Reading: Charting
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Questions 1-3: The (real) chart above shows the correlation between SAT math test score and family income based on data provided by FairTest.

1. According to the data in the Score vs. Income chart, which is the best estimate of the average number of points by which the median score increases for every $10,000 in additional family income?

(A) 2
(B) 5
(C) 10
(D) 20
(E) 40

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The gap between the lowest income students and the highest income students is about 80 points. The gap is income is $80,000. That's $1000 for one point or $10,000 for ten points.

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2. Which of the following must be true according to the Score vs Income chart?

I. No one whose family earns more than $80,000 scored below 500.
II. For test-takers whose families earn between $40,000 and $60,000, there were more scores below 475 than above 475.
III. The median score of all the test-takers represented in the chart is closer to 500 than it is to 475.

(A) none
(B) I, only
(C) II, only
(D) III, only
(E) II and III, only

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The median rich kid score is about 530 but the lowest rich kid score could be anything so (I) is not true. The median score for middle income kids is about 500 meaning there were the same number above 500 as below 500, so (II) is backwards. It looks like the median should be about 500, BUT that might not be true. If there were lots of test-takers in the 0-20 and 20-40 ranges, the median could be around 475. The chart doesn't say how many people there were in each income range. None of the statements is true so the answer is (A).

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3. If the rate of score increase (in points per dollar of income increase) between the lowest and second lowest income groups persisted for all income groups, at what income (approximately) would the median score on the math SAT first reach 800?

(A) $250,000
(B) $450,000
(C) $650,000
(D) $850,000
(E) $1,000,000

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The rate of score increase is about 30 points for $20,000 for the first two income groups. At this rate, going from about 450 to 800 (an increase of 350 points) is almost 12 jumps of 30 points for a total of (almost) an additional $240,000. The answers are spaced pretty far apart; choice (A) is the only one that's even in the ballpark.

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scores for 100,000 users vs. 1,000,000 non-users for questions 4-7
score users (%) non-users (%)
800 16 1
750-790 40 10
700-740 30 20
600-690 14 30
200-590 0 39

Questions 4-7: Assume that people who use CrushTheTest ("users") and people who do not use CrushTheTest ("non-users") will achieve scores on the math SAT according to the table above. A test score is always a multiple of 10.

4. The median score for all users could be:

(A) 700
(B) 720
(C) 740
(D) 755
(E) none of these

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Since 56% of users get 750 or above, the median has to be between 750 and 790. If there are an even number of scores, the median could be the average of 750 and 760 or 755. The answer is (D).

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scores for 100,000 users vs. 1,000,000 non-users for questions 4-7
score users (%) non-users (%)
800 16 1
750-790 40 10
700-740 30 20
600-690 14 30
200-590 0 39

5. If test-takers scoring in any of the ranges in the table are equally likely to receive any score in the range, what will be the ratio of the number of non-users scoring 720 to the number of users scoring 720?

(A) 2/3
(B) 3/2
(C) 3
(D) 2.5
(E) 6.67

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Just looking at the percentages in the table, you might say the non-users scoring 720 to users scoring 720 would be 2 to 3. But there are 10 times as many users so the actual ratio is 20 to 3 or 6.67. The answer is (E).

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scores for 100,000 users vs. 1,000,000 non-users for questions 4-7
score users (%) non-users (%)
800 16 1
750-790 40 10
700-740 30 20
600-690 14 30
200-590 0 39

6. If test-takers scoring in any of the ranges in the table are equally likely to receive any score in the range, how many out of a randomly-selected group of 500 non-users would be expected to receive a 650?

(A) 150
(B) 120
(C) 90
(D) 15
(E) 12

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There are 10 scores between 600 and 690 so 1 out of 10 who score in that range get a 650. Out of 500 non-users, 30% or 150 would be in the 600 to 690 range and 15 (1 out of 10) would get a 650. The answer is (D).

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scores for 100,000 users vs. 1,000,000 non-users for questions 4-7
score users (%) non-users (%)
800 16 1
750-790 40 10
700-740 30 20
600-690 14 30
200-590 0 39

7. If users scoring between 750 and 790 were equally likely to receive any score in that range, then, to the nearest point, the average score received by users scoring between 750 and 800 inclusive is:

(A) 761
(B) 766
(C) 769
(D) 775
(E) 779

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Each of the 5 scores between 750 and 790 is achieved by 8% of the people (40/5=8). If you average 750, 760, 770, 780, 790, 800, and 800 (the 800 counts twice because it is achieved by 16% of the people) you'll get 778.57. You could also do (770·40+800·16)/56 and get the same answer. If you only count the 800 once, you would get 775 since that is right in the middle. If you count it twice, the answer has to be more than 775. The answer is (E).

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Questions 8-10: The figure above shows a (fictional) ETS budget with spending divided into five categories.

8. The number of (fictional) ordinary employees is five times the number of big shots. The ratio of the average big-shot salary to the average ordinary employee salary is therefore:

(A) 8 to 5
(B) 8 to 1
(C) 5 to 3
(D) 5 to 2
(E) 10 to 1

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You might as well assume 1 big shot and 5 ordinary employees. So the big shot gets 40% and the ordinary employees get 5% each. That's 8 to 1 or (B).

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9. To produce a question, the (fictional) ETS has to pay Dr. Smith $100 to write five proposed questions and then must pay Dr. Jones $100 to choose one of them to become an actual test question. If the average test produced by ETS has 100 questions, how many different tests can they inflict upon us per year if they follow the budget above and if each question appears on only one test?

(A) 1250
(B) 1000
(C) 750
(D) 500
(E) 250

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It costs 200 dollars to produced a question which translates to 20,000 dollars per test. The producing questions budget is 5% or 5 million dollars. Dividing this by 20,000 yields 250 tests or (E).

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10. In response to criticism of ambiguous questions on its tests, the (fictional) ETS decided it would increase the dollar amount of its public relations (PR) budget by 40% by allocating money from salaries for ordinary employees to PR. After this change, what is the new percentage of the budget spent on salaries for ordinary employees?

(A) 17%
(B) 18%
(C) 19%
(D) 20%
(E) 21%

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The PR budget starts out as 20% of the total. To increase the dollar amount by 40% you have to increase the percentage from 20% to 28% (8 is 40% of 20). So the ordinary employees are down to 17% (25–8=17). The answer is (A).

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