Percent is one of the major concepts on GRE and GMAT as it involves and interfaces with most of the other topics.
Percent is expressed as the number out of 100.
All Percentage Problems deals with the basic formula:
Percent = Part/Original whole x 100
I. What is 15% of 30? — find the part
Part = Percent x original whole/100
= 15 x 30/100
II. 5 is what percent of 45? — find the percentage
Percent = 5/45 x 100
III. 25 is 3% of what number? – find the whole
Original whole = Part / Percent x 100
= 25/3 x 100
When the values are not assigned in questions, it is better to choose that value as 100. It makes calculations very simple and fast.
For example: Bag B contains 20% more marbles than bag A, what percent of marbles have to be transferred from bag B to bag A to make the number of marbles in both the bag equal?
Solution: In this example, it is not mentioned how many marbles each bag has so we can assign some number. Let’s say bag A contains 100 marbles, bag B has 20% more marbles than bag A, so bag B contains 120 marbles. To make the number of marbles in both the bags equal, we need to transfer 10 marbles from bag B to bag A so each bag will have 110 marbles.
Therefore percent of marble to be transferred from bag B = 10/120 x 100
Increasing or decreasing:
The percent increase or decrease problems require a slightly deeper knowledge of percentages. The difference between finding a percentage and finding a percentage increase (or decrease) is that finding an increase requires you to use the AMOUNT of increase rather than just the ‘part’. Because of this, the formula looks like this:
Percent increase = amount of increase/Original whole x 100
Percent decrease = amount of decrease/Original whole x 100
The cost of an item goes from $75 to $100. What is the percent increase?
Solution: Percent increase = (25)/ (75) which give us 1/3 or 33.3%
The 25 was calculated as 100 – 75 = 25, because the cost increased by $25.
Another way to look at percentage increase or decrease is to think of it as ‘percentage change. We will know if it is an increase or decrease based on whether the original value went up or down. When you see the word PROFIT or LOSS in a percentage problem, you should instantly think ‘percentage change‘.
Sometimes the GMAT will ask you to find the original number after a percent increase or decrease. Many test takers will incorrectly read this problem as a basic “find the whole” problem. The key is to notice the words ‘increased by’ or ‘decreased by.’ This requires us to adjust our percentage appropriately:
For percentage increase: Add 1 to the percentage. — 12% becomes 1.12
For percentage decrease: Subtract 1 from the percentage. — 12% becomes 0.88
As GRE and GMAT Quant is completely based on the basics of mathematics, we at Option Training Institute, FZ LLC, train students in the basics before embarking on advanced strategy training.