Ann can have her bicycle repaired for $50, or she can trade

What we want to figure out is:

(New Bike Cost) = (Old Bike Cost) x (1+n) where n is the percentage increase in cost.

So:
New Bike Cost = $107 - $22 = $85
Old Bike Cost = $50

Plugging it in:

85 = 50(1+n)
n = (85/50) -1 = 70%. Answer is C.

This is an easy question. Yet, as per the stats on this question, 1 out of 3 students who attempted it, got it wrong.

This happened probably because the question statement is wordy and seems convoluted. So, even though a student knows the concept of percentages well, he may not be able to frame the required equation.

If you've faced this challenge in this, or any other word problem, then please read on for the approach that you should apply in such questions.


At e-GMAT, we call this approach: 'From Unknown to Known.'

By Unknown, we mean, the piece of information that the question is asking you to find

By Known, we mean, the given pieces of information.

Here's how I would solve this question using our Approach:

Let the cost of purchasing the new bicycle (CPNB) be x% greater than the cost of getting the bicycle repaired (CR).

(Note that x is the unknown here. This is what the question is asking us to find.)

So, we can write: CPNB = (1+\(\frac{x}{100}\))CR . . . (1)

From (1), it's clear that to find the value of x, we need to find the values of CPNB and CR.

CR = $50 (given)

And, CPNB = (selling price of new bicycle) - (credit note) = 107 - 22 = $85

So, from (1) we get:

85 = (1+\(\frac{x}{100}\))50

Upon solving this equation further, we get x = 70%

As you can see, this solution is not too different from the solutions posted above, in terms of the equations formed and the calculations done. The point of difference lies in the order in which I went about forming the equations and doing the calculations. I first wrote an expression for the unknown, and then, thought about finding whatever I needed (CPNB and CR) to get to the value of the unknown.

This approach of going 'From Unknown to Known' gives you a sense of direction in questions where you feel at a loss about what to do with all the data points, or how to even start. This approach acts as a compass that helps you navigate through the maze of given data, one step at a time, and there lies the power of this approach.

Hope this discussion was useful for you!

Best Regards

Japinder

cost of repair = 50.
cost of new bike = 107, 85 after the 22 has been reducted.

85-50=35

35/50=7/10 = 70% = C

I liked the explanation of AjChakravarthy. I couldn't understand any answers why 70 is answer until I saw down.

Getting a new bicycle by trading her old one would cost Ann 85$(107-22), while repairing her old one would be 50$.
to make percentage problem easier, we will multiple both numbers by 2 (which will not change the ratio between the two numbers). So we get 100 vs 170, which tells us that 70% is the answer (C)

The cost of the new bicycle is 85 dollars after she trades in her current bicycle. So we need to determine 85 is what percent greater than 50:

(85 - 50)/50 * 100 = 35/50 * 100 = 70 percent

Answer: C

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