The topic of percentages is one of the easiest that you will tackle on the GMAT. We are all accustomed to calculating percentages in our daily lives, and any potential question on this topic would seem to be a cakewalk to most. While that is generally true, there are also some traps and pitfalls that the GMAT will lay down for you. Be careful not to get caught in them! Here are some handy tips, tricks, and trap warnings to help you negotiate your way around GMAT questions on this topic:
Error Type 1: Using the wrong base when calculating percentage change
The percentage increase in a quantity when it is increased by a certain amount is [(new value – old value)/old value] x 100. Similarly the percentage decrease is [(old value-new value)/old value] x 100. This point seems to be fairly obvious. However, an exam situation can play tricks on anyone and cause them to make silly mistakes in a hurry.
A common error involves taking the new value in the denominator. If the price of a product increases from 120 to 140, the percentage increase is (20/120)*100 = 16.67%, not (20/140)*100 = 14.28%.
Another example: If a is 60% of b, what % of a is b?
Answer: The question asks us for b as a percentage of a. The correct way to approach this is to see that a = 0.60(b) and so b as a % of a = (b/0.60b) * 100 = 166.67%.
Error Type 2: Not being able to differentiate between a quantity change and a percentage change
The increase in a quantity X when it is increased successively by a% and then by b% is X/100(a+ b+ ab/100) but the percentage increase is (a+b+ab/100)%
This is a common error test-takers make. If the population of a town is 10,000 and it grows by 10% in year 1 and by 15% in year 2, then the increase in population after 2 years = 10000/100 (10+15+150/100) = 2650. However the percentage increase in the population from the start of year 1 to the end of year 2 is (10+15+150) = 26.5%
Note here that the overall percentage increase is dependent on just the percentage changes, not on the initial value. However, the change in the quantity is dependent on the initial value of the quantity
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