Practice Problems
5.1 DI X-Ray
 
5.2 DI Fundamentals
 
 
5.3 DI Step Method
 
5.4 Practice Problems
 
Practice Problems
The best way to reinforce all we’ve taught you in this chapter is to try some DI problems on your own. Keep the fundamentals and step method in mind as you try the questions in the following set. Note that each DI question set will contain two questions. We’ve provided five in this set for additional practice. See how you make out and then check out the explanations that follow.

Directions: Questions 1–5 refer to the following graphs. For each question, select the best of the answer choices given.

1. In which of the following years was the difference between School District X’s budget for entrées and its budget for desserts the lowest?
(A) 1974
(B) 1975
(C) 1976
(D) 1977
(E) 1978
2. Which of the following statements can be inferred from the data?
  I. School District X’s entrée budget increased from the previous year in every year its dessert budget increased from the previous year.
 II. School District X’s dessert budget in 1975 was within $2,000 of its 1975 combined budget for turkey, lamb, and duck.
III. School District X budgeted a greater amount for pork in 1975 than it budgeted for pork in 1974.
(A) I only
(B) II only
(C) III only
(D) I and II
(E) II and III
3. Which of the following is the closest approximation for the amount School District X’s budget for chicken in 1975 exceeded its budget for desserts in 1974?
(A) $4,000
(B) $24,000
(C) $32,000
(D) $120,000
(E) $125,000
4. What was the approximate percent decrease in School District X’s dessert budget from 1977 to 1978?
(A) 8%
(B) 12%
(C) 20%
(D) 40%
(E) 75%
5. What was School District X’s approximate budget for vegetarian entrées in 1975?
(A) $7,500
(B) $13,000
(C) $21,500
(D) $37,500
(E) $58,250
Guided Explanations
1. A
Step 1: Get the Specs. The two graphs concern a food budget for School District X. Evidently GRE–land has only one name for schools: X (see the traveling to school questions earlier in the chapter). Be that as it may . . .
The first line graph depicts the budgets for both entrées and desserts over the course of five years. The key to the right tells us which line is which. The left label on the y-axis indicates that the figures for entrées are in thousands of dollars, and the right label tells us that the figures for desserts are also in thousands of dollars. Note, however, that the two y-axes contain radically different numerical scales. (Those who missed this were in for a big surprise here in question 1.) The two budgets appear to follow a similar pattern, but we’ll have to be careful about the different scales.
The circle graph shows the percentage breakdown of different types of entrées served in 1975, so it represents a subset of data from the first graph. We should expect at some point to have to bounce these percentages from the circle graph off the 1975 entrée number from the line graph. The box to the right provides the legend for the circle graph, which enables us to figure out which slice represents which type of entrée. There were five main types: chicken, beef, pork, vegetarian, and “other,” which the note informs us consists of turkey, lamb, and duck. So in actuality, there were seven types of entrées served; only three of them are grouped together in a single slice of the pie.
Step 2: Grill the Interrogator. The first question concerns the difference between the entrée and dessert budgets across the board, so it appears that only the line graph will be in play here.
Step 3: Gather the Data. Normally a quick bit of eyeballing would work fine for a question like this, except for the fact that, as we mentioned, the two y-axis scales are radically different. Anyone going with a quick general scan of the line graph would no doubt choose 1977, choice D, as the year with the smallest difference in budgets. However, since the scales are different for the two budgets, we’ll have to approximate the actual numbers to calculate the differences. You can approximate the values of each year if you remember to read the entrée number off the left vertical axis and the dessert number off the right.
Step 4: Power Through. Since the entrée budget increases far faster than the dessert budget, the smallest difference between them is likely to occur when the entrée budget is the smallest. This happens in 1974. Here the entrée budget is roughly $95,000 and the dessert budget is roughly $8,000. The difference between these two budgets, roughly $87,000, turns out to be less than that for any of the other years, each of which exhibits a difference of more than $100,000. A is therefore correct.
2. B
Step 1: Get the Specs. We performed this step for question 1, so we don’t need to repeat it here.
Step 2: Grill the Interrogator. The next question is in Roman numeral format, which means we’ll simply have to test each statement individually to see which can be inferred.
Steps 3 and 4: Gather the Data/Power Through. Since we have to essentially work out three separate problems, we’ll combine these steps as we first gather the data and power through statement I and then repeat the same process for statements II and III.
Statement I isn’t true because eyeballing alone shows that the school district’s dessert budget rose from 1975 to 1976, while its entrée budget fell during the same period. That eliminates choices A and D.
Statement II is inferable: The 1975 dessert budget looks to be just about in the middle of $10,000 and $15,000, so it’s approximately $12,500. Turkey, lamb, and duck compose the “other” category in the circle graph, and we can see from that figure that these made up 10% of the entrée budget in 1975, which we can approximate as 10% of 125,000, or $12,500 as well. So the budgets in question in statement II are nearly equal, and certainly within $2,000 of each other.
