﻿ Real World Math - How to Crack the Math Section - Cracking the GRE Premium Edition (2016) ﻿

## Cracking the GRE Premium Edition (2016)

### Part IIIHow to Crack the Math Section

9The Geography of the Math Section

### Real World Math

Real world math is our title for the grab bag of math topics that will be heavily tested on the GRE. This chapter details a number of important math concepts, many of which you’ve probably used at one point or another in your daily adventures, even if you didn’t recognize them. After completing this chapter, you’ll have brushed up on important topics such as ratios, proportions, and averages. You’ll also learn some important Princeton Review methods for organizing your work and efficiently and accurately answering questions on these topics.

EVERYDAY MATH

A few years ago when ETS reconfigured the GRE, they wanted the Math section to test more of what they call “real life” scenarios that a typical graduate student might see. You can therefore expect the math questions on the GRE to heavily test topics such as proportions, averages, and ratios—mathematical concepts that are theoretically part of your everyday life. Regardless of whether that’s true of your daily life or not, you’ll have to master these concepts in order to do well on the GRE Math section.

The math on the GRE
is supposed to reflect
the math you use in your
day-to-day activities.

RATIOS AND PROPORTIONS

If you’re comfortable working with fractions and percentages, you’ll be comfortable working with ratios and proportions, because ratios and proportions are simply special types of fractions. Don’t let them make you nervous. Let’s look at ratios first and then we’ll deal with proportions.

What Is a Ratio?

Recall that a fraction expresses the relationship of a part to the whole. A ratio expresses a different relationship: part to part. Imagine yourself at a party with 8 women and 10 men in attendance. Remembering that a fraction expresses a part-to-whole relationship, what fraction of the partygoers are female? , or 8 women out of a total of 18 people at the party. But what’s the ratio, which expresses a part to part relationship, of women to men? , or as ratios are more commonly expressed, 8 : 10. You can reduce this ratio to 4 : 5, just like you would a fraction.

A ratio is just another
type of fraction.

On the GRE, you may see ratios expressed in several different ways:

x : y
the ratio of x to y
x is to y

In each case, the ratio is telling us the relationship between parts of a whole.

Every Fraction Can Be a Ratio, and Vice Versa

Every ratio can be expressed as a fraction. A ratio of 1 : 2 means that the total of all the parts is either 3 or a multiple of 3. So, the ratio 1 : 2 can be expressed as the fraction , or the parts of the ratio can be expressed as fractions of the whole as  and . Likewise, the fraction  expresses the ratio 1 : 3. So if a question says “the ratio of x to 2y is ,” then that would be expressed as .

Treat a Ratio Like a Fraction

Anything you can do to a fraction you can also do to a ratio. You can cross-multiply, find common denominators, reduce, and so on.

Find the Total

The key to dealing with ratio questions is to find the whole, or the total. Remember: A ratio tells us only about the parts, not the total. In order to find the total, add the numbers in the ratio. A ratio of 2 : 1 means that there are three total parts. A ratio of 2 : 5 means that we’re talking about a total of 7 parts. And a ratio of 2 : 5 : 7 means there are 14 total parts. Once you have a total you can start to do some fun things with ratios.

For example, let’s say you have a handful of pennies and nickels. If you have 30 total coins and the pennies and nickels are in a 2 : 1 ratio, how many pennies do you have? The total for our ratio is 3, meaning that out of every 3 coins, there are 2 pennies and 1 nickel. So if there are 30 total coins, there must be 20 pennies and 10 nickels. Notice that  is the same as , is the same as 2 : 1!

Like a fraction, a ratio
expresses a relationship
between numbers.

When you are working with ratios, there’s an easy way not only to keep track of the numbers in the problem but also to quickly figure out the values in the problem. It’s called the Ratio Box. Let’s try the same question, but with some different numbers; if you have 24 coins in your pocket and the ratio of pennies to nickels is 2 : 1, how many pennies and nickels are there? The Ratio Box for this question is below, with all of the information we’re given already filled in.

