GRE Data Analysis will, true to its name, require you to analyze data. Sometimes the data will be a series of large values in a graph or table, and you may feel tempted to punch lots of numbers into your calculator. Yet the necessary math may be simpler—and less error-prone—than you realize. Try this table-based problem to see what I mean.

### Data Analysis: Tables, Percents

Difficulty Level: 2 (Low)

In the Official GRE Quantitative Reasoning Practice Questions, Volume 1, a numeric entry question gives you a small table of large numbers and asks you to calculate a percentage. It’s not hard to get the answer. But it’s also not hard to do more math than needed or even to use the wrong values. In fact, up to 40% of test takers would likely get the question incorrect. Here’s a problem much like it.

JANUARY 2015

Country | Population (in thousands) |

Germany | 81,198 |

France | 66,415 |

United Kingdom | 64,875 |

Italy | 60,796 |

Spain | 46,450 |

The population of the five most populous countries in the European Union in January 2015 are listed in the table above. The total population of the European Union in January 2015 was 508,451,000 Based on the data shown, the population of the three most populous countries combined was what percent of the total population of the European Union in 2015?

Give your answer to the nearest whole percent.

⇓SOLVED⇓

### The Explanation

First, here are a couple of mistakes that are easy to make on this question. One involves misreading the table, and the other involves misreading the question.

**Order of Magnitude Error**. The populations in the table refer to the number of thousands of people in each country. That means each number has an implied ‘000’ at the end. For instance, Germany’s population is 81,198,000—that is, 81 million, 198 thousand.Still, you might forget about that ‘000’ and attempt this calculation:

- 81,198 + 66,415 + 64,875508,451,000
*INCORRECT*

When you try this math with your onscreen calculator, you’ll have to stop short. You can’t enter more than eight digits in the calculator you get during the exam, so 508,451,000 won’t fit. Regardless, the result (~0.04%) would be so small that the nearest whole percent would be 0! Surely, the three most populous countries in the EU make up more than 0% of the total EU population.

To avoid this error, drop the ‘000’ from the total population to match the country populations. Round all the values (as seen below) to simplify them even further.

- 81,198 + 66,415 + 64,875508,451,000
**Number of Data Points Error**. The question asks you to combine the population of the THREE most populous countries. In place of—or even in addition to—using the wrong order of magnitude, you might use the wrong number of data points, most likely all FIVE, rather than just the relevant three.

Now, here is a fast and accurate way to knock out this challenge. It just takes doing a little mental math before turning to your calculator.

**Step 1: Round the relevant population values and drop the trailing zeros.** You can round each population to the nearest hundred-thousand and get the same answer that you would using the unrounded population values, down to the ten-thousandth’s place. (In either case, you get ~0.4179, which becomes 42%.)

- Germany 81,198,000 ⇒ 81,200,000 ⇒
**812** - France 66,415,000 ⇒ 66,400,000 ⇒
**664** - United Kingdom 64,875,000 ⇒ 64,900,000 ⇒
**649** - European Union 508,451,000 ⇒ 508,500,000 ⇒
**5085**

**Step 2: Calculate the required percent and round to the nearest whole number. **Now you punch some buttons on your calculator and put the rounded percent value in the numeric entry box.

- 812 + 664 + 6495085 ≅ 0.418 ≅
**42%**

Overall, this challenge should’ve been pretty easy. If you read carefully and rounded wisely, you got the right answer fairly quickly. Still, don’t underestimate the risk of making silly mistakes. Think before you calculate and check your work after, even—or perhaps especially—when you’re doing a seemingly easy Data Analysis question.

Ready for another Data Analysis challenge? Check out these posts.

- GRE Data Analysis Challenge: Compare Standard Deviations
- GRE Data Analysis Challenge: Probability at Maximum Difficulty

Image: EU location on the world map by Ssolbergj.

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