ACT Test Math Practice

How many irrational numbers are there between 1 and 6 ?

If you chose this answer, you know 1 and 6 are real numbers and that there are an infinite number of irrational numbers between any two real numbers.

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?

If you divide 2,727 miles by 27 miles per gallon you will get the number of gallons: = 101. Then, multiply the number of gallons by the cost per gallon: 101(4.04) = 408.04. This gives the cost of gas for this car to travel 2,727 typical miles.

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

42 is the correct answer since it is the largest number that is a factor of all three numbers given. You can find the greatest common factor by writing out the prime factorization of all three numbers, and then taking each of the common prime factors to the lowest power that appears for that factor: 42 = 2 × 3 × 7; 126 = 2 × 32 × 7; and 210 = 2 × 3 × 5 × 7. So the greatest common factor is 2 × 3 × 7 = 42.

A typical high school student consumes 67.5 pounds of sugar per year. As part of a new nutrition plan, each member of a track team plans to lower the sugar he or she consumes by at least 20% for the coming year. Assuming each track member had consumed sugar at the level of a typical high school student and will adhere to this plan for the coming year, what is the maximum number of pounds of sugar to be consumed by each track team member in the coming year?

54 is the correct answer. For each member of the track team to consume 20% less sugar, the track member will consume 100% - 20% = 80% of the level of a typical high school student. 80% of 67.5 = 0.80(67.5) = 54

In the figure below, ray was constructed starting from rays and . By using a compas D and G were marked equidistant from E on rays and . 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:

If you draw line segments DF and FG, you can show ΔDEF ≅ ΔGEF by SSS (side-side-side congruence). So, ∠DEF ≅ ∠GEF because corresponding parts of congruent triangles are congruent.

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 + 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?

If you substitute D with 150 in the expression, you get + 4(150) - 250 = + 600 - 250 = 1,250.

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

The question states that PS and QR are parallel. If you treat PQ as a transversal, then ∠P and ∠Q are interior angles on the same side of a transversal, so their measures add up to 180°. Since the measure of ∠P is 70°, the measure of ∠Q is 180° - 70° = 110°.

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?

This is the correct answer. If x = sales for the first year, then x + 3 = sales for the second year. Since sales for the third year were double the sales for the second year, sales for the third year = 2(x + 3). Sales for the third year were 38, so 2(x + 3) = 38. To solve this equation, you could first divide each side by 2 to get x + 3 = 19. Then, by subtracting 3 from both sides, x = 16.

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?

Twice a number means to multiply the number by 2, and 3 less than a number means to subtract 3 from the number. Combining these, you get l = 2w - 3.

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

When you use x = 3 and y = 5 in the given expressions, 3x2 - 2y = 3(3)2 - 2(5) = 27 - 10 = 17 and 2x2 - 3y = 2(3)2 - 3(5) = 18 - 15 = 3. Then subtract 3 from 17 to get 14.

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

You can solve this problem by first subtracting 2x from each side of the equation to get 3 = x - 4. Then add 4 to each side, so x = 7.