GRE Diagnostic Math Section 2 EXPLAINED.pages
Rules; 20 Questions, 35 Minutes, Section (4 of 4)
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GRE Diagnostic Math Section 2 EXPLAINED.pages
1. Over the whole five 5-year periods shown in the table, in which of the categories below does XYZ publishers publish the greatest number of new titles? A. Fiction – crime B. Fiction – historical C. Fiction – other D. Autobiography & Biography E. Non-fiction – general Correct Answer: D Explanation: This is an easy question as there is no need to calculate. Visual inspection of the table shows that Autobiography & Biography has higher numbers than any other category in six out of the seven periods. 2. In how many of the categories shown on the table does the number of new titles by female authors exceed the number of new titles by male authors in the ten-year period represented by periods 4 and 5? A. 1 B. 2 C. 3 D. 4 E. 5 Correct Answer: C Explanation: In Historical Fiction, Romantic Fiction and Autobiography & biography the number of new titles by female authors is greater than the number by male authors. (In period 4 for Autobiography &Biography the numbers are the same but there is one more new title by a female author in period 5.)
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GRE Diagnostic Math Section 2 EXPLAINED.pages
3. Which of the following can be correctly deduced from the table? (Select ALL that apply) A. In the Fiction – sci-fi category over the 25-years depicted in the table the ratio of new titles by female authors to those by male authors is 1:6 B. The average (arithmetic mean) number of titles published each five-year period in the category Fiction - Historical is 8.6 C. The total number of new titles published in period 5 is greater than the total number of new titles published in period 1 Correct Answer: B Explanation: Choice A is incorrect as there are 4 titles by female authors and 26 by male, making the ratio 4: 26 or 2:13. (Note that the fraction of new titles by female authors is 1/6). Choice B is correct as the total number of titles in the five periods (adding ‘male’ and ‘female’ numbers) is 15 + 10 + 10 + 5 + 3 = 43 and the average over the five periods is obtained by dividing the total by 5 to give 8.6. Choice C is incorrect as a total of 178 new titles were published in period 1 and 175 in period 5. These numbers are close and so although this question is easy, it is time consuming.
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GRE Diagnostic Math Section 2 EXPLAINED.pages
4. If the gender ratio is defined by the publisher as the number of new titles published by male authors divided by the number of titles published by female authors, then, in Period 3, in how many of the seven categories shown in the table is the gender ratio less than or equal to 2? A. 1 B. 2 C. 3 D. 5 E. 6 Correct Answer: C Explanation: If you go down the column that represents Period 3 and divide the ‘male’ numbers by the ‘female’ then you will see that the first two are less than 1 and all the others are greater than 2 except Fiction – other which is exactly 2. (There is no need to find the exact fraction in each case: just identify those less than and those greater than 2). 5. Which of the following figures is the closest to the value of new titles in the Fiction-romantic category in period 5, as a percent of new titles in all the Fiction categories in Period 5? A. 30 B. 22 C. 20 D. 15 E. 12 Correct Answer: C Explanation: There are five categories of Fiction with a total of 106 new titles. Romantic fiction accounts for 20 of them. The percentage is therefore (20/106)x100 which is just under 19, making 20 the closest of the figures given.
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GRE Diagnostic Math Section 2 EXPLAINED.pages
6. x is 3 less than y x+5
y+2
A. The quantity on the left is greater B. The quantity on the right is greater C. Both are equal D. The relationship cannot be determined without further information Correct Answer: C Explanation: x is 3 less than y can be written x = y - 3 If we add 5 to both sides we have x + 5 = y + 2 7. p + q = 3, and p-q = 6 q
0
A. The quantity on the left is greater B. The quantity on the right is greater C. Both are equal D. The relationship cannot be determined without further information Correct Answer: B Explanation: These are a pair of simultaneous equations. To solve, we can add them to get 2p = 9. p = 4.5 Substituting in the first equation 4.5 + q = 3; q = -1.5 So 0 is greater than q
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GRE Diagnostic Math Section 2 EXPLAINED.pages
8. A circle and a line lie in the same plane. The greatet possible number of points that are on both the circle and the line.
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A. The quantity on the left is greater B. The quantity on the right is greater C. Both are equal D. The relationship cannot be determined without further information Correct Answer: C Explanation: The line can cut through the circle at maximum two points 9. Three boxes contain 20, 25 and 27 sweets respectively. The least number of sweets that need to be transferred so that there is an equal number in each box.
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A. The quantity on the left is greater B. The quantity on the right is greater C. Both are equal D. The relationship cannot be determined without further information Correct Answer: B Explanation: The total number of sweets = 20 + 25 + 27 = 72 If there are an equal number in each, there will be 72/3 = 24 To make the numbers equal we will need to remove one from the second box, and three from the third (and put them in the first). This means we must move 4 sweets.
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GRE Diagnostic Math Section 2 EXPLAINED.pages
10. ! The sum of all the integers from -10 to 12 inclusive.