The minute you see the
word “ratio,” draw a Ratio

Remember that ratios are relationships between numbers, not actual numbers, so the real total is 24; that is, you have 24 actual coins in your pocket. The ratio total (the number you get when you add the number of parts in the ratio) is 3.

The middle row of the table is for the multiplier. How do you get from 3 to 24? You multiply by 8. Remember when we talked about finding equivalent fractions? All we did was multiply the numerator and denominator by the same value. That’s exactly what we’re going to do with ratios. This is what the Ratio Box looks like now:

The multiplier is the key
concept in working with
ratios. Just remember that
whatever you multiply one
part by, you must multiply
every part by.

Now let’s finish filling in the box by multiplying everything else.

Therefore, of the 24 coins 16 are pennies and 8 are nick el s.

Let’s try a GRE example.

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Review?

Check out Math Workout
for the GRE
. If you’re in
a hurry, pick up Crash
Course for the GRE
.

Flour, eggs, yeast, and salt are mixed by weight in the ratio of 11 : 9 : 3 : 2, respectively. How many pounds of yeast are there in 20 pounds of the mixture?

1

1

2

2

8

Here’s How to Crack It

The minute you see the word ratio, draw a Ratio Box on your scratch paper and fill in what you know.

First, add all of the numbers in the ratio to get the ratio total.

Now, what do we multiply 25 by to get 20?

So  is our “multiply by” number. Let’s fill it in.

The question asks for the amount of yeast, so we don’t have to worry about the other ingredients. Just look at the yeast column. All we have to do is multiply 3 by  and we have our answer: 3 ×  =  = 2, which is (D).

What Is a Proportion?

So you know that a fraction is a relationship between part and whole, and that a ratio is a relationship between part and part. A proportion is an equivalent relationship between two fractions or ratios. Thus,  and  are proportionate because they are equivalent fractions. But  and  are not in proportion because they are not equal ratios.

The GRE often contains problems in which you are given two proportional, or equal, ratios from which one piece of information is missing. These questions take a relationship or ratio, and project it onto a larger or smaller scale. Proportion problems are recognizable because they always give you three values and ask for a fourth value. Here’s an example:

The key to proportions is
setting them up correctly.

If the cost of a one-hour telephone call is \$7.20, what would be the cost in dollars of a 10-minute telephone call at the same rate?

Here’s How to Crack It

It’s very important to set up proportion problems correctly. That means placing your information on your scratch paper. Be especially careful to label everything. It takes only an extra two or three seconds, but doing this will help you catch lots of errors.

For this question, let’s express the ratios as dollars over minutes, because we’re being asked to find the cost of a 10-minute call. That means that we have to convert 1 hour to 60 minutes (otherwise it wouldn’t be a proportion).

Now cross-multiply.

Now we can enter 1.20 into the box.

Relationship Review

You may have noticed a trend in the preceding pages. Each of the major topics covered—fractions, percents, ratios, and proportions—described a particular relationship between numbers. Let’s review:

• A fraction expresses the relationship between a part and the whole.
• A percent is a special type of fraction, one that expresses the relationship of part to whole as a fraction with the number 100 in the denominator.
• A ratio expresses the relationship between part and part. Adding the parts of a ratio gives you the whole.
• A proportion expresses the relationship between equal fractions, percents, or ratios.
• Each of these relationships shares all the characteristics of a fraction. You can reduce them, expand them, multiply them, and divide them using the exact same rules you used for working with fractions.

AVERAGES

The average (arithmetic mean) of a list of numbers is the sum, or total value, of all the numbers in the list divided by the number of numbers in the list. The average of the list 1, 2, 3, 4, 5 is equal to the total of the numbers (1 + 2 + 3 + 4 + 5, or 15) divided by the number of numbers in the list (which is 5). Dividing 15 by 5 gives us 3, so 3 is the average of the list.

