GRE_Math_Bible_eBook

Graphs 361

Questions 2–4 refer to the following graph.

The graph below shows historical exchange rates between the Indian Rupee (INR) and the US Dollar (USD) between January 10 and February 8 of a particular year.

Easy

2.On which day shown on the graph did the value of the US dollar increase against the Rupee by the greatest amount?

(A)Jan. 10

(B)Jan. 14

(C)Jan. 21

(D)Jan. 23

(E)Feb. 4

Here, the scale of the x-axis is uniform. Hence, growth is greatest when the curve is steepest. The growth curve of the US dollar against the Indian Rupee is the steepest (increased by a bit more than six horizontal lines on the graph) on January 21. Hence, the answer is (C). On February 5th, the growth is the next greatest, growing by a bit less than 6 horizontal lines.

Medium

3.John had 100 dollars. The exchange rate converts the amount in US dollars to a number in Indian Rupees by directly multiplying by the value of the exchange rate. By what amount did John’s $100 increase in terms of Indian Rupees from Jan. 9 to Feb. 8?

(A)5

(B)10

(C)15

(D)25

(E)50

One dollar converted to 39.1 Rupees on Jan. 9. Hence, 100 dollars converts to 39.15 100 = 3915 Indian Rupees. On February 8, it converted to 39.65 Rupees. Hence, on that day, 100 dollars converted to 39.65 100 = 3965 Rupees. The increase in terms of Indian Rupees is 3965 – 3915 = 50. The answer is (E).

Hard

4.On February 8, the dollar value was approximately what percent of the dollar value on January 9?

(A)1.28

(B)12. 8

(C)101.28

(D)112. 8

(E)128

On January 9, the dollar value was 39.15 Rupees, and on February 8 the dollar value was 39.65 Rupees. Hence, the dollar value on February 8th was 39.65/39.15 100 = (39.15 + 0.5)/39.15 100 =

362 GRE Math Bible

100 + 0.5/39.15 100 = (100 + 1.28) = 101.28 percent of the value on January 9th. Hence, the answer is

(C).

Questions 5–7 refer to the following graph.

Pupil/ Teacher Ratio Vs Percentage of High Schools, January 1998.

21

25 9%

11%

22 10%

Pupil/ Teacher Ratio Vs Percentage of High Schools, January 1999.

4% 22

16%

364GRE Math Bible

7.If the areas of the sectors in the circle graphs are drawn in proportion to the percent shown, what is the measure, in degrees, of the sector representing the number of high schools with Pupil/Teacher ratio greater than 27 in 1999?

(A)21.6

(B)30

(C)45.7

(D)56.3

(E)72

From the chart, in 1999, 6% of schools have a Pupil/Teacher ratio greater than 27. Hence, the fraction of the angle that the sector makes in the complete angle of the circle also equals 6% = 6/100. Since the complete angle is 360°, the part of the angle equals 6/100 360 = 21.6°. The answer is (A).

Questions 8–10 refer to the following graph.

Easy

8.What was the number of security holes fixed in 2003?

(A)1500

(B)1700

(C)4500

(D)6000

(E)6300

From the graph, the number of security holes fixed in 2003 is 4500. The answer is (C).

Medium

9.For which year was the ratio of the Security holes to Bugs fixed by the software company the greatest?

(A)1998

(B)1999

(C)2000

(D)2001

(E)2002

Let’s calculate the ratio and find the year in which the ratio is the greatest:

Choice (A): Year 1998. The number of security holes to bugs fixed is 5000/1500 = 10/3 = 3.33.

366GRE Math Bible

Questions 11–15 refer to the following discussion.

The graphs below provide data on a common entrance examination conducted in different years.

Number of Questions

Time Per Question (in seconds)

CEE Exam Difficulty Level

'D' level (Difficulty level)-out of 10. CEE 2000 is taken as baseThe most difficult of All Exams.

Graphs 367

Easy

11.Which year had the second most difficult exam?

(A)2000

(B)2001

(C)2002

(D)2004

(E)2006

Refer to the graph CEE Exam Difficulty Level. The graph starts at 0 for each exam and ends at 10 for the most difficult exam, CEE 2000. So, the difficulty actually increases with ‘D-level’ value. The second highest value corresponds to the Exam CEE 2001. The answer is (B).

Medium

12.By approximately what percent did the number of questions decrease from CEE 2000 to CEE 2006?

(A)11

(B)22

(C)27

(D)33

(E)37

From the graph, the number of questions in CEE 2000 is 55. The number in CEE 2006 is 40. Hence, the

(C).

Medium

13.In which year were the test takers given the least time to answer all the questions?

(A)2000

(B)2001

(C)2002

(D)2004

(E)2006

The time given can be evaluated as (Number of Questions) (Time Per Question).

Both the number of questions and the time given per question are the least in 2006. Hence, their product should be minimum in that year.

Hence, the total time given is the least in 2006. The answer is (E).

Medium

14.If the Pressure Factor for the examinees in an exam is defined as Difficulty level divided by Average Time (in minutes) given per question, then the Pressure Factor equals which one of the following in CEE 2006?

(A)7.5

(B)10

(C)12.5

(D)15

(E)17.5

The Pressure Factor in 2006 equals Difficulty level divided by Average Time given per question = 5/40 seconds or 5/(2/3 minutes) = 15/2 per minute. The answer is (A).

Graphs 369

Questions 16–19 refer to the following graph.

The table below provides the complete semantics of a Common Entrance Test (CET) conducted in different years.

*The Difficulty Factor of the exam is the sum of the products of the number of questions of each type and the corresponding difficulty level. The Stress Factor is the Difficulty Factor divided by the Average Time Per Question.