000 = 17000.

Since 5 more bikes were sold before the $1000 increase, the number of bikes sold before the price increase = 33+5 = 38.
Revenue earned by 38 bikes at a price of $17000 each = 38*17000 = 646000.

New revenue - old revenue = 594000 - 646000 = -52000.
Here, the difference between the revenues is TOO SMALL.

Since D yields a result that is TOO BIG, while B yields a result that is TOO SMALL, the correct answer choice must be BETWEEN B AND D.

The correct answer is C.

RBBmba@2014 wrote:Hi Mitch - could you please help me resolve my query as in the immediate above post ?

Much thanks in advance!

RBBmba@2014 wrote:A motorcycle importer is planning on increasing the price of a certain model by $1000. At this new price 5 fewer motorcycles will be sold per month, but the total revenues will increase by $26,000 to $594,000. What is the number of motorcycles the manufacturer will sell at this new price?

(A) 51
(B) 61
(C) 66
(D) 71
(E) 76[

GMATGuruNY wrote:

RBBmba@2014 wrote:Hi Mitch - could you please help me resolve my query as in the immediate above post ?

Much thanks in advance!

If one answer choice seems more likely to be correct than the other answer choices, start with that answer choice.
In the original problem, only C divides evenly into 594,000, so we should test C first.

If all of the answer choices seem viable, I typically test D first.
If D does not work, and I cannot tell which of the remaining answer choices is correct, I then test B.
In the revised problem, all of the answer choices divide evenly into 594,000, making it harder to identify the answer choice most likely to be correct.
For this reason, I first tested D and then B.
The result is that I was able to determine the correct answer choice by testing only two options.

Matt@VeritasPrep wrote:

RBBmba@2014 wrote:A motorcycle importer is planning on increasing the price of a certain model by $1000. At this new price 5 fewer motorcycles will be sold per month, but the total revenues will increase by $26,000 to $594,000. What is the number of motorcycles the manufacturer will sell at this new price?

(A) 51
(B) 61
(C) 66
(D) 71
(E) 76[

Working with the answers is the best way, as Mitch demonstrated. The only other way that occurs to me is actually solving it, which would give us something like

(x + 5) * p = 568,000
x * (p + 1000) = 594,000

We want to solve for x, so we have to eliminate p. We know that p = (568,000)/(x+5), so we sub that into the second equation and get

x * ((568,000)/(x+5) + 1000) = 594,000

(568000x / (x+5)) + 1000x = 594,000

568x + x(x+5) = 594(x+5)

x² + 573x = 594x + 2970

x² - 21x - 2970 = 0

(x - 66)(x + 45) = 0

so x = 66 or x = -45 ... but we can't sell a negative number of bikes!

(Incidentally, the second to last step is unnecessary. Since both of our solutions should be integers (it's a GMAT problem, after all), we just need a factor of 2970.)

RBBmba@2014 wrote:

GMATGuruNY wrote:

RBBmba@2014 wrote:Hi Mitch - could you please help me resolve my query as in the immediate above post ?

Much thanks in advance!

If one answer choice seems more likely to be correct than the other answer choices, start with that answer choice.
In the original problem, only C divides evenly into 594,000, so we should test C first.

If all of the answer choices seem viable, I typically test D first.
If D does not work, and I cannot tell which of the remaining answer choices is correct, I then test B.
In the revised problem, all of the answer choices divide evenly into 594,000, making it harder to identify the answer choice most likely to be correct.
For this reason, I first tested D and then B.
The result is that I was able to determine the correct answer choice by testing only two options.

Thanks for your reply Mitch. Got your point but what I was emphasizing is that if we get integer values from both 549000/66 and 568000/71 (let's consider the revised problem) then why we'd go on testing any other option and why we'd start with any other option except C ?

Now, had the case been such that we don't get integer values in any of the cases with option C (i.e. either before or after price increase at least, if not in both the cases) the we should go on checking with option D/B accordingly... Thoughts ?

P.S: Isn't it safe to consider this 'integer' aspect ? It saves time,I think!