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