There are 84 people on a tour bus. What’s the probability that an adult is wearing sunglasses?

(1) There are 30 people wearing sunglasses.

(2) Two thirds of the people are adults.

**What questions are really about: Understanding and rephrasing**

You may be surprised to know that the most important thing you should learn from the question is not probability, but instead the essence of problem solving: Understanding and rephrasing a problem. Data sufficiency problems effectively capture this subtlety. In fact, data sufficiency problems are a very small simulation of a business problem. You are required to read, understand and determine whether or not you have enough data to solve a problem in a limited amount of time.

In this 40 min video, you can see an excellent explanation about reframing problems in a more general business sense.

This has important implications on solving GMAT quant problems. You can make your job a lot easier by rephrasing problems. For instance, if a question asks: Is y + 1 an odd integer?

You could try and determine whether or not y + 1 is an odd integer, but it is certainly simpler to determine whether y is an even integer. It is simpler to think of ‘y’ than of ‘y + 1’.

If y is even, then y + 1 must be odd.

Take the question you have just tried for example. It does ask about probability, but more precisely, it asks about the number of adults wearing sunglasses. This is a more precise and concise rephrasing of the problem. If you can determine that number then you can solve the problem.

**Obsession with ‘methods’ and ‘tricks’**

It is very common in the GMAT prep phase to obsess over the ’tricks’ one needs to remember for the exam or over the way one should solve a particular type of problem. This is a typical question by students: “But if I get this in the exam then how do I solve it?” or “If the question had been like that, then what would the answer have been?” or “If the statement had been like that then would the answer have been sufficient?”. This anxiety-induced obsession with the particulars of a certain question is typical towards the end of one’s preparation period as the exam date draws near and is counter-productive towards actually learning how to solve problems.

It is good to obsess over learning, but not so good to obsess over remembering certain methods or particular details. Your objective while studying is to learn how to solve problems, not how to solve particular problems on the official guide.

To learn how to solve problems means learning first to fully understand the problem, extracting as much information from the given data as possible, and rephrasing the problem if possible. Focus more on understanding problems than on remembering solutions or certain quick methods or tricks.

**Try this other example:**

An elevator starts moving upwards at a speed of 3.5 meters/sec inside a vertical shaft in a high rise building. Is the vertical distance that the elevator travels more than 287 meters? (Assume that the elevator is always traveling at constant speed).

(1) The elevator traveled for more than 83 seconds.

(2) The elevator traveled for less than 85 seconds.

Highlight the section below this line to see the answer:

A common approach is to calculate the distance for each statement and check. However, let’s see if we can rephrase:

distance = speed x time

speed x time > 287 ?

3,5 x time > 287?

time > 82 secs?

The question is now about how long the travel time was. Given the answers choices. We can quickly confirm that statement (1) is sufficient but statement (2) is not.