GRE average problems
always give you two of
the three numbers needed.

ETS always refers to an average as an “average (arithmetic mean).” This confusing parenthetical remark is meant to keep you from being confused by other more obscure kinds of averages, such as geometric and harmonic means. You’ll be less confused if you simply ignore the parenthetical remark and know that average means total of the elements divided by the number of elements.

Think Total

Don’t try to solve average problems all at once. Do them piece by piece. The key formula to keep in mind when doing problems that involve averages is

The minute you see the
word average, draw
an Average Pie on your
scratch paper.

Here’s how the Average Pie works. The total is the sum of the numbers being averaged. The number of things is the number of different elements that you are averaging. And the average is, naturally, the average.

Say you wanted to find the average of 4, 7, and 13. You would add those numbers to get the total and divide that total by three.

Mathematically, the Average Pie works like this:

Which two pieces of the
pie do you have?

The horizontal bar is a division bar. If you divide the total by the number of things, you get the average. If you divide the total by the average, you get the number of things. If you have the number of things and the average, you can simply multiply them together to find the total. This is one of the most important things you need to be able to do to solve GRE average problems.

Using the Average Pie has several benefits. First, it’s an easy way to organize information. Furthermore, the Average Pie makes it clear that if you have two of the three pieces, you can always find the third. This makes it easier to figure out how to approach the problem. If you fill in the number of things, for example, and the question wants to know the average, the Average Pie shows you that the key to unlocking that problem is finding the total.

Try this one.

The average (arithmetic mean) of seven numbers is 9 and the average of three of these numbers is 5. What is the average of the other four numbers?

4

5

7

10

12

Draw a new Average Pie
each time you encounter
the word average in a
question.

Here’s How to Crack It

Let’s take the first sentence. You have the word average, so draw an Average Pie and fill in what you know. We have seven numbers with an average of 9, so plug those values into the Average Pie and multiply to find the total.

Now we also know that three of the numbers have an average of 5, so draw another Average Pie, plug those values into their places, and multiply to find the total of those three numbers.

The question is asking for the average of the four remaining numbers. Draw one more Average Pie and plug in 4 for the number of things.

In order to solve for the average, we need to know the total of those four numbers. How do we find this? From our first Average Pie we know that the total of all seven numbers is 63. The second Average Pie tells us that the total of three of those numbers was 15. Thus, the total of the remaining four has to be 63 – 15, which is 48. Plug 48 into the last Average Pie, and divide by 4 to get the average of the four numbers.

The average is 12, which is (E).

Let’s try one more.

The average (arithmetic mean) of a set of 6 numbers is 28. If a certain number, y, is removed from the set, the average of the remaining numbers in the set is 24.

 Quantity A Quantity B y 48

Quantity A is greater.

Quantity B is greater.

The two quantities are equal.

The relationship cannot be determined from the information given.

Here’s How to Crack It

All right, let’s attack this one. The problem says that the average of a set of six numbers is 28, so let’s immediately draw an Average Pie and calculate the total.

If a certain number, y, is removed from the set, there are now five numbers left. We already know that the new average is 24, so draw another Average Pie.

The difference between the totals must be equal to y. 168 − 120 = 48. Thus, the two quantities are equal, and the answer is (C).

Up and Down

Averages are very predictable. You should make sure you automatically know what happens to them in certain situations. For example, suppose you take three tests and earn an average score of 90. Now you take a fourth test. What do you know?

If your average goes up as a result of the fourth score, then you know that your fourth score was higher than 90. If your average stays the same as a result of the fourth score, then you know that your fourth score was exactly 90. If your average goes down as a result of the fourth score, then you know that your fourth score was less than 90.

