Problem Solving

vinni.k wrote:To offset miscellaneous costs, a dealership decides to increase the prices of all of its motorcycles by 7 percent plus an additional $350. One motorcycle incurs a 9 percent increase in price because of these changes. What was the original price of this motorcycle?

(A) $15,000
(B) $16,300
(C) $16,500
(D) $17,500
(E) $18,500

OA is D

The wording of this question seems ambiguous
Here's a solution from the Book(veritas):-

Here we apply a percent increase plus a surcharge to yield a larger percent increase. If the original price is our unknown x, we can describe the relationship as 1.07x + 350 = 1.09x. Algebra demands that we subtract 1.07x from both sides, yielding $350 = .02x. Multiply both sides by 50 to get x = $17500, or D.

In my opinion, the highlighted part above doesn't match the given question.

Dealership decides to increase the prices of all of its motorcycles by 7 percent + additional $350.

So, let the price of all of its motorcycles = x
So, after increase = 1.07x + 350

Now, One motorcycle incurs a 9 percent increase in price. What was the original price of this motorcycle?

Let the price of this one motorcycle be y which is increased by 9 percent = 1.09y
I need to find y
My equation becomes --> 1.07x + 350 = 1,09y

I think the wording of the question is ambiguous. Price of all its motorcycles v/s Price of this one motorcycle.
How can there be one variable X for both the above (All V/s This One)

Thanks

vinni.k wrote:

Brent@GMATPrepNow wrote:
I'm not entirely sure this question is ambiguous.
I read it as: one of the motorcycles (we'll name it Clark) gets a 7% price increase PLUS an additional increase of $350
These changes are equivalent to a 9% price increase (for Clark)

As we can see, it doesn't make a difference whether each motorcycle has the same original price. What matters is that increasing a price by 7% and then adding $350 to the price is EQUIVALENT to increasing the price by 9%

So, if c = the original price of Clark, then the NEW PRICE = 1.07c + 350
Likewise. if c = the original price of Clark, then a 9% price increase means the NEW PRICE = 1.09c

So, we can write: 1.07c + 350 = 1.09c

Cheers,
Brent

Thanks Brent,

Suppose there are three motorcyles Aye, Bee, and Clark
The price of all of these motorcycles increases by 7 percent.
Now this motorcycle Clark which can be denoted as c, increases by 9% because it's price was increased by 7% when the price of all motorcyles were increased.
I hope i am understanding you clearly.
As Clark is a part of Aye, and Bee. So, we are increasing the price of Clark too, thereby equivalent to 9%

Let me know if i am good on this doubt now.

vinni.k wrote:To offset miscellaneous costs, a dealership decides to increase the prices of all of its motorcycles by 7 percent plus an additional $350. One motorcycle incurs a 9 percent increase in price because of these changes. What was the original price of this motorcycle?

(A) $15,000
(B) $16,300
(C) $16,500
(D) $17,500
(E) $18,500