The given question is a GMAT 500 level problem solving question from the topic Percentages. The concept tested in this GMAT sample question is finding out % increase and % decrease from a base value.

Question 8: The difference between the value of a number increased by 12.5% and the value of the original number decreased by 25% is 30. What is the original number?

1. 60
2. 80
3. 40
4. 120
5. 160

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Video Explanation

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Explanatory Answer | GMAT Percentage Q8

Step 1 of solving this GMAT Percentage Question: Deduce the given data from the question stem

These are classic word problems. What is tested is one’s ability to translate what is given in words into mathematical equations and expressions. Invest adequate time to understand what is stated and write correct equations. Usually, solving these equations will not be an issue.

Let the original number be x.
Let A be the value obtained when x is increased by 12.5%.
Therefore, A = x + 12.5% of x
Let B be the value obtained when x is decreased by 25%.
Therefore, B = x − 25% of x

Step 2 of solving this GMAT Percentage Question: Compute the value of the original number

The difference between the value of x increased by 12.5% (i.e., A) and the value of x decreased by 25% (i.e., B) is 30.
i.e., A − B = 30
i.e., x + 12.5% of x − (x − 25% of x) = 30
x + 12.5% of x − x + 25% of x = 30
37.5% of x = 30

x = \\frac{30}{37.5}) × 100 = 80
The original number is 80

Choice B is the correct answer.