MEDIAN, MODE, AND RANGE

The median is the middle value in a list of numbers; above and below the median lie an equal number of values. For example, in the list of numbers (1, 2, 3, 4, 5, 6, 7) the median is 4, because it’s the middle number (and there are an odd number of numbers in the list). If the list contained an even number of integers such as (1, 2, 3, 4, 5, 6) the median is the average of 3 and 4, or 3.5. When looking for the median, sometimes you have to put the numbers in order yourself. What is the median of the list of numbers (13, 5, 6, 3, 19, 14, 8)? First, put the numbers in order from least to greatest, (3, 5, 6, 8, 13, 14, 19). Then take the middle number. The median is 8. Just think median = middle and always make sure the numbers are in order.

Don’t confuse
median and mode!

The mode is the number in a list of numbers that occurs most frequently. For example, in the list (2, 3, 4, 5, 3, 8, 6, 9, 3, 9, 3) the mode is 3, because 3 shows up the most. Just think mode = most.

When you see the word
median in a question, put
the numbers in the
problem in order.

The range is the difference between the greatest and the least numbers in a list of numbers. So, in the list of numbers (2, 6, 13, 3, 15, 4, 9), the range is 15 (the greatest number in the list) – 2 (the least number in the list), or 13.

Here’s an example:

Set F = {4, 2, 7, 11, 8, 9}

What do we need to do to
the numbers in this set?

 Quantity A Quantity B The range of Set F The median of Set F

Quantity A is greater.

Quantity B is greater.

The two quantities are equal.

The relationship cannot be determined from the information given.

Here’s How to Crack It

Let’s put the numbers in order first, so it’ll be easier to see what we have: {2, 4, 7, 8, 9, 11}. First, let’s look at Quantity A: The range is the greatest number, or 11, minus the least number, or 2. That’s 9. Now let’s look at Quantity B: The minute you see the word median, be sure to put the numbers in order. The median is the middle number of the set, but because there are two middle numbers, 7 and 8, we have to find the average. Or do we? Isn’t the average of 7 and 8 clearly going to be smaller than the number in Quantity A, which is 9? Yes, in quant comp questions, we compare, not calculate. The answer is (A).

STANDARD DEVIATION

Standard deviation is one of those phrases that math people like to throw around to scare non-math people, but it’s really not that scary. The GRE might ask you questions about standard deviation, but you’ll never have to actually calculate it; instead, you’ll just need a basic understanding of what standard deviation is. In order to understand standard deviation, we must first look at something all standardized testers should be familiar with, the bell curve.

You’ll never have to calculate
the standard deviation
on the GRE.

The first thing to know about a bell curve is that the number in the middle is the mean.

The minute you see the terms standard deviation or normal distribution, draw a bell curve and fill in the percentages.

Draw a Bell Curve!

When you see terms like
“standard deviation” and
“normal distribution” in
GRE math questions, draw
your bell curve and fill in
the information you know.

Imagine that 100 students take a test and the results follow a normal distribution. When you see the phrase normal distribution, draw a bell curve. Let’s say that the average score on this test is an 80. Put 80 in the middle of the curve. You also know that 2% of the students got a 96 or higher. Put a 96 above the right 2% line on the curve.

Standard deviation measures how much a score differs from the norm (the average) in even increments. The curve tells us that a score earned by only 2% of the students is two standard deviations from the norm. If the norm is 80 and 96 is two standard deviations away, then one standard deviation on this test is 8 points. Why? Remember that standard deviations are even increments. If the average is 80 and the score two standard deviations from the norm is 96, then the difference is 16. So, one standard deviation is half of that difference, or 8. The score at one standard deviation greater than the norm is, therefore, 88. Two standard deviations above the norm is 96, while two standard deviations below the norm is 64. One standard deviation below the norm is 72. Fill these in on your bell curve.

Now you know quite a bit about the distribution of scores on this test. 68 percent of the students received a score between 72 and 88. 98 percent scored above a 64. That’s all there is to know about standard deviations. The percentages don’t change, so memorize those. When you see the phrase, just draw a bell curve and fill in what you know. Here’s what the curve looks like for this test:

When it comes to standard deviation, the percentages don’t change, so memorize those: 2, 14, and 34.

