An important area of GMAT Quant is percentage change. Recently a student asked me for help with the following percentage question from the 2016 Official Guide:

*Last year the price per share of Stock X increased by k percent and the earnings per share of Stock X increased by m percent, where k is greater than m. By what percent did the ratio of price per share to earnings per share increase, in terms of k and m?*

The student realized that one approach is to plug in numbers, but the question somehow still didn’t make much sense to him. (This plug-in-numbers approach was discussed in my previous blog post on solving percentage questions.

We use the same method for this current question, but the question is more challenging. Therefore, it’s important to be clever about which numbers we plug in with:

- A safe bet with percentage questions is to use 100 as your base number for both starting price and earnings. So let's imagine that the price per share goes from 100 to 300, a 200% increase. Thus,
*k* is 200. - We know that
*m* must be smaller than *k*. Imagine earnings per share go from 100 to 150 – a 50% increase. Thus *m* is 50.

The ratio of price per share to earnings per share has gone from 1:1 (100:100) to 2:1 (300:150), an increase of 100%. That’s the reason we chose to make *m* 50: to achieve an easy number to work with. An increase in the ratio of price per share to earnings per share of 100% should be easy to work with when we plug in the values of k and m to the answer choices.

Remember, we are looking for an answer that gives us 100:

- Check A: 200/50 = 4
- B: k-m = 150
- C: 100(k-m) / (100 + k) = 100 (200-50) /(100 + 200) = 15,000/400 = 150/4 = 75/2 = 37.5
- D: 100(k-m) / (100 + m) = 100 (200-50) /(100 + 50) = 15,000/150 = 1500/15 = 100. D is correct.
- Quickly check E just in case we have made an error: 100(k-m) / (100 + k + m) = 100 (200-50) /(100 + 200 + 50) = 15,000/350 = 1500/35 = 300/7 = something between 40 and 50. The correct answer is definitely D.

There are always several approaches to solving questions. Some may involve complicated algebraic calculations. You will usually find it easier and quicker to plug in numbers. Just be clever about which numbers you choose so that your calculations become easier.

Original Article: https://gmat.economist.com/blog/quantitative/gmat-quant-percentage-change-questions

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