ACT Math Set One (From ACT.org)

A car averages 27 miles per gallon. If gas costs $4.04 per gallon, which of the following is closest to how much the gas would cost for this car to travel 2,727 typical miles?

• $44.44

• $109.08

• $118.80

• $408.04

• $444.40

When x = 3 and y = 5, by how much does the value of 3x² – 2y exceed the value of 2x² – 3y ?

• 4

• 14

• 16

• 20

• 50

What is the value of x when 2x + 3 = 3x – 4 ?

• -7

• 1

• 7

• -1/5

• 1/5

What is the greatest common factor of 42, 126, and 210 ?

• 42

• 2

• 6

• 14

• 21

Sales for a business were 3 million dollars more the second year than the first, and sales for the third year were double the sales for the second year. If sales for the third year were 38 million dollars, what were sales, in millions of dollars, for the first year?

• 16

• 17.5

• 20.5

• 22

• 35

In the figure below, ray EF was constructed starting from rays ED and EG. By using a compass D and G were marked equidistant from E on rays ED and EG. The compass was then used to locate a point F, distinct from E, so that F is equidistant from D and G. For all constructions defined by the above steps, the measures of ∠DEF and ∠GEF:

• are not equal

• are equal

• sum to 30 degrees

• sum to 45 degrees

• sum to 60 degrees

Abandoned mines frequently fill with water. Before an abandoned mine can be reopened, the water must be pumped out. The size of pump required depends on the depth of the mine. If pumping out a mine that is D feet deep requires a pump that pumps a minimum of (D² /25) + 4D – 250 gallons per minute, pumping out a mine that is 150 feet deep would require a pump that pumps a minimum of how many gallons per minute?

• 1750

• 1250

• 800

• 500

• 362

The length, in inches, of a box is 3 inches less than twice its width, in inches. Which of the following gives the length, l inches, in terms of the width, w inches, of the box?

• l = w + 3

• l = w – 3

• l = 2w + 3

• l = 2w – 3

In quadrilateral PQRS below, sides PS and QR are parallel for what value of x ?

• 158

• 132

• 120

• 110

• 70

How many irrational numbers are there between 1 and 6 ?

• 1

• 3

• 4

• 10

• Infinitely many