Here’s an example of how ETS might test standard deviation:

 Quantity A Quantity B The standard deviation of a list of data consisting of 10 integers ranging from −20 to −5 The standard deviation of a list of data consisting of 10 integers ranging from 5 to 20

Quantity A is greater.

Quantity B is greater.

The two quantities are equal.

The relationship cannot be determined from the information given.

Here’s How to Crack It

ETS is hoping you’ll make a couple of wrong turns on this problem. The first trap they set is that one list of numbers contains negative integers while the other doesn’t—but this doesn’t mean that one list has a negative standard deviation. Standard deviation is defined as the distance a point is from the mean, so it can never be negative. The second trap is that ETS hopes you’ll waste a lot of time trying to calculate standard deviation based on the information given. But you know better than to try to do that. Remember that ETS won’t ask you to calculate standard deviation; it’s a complex calculation. Plus, as you know, you need to know the mean in order to calculate the standard deviation and there’s no way we can find it based on the information here. Thus, we have no way of comparing these two quantities, and the answer is (D).

Now let’s try a question that will make use of the bell curve.

The fourth grade at School X is made up of 300 students who have a total weight of 21,600 pounds. If the weight of these fourth-graders has a normal distribution and the standard deviation equals 12 pounds, approximately what percentage of the fourth-graders weigh more than 84 pounds?

12%

16%

36%

48%

60%

Here’s How to Crack It

This one’s a little tougher than the earlier standard deviation questions. The first step is to determine the average weight of the students, which is  = 72 pounds. If the standard deviation is 12 pounds, then 84 pounds places us exactly one standard deviation above the mean, or at the 84th percentile (remember the bell curve?). Because 16 percent of all students weigh more than 84 pounds, the answer is (B).

RATE

Rate problems are similar to average problems. A rate problem might ask for an average speed, distance, or the length of a trip, or how long a trip (or a job) takes. To solve rate problems, use the Rate Pie.

A rate problem is really
just an average problem.

The Rate Pie works exactly the same way as the Average Pie. If you divide the distance or amount by the rate, you get the time. If you divide the distance or amount by the time, you get the rate. If you multiply the rate by the time, you get the distance or amount.

Let’s take a look.

It takes Carla three hours to drive to her brother’s house at an average speed of 50 miles per hour. If she takes the same route home, but her average speed is 60 miles per hour, what is the time, in hours, that it takes her to drive home?

2 hours

2 hours and 14 minutes

2 hours and 30 minutes

2 hours and 45 minutes

3 hours

Here’s How to Crack It

The trip to her brother’s house takes three hours, and the rate is 50 miles per hour. Plug those numbers into a Rate Pie and multiply to find the distance.

So the distance is 150 miles. On her trip home, Carla travels at a rate of 60 miles per hour. Draw another Rate Pie and plug in 150 and 60. Then all you have to do is divide 150 by 60 to find the time.

So it takes Carla two and a half hours to get home. That’s (C).

Try another one.

A machine can stamp 20 envelopes in 4 minutes. How many of these machines, working simultaneously, are needed to stamp 60 envelopes per minute?

5

10

12

20

24

Here’s How to Crack It

First we have to find the rate per minute of one machine. Plug 20 and 4 into a Rate Pie and divide to find the rate.

The rate is 5. If one machine can stamp 5 envelopes per minute, how many machines do you need to stamp 60 per minute? 60 ÷ 5 = 12, or (C).

CHARTS

Every GRE Math section has a few questions that are based on a chart or graph (or on a group of charts or graphs). But don’t worry; the most important thing that chart questions test is your ability to remember the difference between real-life charts and ETS charts.

In real life, charts are often provided in order to display information in a way that’s easier to understand. Conversely, ETS constructs charts to hide information you need to know and to make that information harder to understand.

Chart questions frequently
test percents, percent
change, ratios, proportions,
and averages.

