ACT math tests 1-4 (crackact.com) (unfinished)

William earned $3,200 per month as a teacher for the ten months from September to June. Then he took a job as a barista at a local café, where he earned $2,000 per month during July and August. What was his average monthly pay for the 12 months? A.$2,400 B.$2,500 C.$2,600 D.$2,800 E.$3,000

E. William earned $3,200 ×10 = $32,000 as a teacher, and he earned $2,000 ×2 = $4,000 as a barista. So he earned $32,000 + $4,000 = $36,000 over the 12 months. Plug these values into the formula for the mean: Mean = Sum of values/number of values= 36,000/12 = 3,000

3. If 5x+ 3 = 10x- 17, what is the value of x? A.1 B.2 C.3 D.4 E.5

Correct Answer: D Explanation: D. Solve for x: 5x + 3= 10x - 17 20 = 5x 4 = x or x = 4

1. Which of the following numbers completes the sequence 3, 8, 14, 21, 29, ___? A.35 B.36 C.37 D.38 E.39

Correct Answer: D Explanation: D. The numbers increase at a somewhat steady rate, so you have to figure out how much you have to add to each number to produce the next in the sequence: 3 + 5= 8; 8 + 6= 14; 14 + 7= 21; 21 + 8= 29, and so on. The rule for the sequence is to add successively larger numbers to each number; therefore, the next number is 29 + 9= 38.

2. Beth got a job painting dorm rooms at her college. At top speed, she could paint 5 identical rooms during one 6-hour shift. How long did she take to paint each room? F.50 minutes G.1 hour and 10 minutes H.1 hour and 12 minutes J.1 hour and 15 minutes K.1 hour and 20 minutes

Correct Answer: H Explanation: Six hours equals 360 minutes, so Beth paints 5 rooms in 360 minutes. She paints 1 room in 360 ÷ 5 = 72 minutes, which equals 1 hour and 12 minutes.

When you multiply a number by 4 and then subtract 7, the result is the same as if you first subtracted 7 from the same number and then multiplied by 11. What is the number? F.10 G.13 H.19 J.23 K.31

F. Let x equal the number and then change the words into an equation and solve for x: 4x- 7 = 11(x- 7) 4x- 7 = 11x- 77 70 = 7x 10 = x

The number 4 is the smallest positive integer that has exactly three factors: 1, 2, and 4. If k is the next-highest integer that also has exactly three factors, what is the sum of the three factors of k? F.13 G.14 H.16 J.18 K.20

F. The greatest of the five possible answers is 20, so kis less than 20. Use trial and error to find the value of k: Factors of 5:1 & 5 Factors of 6:1, 2, 3, & 6 Factors of 7:1 & 7 Factors of 8:1, 2, 4, & 8 Factors of 9:1, 3, & 9 Therefore, k= 9, and the sum of the factors of k is 1 + 3 + 9 = 13.

If a and b are the two values of t that satisfy the equation t^2- 6t + 8 = 0, with a > b,what is the value of a - b? F.2 G.4 H.6 J.8 K.10

Factor the left side of the equation: t2- 6t+ 8 = 0 (t- 2)(t- 4) = 0 Split this equation into two equations and solve: t- 2 = 0 t- 4 = 0 t= 2 t= 4 Thus, a= 4 and b= 2. So a- b= 4 - 2 = 2.

Which of the following is equal to (n- 3)2 if n= 11? A.(n+ 6)(n- 6) B.(n+ 5)(n- 7) C.(n+ 4)(n- 8) D.(n+ 3)(n- 9) E.(n+ 2)(n- 10)

If n= 11, then: (n- 3)2= (11 - 3)2= 82= 64 Substitute 11 for N into each answer until you find one that equals 64: (n+ 5)(n- 7) = (16)(4) = 64

If you multiply two integers together and then add 4, the result is 40. Which of the following could NOT be the sum of the two numbers? F.12 G.13 H.15 J.18 K.20

J. Let the two integers equal x and y,and then create the following equation and simplify: xy+ 4 = 40 xy= 36 So x and y are a pair of integers that equal 36. Try adding all possible combinations of two integers that multiply out to 36: 1 ×36 = 36 1 + 36 = 37 2 ×18 = 36 2 + 18 = 20 3 ×12 = 36 3 + 12 = 15 4 ×9 = 36 4 + 9 = 13 6 ×6 = 36 6 + 6 = 12 This list of sums includes 12, 13, 15, and 20, but not 18. Thus, no pair of integers both satisfies the original equation and adds up to 18.

What is the slope of a line on a standard xy-plane that passes through the point (1, 3) and (4, -3)? A.-1 B. 2 C.-2 D.1/2 E.-1/2

Plug the values for the coordinates into the formula for the slope of a line: Slope = y2 - y1/x2 - x1 = -3-3/4-1= -6/3 = -2 Slope = -2

A square field has an area of 22,500 square feet. To the nearest foot, what is the diagonal distance across the field? F.150 feet G.178 feet H.191 feet J.212 feet K.260 feet

The area of the field is 22,500 square feet, so plug this value into the formula for the area of a square to find the length of the side: A = S^2 22,500 = s^2 150 = S So the side of the field measures 150 feet. The diagonal of a square is the hypotenuse of a 45-45-90 triangle, which has three sides in a ratio of . Thus, the length of this diagonal is 150 sr2 ~ 212

In the following figure, the two horizontal lines are parallel. Which of the following does NOT equal 180°? A.(p+ r)° B.(p+ t)° C.(q+ s)° D.(r+ s+ t)° E.(t+ u)°

∠p and ∠r are opposite angles on the parallel lines, so they total 180°, which rules out Choice (A). The same is true of ∠q and ∠s,ruling out Choice (C). ∠tand ∠uare supplementary, so they add up to 180°, which rules out Choice (E). Finally, ∠r,∠s,and ∠tare all vertical angles with the three interior angles of a triangle, so they total 180°, ruling out Choice (D). By elimination, the correct answer is Choice (B).