GRE Math Practice

From a total of 5 boys and 4 girls, how many 4-person committees can be selected if the committee must have exactly 2 boys and 2 girls?

60

For which values of x is 5x + 9 < 7x + 6? 

Indicate all possible values of x.

7/4, 8/5, 13/8, 26/17

If √28 + √175 = a√b where a and b are integers each greater than one, then what is the value of (a + b)?

14

If 148 tickets had been sold, the total revenue for an event would be three times the cost of sponsoring the event. (Ticket sales was the only source of revenue.)  All tickets were the same price.  

Column A	Column B
the revenue from the sale of 50 tickets	the cost of sponsoring the event

The quantity in Column A is greater

The following tables show the revenues & costs, in thousands of dollars, for a small company in the year 2007.

The CEO has promised that any increase in revenues from investments in 2008 will go toward increasing the R&D budget. Assume that revenues from investments increase by 40% from 2007 to 2008, and that these additional funds are the only change to the R & D budget. By what percent does the R & D budget increase?

28.3%

The following tables show the revenues & costs, in thousands of dollars, for a small company in the year 2007.

Profit = Revenue – Costs. If costs remain constant from 2007 to 2008, and if revenues increase by 10% in that same period, by what percent will profits increase from 2007 to 2008?

34.7%

The following tables show the revenues & costs, in thousands of dollars, for a small company in the year 2007.

Profit is the difference between revenues and costs. If profits increased 20% from 2006 to 2007, the difference between this year's profit and last year's profit is how much?

$50,500

If f(x) = 12 - x² / 2 and f(2k) = 2k, what is one possible value for k?

2

The four small rectangles have the same dimensions

Column A	Column B
DC/BC	4/3

The two quantities are equal

In the figure below, <ADE = 60°,<EFC = 40°, and <DAE = 55°.  If AB is parallel to CD, what is the value of x?

Note: Figure not drawn to scale

75

A horse is placed in a rectangular pen measuring 10 feet by 5 feet. Two scarecrows, P and Q, are placed on opposite corners of the pen.

Column A	Column B
The distance between the two scarecrows	The distance between the horse and P plus the distance between the horse and Q

The relationship cannot be determined from the information given

In the xy-coordinate system, the distance between points (2√3,− √2) and (5√3,3√2) is approximately

7.7

 x³ > x

x² – x > 0

Which of the following intervals could contain x? Indicate all such intervals.

-1 < x < 0 & 1 < x < 2

The sum of the pre-tax costs of Item A and Item B is $300. In Alumba, each item would be charged a flat 7%. In Aplandia, Item A is subject to 5% tax and Item B is subject to 10% tax. If the tax in Aplandia on the purchase of both items is exactly $3 more than it is in Alumba, then what is the pre-tax price of Item A? 

$120

a + b < 10

a² + b² > 81

Column A	Column B
b	10

The relationship cannot be determined from the information given.

Thomas has $9,600, which he invests in two accounts: a bank account earning 2% simple annual interest and a real estate fund earning 8% simple annual interest. At the end of one year, the real estate fund has earned twice as much interest as the bank account. What is the total interest earned from both accounts?

$384

Truck A travels x miles in t + 2 hours, and truck B travels 2x miles in 4t hours.

Column A	Column B
The speed of truck A in miles per hour	The speed of truck B in miles per hour

The relationship cannot be determined from the information given

1. The two charts below summarize 2013 information for the 44 nations that occupy the continent of Europe.  (The diagram excludes Russia, which occupies both Europe & Asia.) The top chart includes "larger" nations (populations > 500,000), and the bottom chart includes "smaller" nations (populations < 500,000).  Those nations in the "NATO member" row, as of 2013, were members of the NATO military alliance. Those nations in the "Euro" column, as of 2013, used the Euro as their primary currency.

   

             

What is the least number of nations currently not members of NATO that would have to join NATO so that more than 50% of the nations in Europe would be members of NATO?

2

The two charts below summarize 2013 information for the 44 nations that occupy the continent of Europe.  (The diagram excludes Russia, which occupies both Europe & Asia.) The top chart includes "larger" nations (populations > 500,000), and the bottom chart includes "smaller" nations (populations < 500,000).  Those nations in the "NATO member" row, as of 2013, were members of the NATO military alliance. Those nations in the "Euro" column, as of 2013, used the Euro as their primary currency.

                

Of the European nations with national populations more than half a million people, approximately what percent are neither members of NATO nor primary users of the euro?

31%

The two charts below summarize 2013 information for the 44 nations that occupy the continent of Europe.  (The diagram excludes Russia, which occupies both Europe & Asia.) The top chart includes "larger" nations (populations > 500,000), and the bottom chart includes "smaller" nations (populations < 500,000).  Those nations in the "NATO member" row, as of 2013, were members of the NATO military alliance. Those nations in the "Euro" column, as of 2013, used the Euro as their primary currency.

                

Approximately what percent of nations in Europe have a national population less than 500,000 people?

18%

The two charts below summarize 2013 information for the 44 nations that occupy the continent of Europe.  (The diagram excludes Russia, which occupies both Europe & Asia.) The top chart includes "larger" nations (populations > 500,000), and the bottom chart includes "smaller" nations (populations < 500,000).  Those nations in the "NATO member" row, as of 2013, were members of the NATO military alliance. Those nations in the "Euro" column, as of 2013, used the Euro as their primary currency.

                

Of all the nations with populations greater than 500,000 who are not members of NATO, approximately what percent of them use the euro as their primary currency?

35%

The two charts below summarize 2013 information for the 44 nations that occupy the continent of Europe.  (The diagram excludes Russia, which occupies both Europe & Asia.) The top chart includes "larger" nations (populations > 500,000), and the bottom chart includes "smaller" nations (populations < 500,000).  Those nations in the "NATO member" row, as of 2013, were members of the NATO military alliance. Those nations in the "Euro" column, as of 2013, used the Euro as their primary currency.

                

How many nations in Europe have a population more than 500,000, are members of NATO, and do not use the euro as their primary currency?

9

The two charts below summarize 2013 information for the 44 nations that occupy the continent of Europe.  (The diagram excludes Russia, which occupies both Europe & Asia.) The top chart includes "larger" nations (populations > 500,000), and the bottom chart includes "smaller" nations (populations < 500,000).  Those nations in the "NATO member" row, as of 2013, were members of the NATO military alliance. Those nations in the "Euro" column, as of 2013, used the Euro as their primary currency.

                

Consider the single nation in the upper right-hand box of the lower chart.  This has to be which of the following nations?

Iceland (population = 103,000); NATO member; primary currency = krona

A is the center of the circle, and the length of AB is 4√2. The blue shaded region is a square. What is the area of the shaded region?

16(4−π)