Chart Questions

There are usually two or three questions per chart or per set of charts. Like the Reading Comprehension questions, chart questions appear on split screens. Be sure to click on the scroll bar and scroll down as far as you can; there may be additional charts underneath the top one, and you want to make sure you’ve seen all of them.

On charts, look for the
information ETS is trying
to hide.

Chart problems just recycle the basic arithmetic concepts we’ve already covered: fractions, percentages, and so on. This means you can use the techniques we’ve discussed for each type of question, but there are two additional techniques that are especially important to use when doing chart questions.

Take a minute to note the following key bits of information from any chart you see.

• Information in titles:Make sure you know what each chart is telling you.
• Asterisks, footnotes, parentheses, and small print:Often there will be crucial information hidden away at the bottom of the chart. Don’t miss it!
• Funny units:Pay special attention when a title says “in thousands” or “in millions.” You can usually ignore the units as you do the calculations, but you have to use them to get the right answer.

on Charts

Pay attention to small
details like footnotes,
parentheses, tiny print,
and even odd units.
These usually provide key
insights that will enrich
chart.

Approximate, Estimate, and Ballpark

Like some of our other techniques, you have to train yourself to estimate when working with charts and graphs questions. You should estimate, not calculate exactly, in the following situations:

• whenever you see the word approximatelyin a question
• whenever the answer choices are far apart in value
• whenever you start to answer a question and you justifiably say to yourself, “This is going to take a lot of calculation!”

Don’t try to work
with huge values.

Review those “friendly” percentages and their fractions from earlier in the chapter. Try estimating this question:

What is approximately 9.6 percent of 21.4 ?

Here’s How to Crack It

Use 10 percent as a friendlier percentage and 20 as a friendlier number. One-tenth of 20 is 2 (it says “approximately”—who are you to argue?). That’s all you need to do to answer most chart questions.

Chart Problems

Make sure you’ve read everything on the chart carefully before you try the first question.

Approximately how many tons of aluminum and copper combined were purchased in 1995 ?

125

255

325

375

515

How much did Company X spend on aluminum in 1990 ?

\$675,000

\$385,000

\$333,000

\$165,000

\$139,000

Approximately what was the percent increase in the price of aluminum from 1985 to 1995 ?

8%

16%

23%

30%

42%

Here’s How to Crack the First Question

As you can see from the graph on the previous page, in 1995, the black bar (which indicates aluminum) is at 250, and the dark gray bar (which indicates copper) is at approximately 125. Add those figures and you get the number of tons of aluminum and copper combined that were purchased in 1995: 250 + 125 = 375. That’s (D). Notice that the question says “approximately.” Also notice that the numbers in the answer choices are pretty far apart.

Here’s How to Crack the Second Question

We need to use the chart and the graph to answer this question, because we need to find the number of tons of aluminum purchased in 1990 and multiply it by the price per ton of aluminum in 1990 in order to figure out how much was spent on aluminum in 1990. The bar graph tells us that 175 tons of aluminum was purchased in 1990, and the little chart tells us that aluminum was \$2,200 per ton in 1990. 175 × \$2,200 = \$385,000. That’s (B).

Here’s How to Crack the Third Question

Remember that percent increase formula from earlier in this chapter?

Percent change =  × 100

We’ll need to use the little chart for this one. In 1985, the price of aluminum was \$1,900 per ton. In 1995, the price of aluminum was \$2,700 per ton. Now let’s use the formula. 2,700 − 1,900 = 800, so that’s the difference. This is a percent increase problem, so the original number is the smaller one. Thus, the original is 1,900, and our formula looks like this: Percent change =  × 100. By canceling the 0’s in the fraction you get  × 100, and multiplying gives you . At this point you could divide 800 by 19 to get the exact answer, but because they’re looking for an approximation, let’s round 19 to 20. What’s 800 ÷ 20? That’s 40, and (E) is the only one that’s close.