Statement III, however, isn’t inferable since we know nothing of the percentage of the 1974 entrée budget comprising pork; remember, the entrée breakdown represented in the circle graph deals only with the year 1975. For all we know, pork wasn’t on the menu in 1974—or it made up the entire menu. Notice how this Roman numeral format provides the test makers with another way to test your understanding of “not enough information.” Since we don’t know the pork situation in 1974, we can’t infer statement III, and choice B, II only, is correct.
3. B
Step 1: Get the Specs. Been there, done that. Onward!
Step 2: Grill the Interrogator. In this one we’re asked to approximate the difference between the 1975 chicken budget and the 1974 dessert budget, so it appears we’ll need to approximate two values and then do some simple subtraction. It’s therefore looking like we’ll need to use both diagrams for this multistep question. We also know from the question’s wording that the chicken number will be higher, for whatever that’s worth.
Step 3: Gather the Data. Hunting we go: The dessert budget is easier to find since we only need eyeballing for that. Remembering to read the value from the y-axis on the right, we see that the budget for desserts in 1974 clocked in at just under $10,000, so we’ll say approximately $8,000. The chicken budget, however, requires a few steps. In 1975 the total entrée budget was a little more than $120,000, but let’s go ahead and round it down to that nice round number to make things easier. (Remember, we can do that when the question asks for an approximate value.) Moving to the circle graph, we see that chicken represents 26% of the 1975 budget, which we’ll again round off to the more user-friendly figure of 25%.
Step 4: Power Through. We have all the numbers we need from the graphs, so let’s do the math. The 1975 chicken budget is equal to the total entrée budget that year multiplied by the percentage of it devoted to chicken. Since we rounded down a bit, that comes to a little more than 0.25 × $120,000. In this case it helps to convert .25 to , allowing us to calculate the 1975 chicken budget as . We estimated the budget for desserts in 1974 at approximately $8,000, so the difference is roughly $30,000 – $8,000 = $22,000. Scanning the answer choices shows that B, $24,000, is closest to our estimation. Since $30,000 was an underestimate of the true value, it makes sense that the actual answer is slightly larger than our calculation.
4. D
Step 1: Get the Specs. We took care of this in question 1, so on to Step 2.
Step 2: Grill the Interrogator. We’re looking for a rough estimate of the percent decrease in the dessert budget from 1977 to 1978, which means we need to find those approximate figures on the graph and plug them into our handy percent decrease formula. So let’s move on to Step 3 with this plan in mind.
Step 3: Gather the Data.
Percent decrease = difference between the two numbers ÷ greater of the two numbers × 100%
The question tells us exactly what numbers to plug into the formula: Dessert budget numbers from 1977 and 1978. The 1977 dessert budget clocks in just around $20,000 (remember to use the scale on the right side of the graph for dessert budget figures), and the 1978 dessert budget looks to be somewhere close to $12,000.
Step 4: Power Through. With our numbers in place, we simply plug them into the formula: . Multiplying by 100% gives 40%, choice D.
5. C
Step 1: Get the Specs. Already got ‘em, so let’s see what the final question has to offer.
Step 2: Grill the Interrogator. The reference to 1975 and the word vegetarian combine to tell us that we’re again up against another multistep question requiring both graphs to solve. Let’s gather our data.
Step 3: Gather the Data. The first graph tells us that the total entrée budget was approximately $125,000 in 1975. According to the second graph, 17% of this was for vegetarian entrées. We’ll take these figures with us into Step 4.
Step 4: Power Through. We can round up the 17% to 20% to make our lives easier, and then take of $125,000 to get an approximate answer of $25,000. The closest we get to this among the choices is $21,500 in choice C. This makes sense since we overestimated the percentage, and we’d therefore expect the real answer to be a little less than the $25,000 figure we came up with. C’s our pick, and we’re sticking with it.
That finishes off Data Interpretation, our third and final GRE math question type. We hope that by the end of this portion of the book the Math section seems more manageable to you. Sure, there’s a lot to know, but the concepts are tested in systematic and predictable ways in the three question formats we’ve discussed. We’ve provided you with strategies and step methods to handle each one. If you apply what you’ve learned to the questions in the practice test at the end of the book, and to all other practice questions you face, you should be in fine form to handle the math section on test day.
By the way, in case you were wondering, here’s the reason the light goes off when you close the refrigerator door: A little man lives in your refrigerator, and he turns it off every time. At SparkNotes, we draw on many different resources to make sure you get the most accurate and up-to-date information. And now, we imagine many of you will be delighted to leave math and head straight into a totally different world: the GRE Verbal section.
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