Percent is one of the major concepts on GRE and GMAT as it involves and interfaces with most 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

Example:

I. What is 15% of 30? — find the part

Part = Percent x original whole/100

= 15 x 30/100

= 4.5

II. 5 is what percent of 45? — find the percentage

Percent = 5/45 x 100

= 11.11%

III. 25 is 3% of what number? – find the whole

Original whole = Part / Percent x 100

= 25/3 x 100

= 833.33

When the values are not assigned in questions, choosing that value as 100 is better. It makes calculations very simple and fast.

For example, Bag B contains 20% more marbles than Bag A; what percent of marbles must be transferred from Bag B to Bag A to equal the number of marbles in both bags?

Solution: This example needs to mention how many marbles each bag has so we can assign some number. 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 bags equal, we need to transfer 10 from bag B to bag A so that each bag will have 110 marbles.

Therefore, the percent of marble to be transferred from bag B = 10/120 x 100

= 8.33%

Increasing or decreasing:

The percent increase or decrease problems require a slightly deeper knowledge of percentages. The difference between finding a percentage and 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

Example:

The cost of an item goes from $75 to $100. What is the percent increase?

Solution: Percent increase = (25)/ (75), which gives 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 are 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.

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