Real World Math Drill

Now it’s time to try out what you have learned on some practice questions. Try the following problems and then check your answers in Part V.

1 of 12

Sadie sells half the paintings in her collection, gives one-third of her paintings to friends, and keeps the remaining paintings for herself. What fraction of her collection does Sadie keep?

2 of 12

5x − 2y = 2y − 3x

 Quantity A Quantity B x y

Quantity A is greater.

Quantity B is greater.

The two quantities are equal.

The relationship cannot be determined from the information given.

Questions 3 through 5 refer to the following graph.

3 of 12

If the six New England states are ranked by population in Year X and Year Y, how many states would have a different ranking from Year X to Year Y ?

None

One

Two

Three

Four

4 of 12

In Year X, the population of Massachusetts was approximately what percent of the population of Vermont?

50%

120%

300%

800%

1,200%

5 of 12

By approximately how much did the population of Rhode Island increase from Year X to Year Y ?

750,000

1,250,000

1,500,000

2,250,000

3,375,000

6 of 12

A water jug with a capacity of 20 gallons is 20 percent full. At the end of every third day, water is added to the jug. If the amount of water added is equal to 50 percent of the water in the jug at the beginning of that day, how many days does it take for the jug to be at least 85% full?

4

6

12

15

20

7 of 12

Towns A, B, C, and D are all in the same voting district. Towns A and B have 3,000 people each who support referendum R and the referendum has an average (arithmetic mean) of 3,500 supporters in towns B and D and an average of 5,000 supporters in Towns A and C.

 Quantity A Quantity B The average number of supporters of Referendum R in Towns C and D The average number of supporters of Referendum R in Towns B and C

Quantity A is greater.

Quantity B is greater.

The two quantities are equal.

The relationship cannot be determined from the information given.

8 of 12

A company paid \$500,000 in merit raises to employees whose performances were rated AB, or C. Each employee rated A received twice the amount of the raise that was paid to each employee rated C; and each employee rated B received one-and-a-half times the amount of the raise that was paid to each employee rated C. If 50 workers were rated A, 100 were rated B, and 150 were rated C, how much was the raise paid to each employee rated A ?

\$370

\$625

\$740

\$1,250

\$2,500

Questions 9 through 11 refer to the following graphs.

9 of 12

In 2013, the median reading test score for ninth-grade students was in which score range?

Below 65 points

65–69 points

70–79 points

80–89 points

90–100 points

10 of 12

If the number of students in grades 9 through 12 comprised 35 percent of the number of students in School District X in 1995, then approximately how many students were in School District X in 1995 ?

9,700

8,700

3,400

3,000

1,200

11 of 12

Assume that all students in School District X took the reading test each year. In 2013, approximately how many more ninth-grade students had reading test scores in the 70–79 point range than in the 80–89 point range?

470

300

240

170

130

12 of 12

One ounce of Solution X contains only ingredients a and b in a ratio of 2 : 3. One ounce of Solution Y contains only ingredients a and b in a ratio of 1 : 2. If Solution Z is created by mixing solutions X and Y in a ratio of 3 : 11, then 630 ounces of Solution Z contains how many ounces of a ?

68

73

89

219

236

Summary

○A ratio expresses a part to part relationship. The key to ratio problems is finding the total. Use the ratio box to organize ratio questions.

○A proportion expresses the relationship between equal fractions, percents, or ratios. A proportion problem always provides you with three pieces of information and asks you for a fourth.

○Use the Average Pie to organize and crack average problems.

○The median is the middle number in a set of values. The mode is the value that appears most frequently in a set. The range of a set is the difference between the largest and smallest values in the set.

○You will never have to calculate standard deviation on the GRE.

○Standard deviation problems are really average and percent problems. Make sure you know the percentages associated with the bell curve: 34%, 14%, 2%.

○Use the Rate Pie for rate questions.

○On chart questions, make sure you take a moment to understand what information the chart is providing. Estimate answers to chart questions whenever possible.

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