23
A. The quantity on the left is greater B. The quantity on the right is greater C. Both are equal D. The relationship cannot be determined without further information Correct Answer: C Explanation: The sum of the integers from -10 to 10 inclusive is 0. (-10 + 10, -9 + 9, -8 + 8 etc.) This leaves only 11 and 12 to be added = 23 11. There are 28 students in a class all born in 1990 The probability that all their birthdays are in February
The probability that all their birthdays fall on a Friday
A. The quantity on the left is greater B. The quantity on the right is greater C. Both are equal D. The relationship cannot be determined without further information Correct Answer: B Explanation: There are 12 months in a year so each student has a 1/12 chance of being born in a particular month. There are only 7 days in a week, so each student has a 1/7 chance of being born on a particular day of the week The chances that all will be born on a particular day of the week is thus higher than the chances of them all being born in the same month.
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GRE Diagnostic Math Section 2 EXPLAINED.pages
12. C is the midpoint of segment AE and AB < DE BC
CD
A. The quantity on the left is greater B. The quantity on the right is greater C. Both are equal D. The relationship cannot be determined without further information Correct Answer: A Explanation: BC = AC - AB CD = CE - DE, but AC and CE are both equal. Since DE is greater than AB, CD must be less than BC. (We are taking off a smaller amount from half the segment, when we subtract AB from AC.)
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GRE Diagnostic Math Section 2 EXPLAINED.pages
13. This question and the next refer to the following: The graph shows the sales figures for a certain company in five consecutive years. Percentage increase in sales from 1989 to 1991
Percentage fall in sales from 1991 to 1993
A. The quantity on the left is greater B. The quantity on the right is greater C. Both are equal D. The relationship cannot be determined without further information Correct Answer: A Explanation: From 89 to 91 the rise is 2000. From 91 to 93 the fall is 2000. But the percent increase is (2000/1000) x 100; and the percent fall is (2000/3000) x 100 Therefore, the percent rise is greater.
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GRE Diagnostic Math Section 2 EXPLAINED.pages
14. Refer to the previous question The mean (average) of the 5 annual sales figures
The median of the 5 annual sales figures
A. The quantity on the left is greater B. The quantity on the right is greater C. Both are equal D. The relationship cannot be determined without further information Correct Answer: B Explanation: To find the mean, add all the values and divide by 5. (1000 + 2000 + 3000 + 2000 + 1000)/5 = 9000/5 = 1800 To find the median, arrange the numbers in order of magnitude and find the middle term 1000,1000,2000,2000,3000. The median = 2000
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GRE Diagnostic Math Section 2 EXPLAINED.pages
15. n is a positive integer p = 8 x 9 x 11 x n The remainder when p is divided by 6
The remainder when p is divided by 33
A. The quantity on the left is greater B. The quantity on the right is greater C. Both are equal D. The relationship cannot be determined without further information Correct Answer: C Explanation: Since p has factors 8 and 9, it will be divisible by 6. Since p has factors 11 and 9, it will be divisible by 33. There will be no remainder in either case. 16. Let the function f be defined by f(x) = x - 1 What is the value of y if y is a positive integer such that 1/3 f(y") = 5? Correct Answer: 4 Explanation: We can find f(y") by plugging in to get f(y") = y" -1 Now we take 1/3 of this value as equal to 5; (y" â&#x20AC;&#x201C; 1)/3 = 5; thus y" = 16 and y = 4
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GRE Diagnostic Math Section 2 EXPLAINED.pages
17. The amount of time taken to paint a wall is inversely proportional to the number of painters working on the job. If it takes 3 painters 5 days to complete such a job, how many days longer will it take if there are only 2 painters working? Correct Answer: 2.5 Explanation: For inverse proportions remember the formula x₁y₁ = x₂y₂ Here initial painters x days = final painters x days; 3 x 5 = 2 x days Total days taken will be 15/2 = 7.5, but there is a catch: you were asked how much longer it would take. Initial time was 5 days so it will take 2.5 days longer. 18. Line l and line m lie in the same plane but have no points in common. They are both tangent to a circle of area 9#. What is the shortest distance between any point on l and any point on m? Correct Answer: 6 Explanation: The description tells us that l and m are parallel lines with the circle lying between and touching both. Area of the circle = #r" = 9 #. Radius = 3 and diameter = 6. 19. A box contains 5 chocolates with soft centers, 6 with nut centers, and 11 with hard caramel centers. Three students take turns to take a chocolate at random from the box and eat it. If the probability that all three students take soft centers is 1/x, what is the value of x? Correct Answer: 154 Explanation: The total number of chocolates to start with is 22. The first student has a chance of 5/22 of taking a soft center. The second student has a only 21 sweets left of which 4 could be soft: his chance is therefore 4/21. Similarly the third student has a chance of 3/20 Total probability is obtained by multiplying all these chances together: (5/22) (4/21)(3/20) = 1/154 [It is best to cancel the terms down rather than using a calculator because we want a fraction not a decimal]
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GRE Diagnostic Math Section 2 EXPLAINED.pages
20. At one point in a game the shooting team has a ratio of hits to misses of 5:1. After the team misses the next three shots, which are the last in the game, its ratio of hits to misses is 5:2. What is the total number of shots taken by the team in the game? Correct Answer: 21 Explanation: A ratio of 5: 2 means 5x: 2x. Total shots = 7x. The last three shots added one unit to the ratio, and so x = 3. 7x = 21
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