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7/21/2019 ACT Test3 Answers

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ACT Math Practice Test 1

Test your ACT Math Skills

Here are the results of your quiz:

Correct answers are marked with a , while wrong answers have a next to them.

1 Not

Answered

A size 6 dress that usually sells for $60 is on sale for 30% off. Shondra has a store credit card that gives heran additional 10% off the reduced price of any item. Excluding sales tax, what is the price she pays for thedress?

a) $22.20

b) $24.75

c) $34.00

d) $36.00

e) 37.80Your answer is wrong! The correct answer is "e". Take it step by step. $60 x .30 = $18, which means thedress is discounted to $42. Shondra's second discount: $42 x .10 = $4.20 off the discounted price, whichcomes to $37.80. Choice D is the distracter here, because it discounts the dress at 40%, but that's wrong

because Shondra gets 10% off the reduced price. Read carefully. (more information)

2 Not What is the least common multiple of 25, 16, and 40?
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2/9

Answered

a) 4

b) 32

c) 320

d) 400

e) 16,000Your answer is wrong! The correct answer is "d". First, you have to remember that a least commonmultiple is the smallest number that will divide evenly by 25, 16, and 40. That gets rid of answer choiceA. Then, you just choose one of the larger numbers that's divisible by all three. Can't figure it out in yourhead? Take a guess and do the math - it's easy enough. Answer E is wrong because although it's amultiple of all three, it's not the smallest. (more information)

3 Not

Answered

If a sphere is intersected by two different planes NOT occupying the exact same space, how many sections isit possible to end up with?

a) only 2

b) only 2 or 4

c) only 3

d) only 3 or 4

e) only 2, 3, or 4Your answer is wrong! The correct answer is "d". Imagine cutting an orange. There is no way you cancut an orange with two different planes and get two pieces, so eliminate any choice that has "2" in it.Bye-bye to A, B and E. That leaves choice C and D. We know, easily, that you can get four slices of anorange by cutting it twice (slice the orange in half lengthwise, put the halves back together, slice it in half

idth-wise) so that eliminates choice C, which leaves only D as the correct answer. ( more information)

4 Not

Answered

If y = 0.25(100-y), what is the value of y?

a) 200

b) 75

c) 25

d) 20

e) 18Your answer is wrong! The correct answer is "d". Solve for y, people! Get rid of the .25 by dividing bothsides by it, and you get 4y = 100-y. Add y to both sides to get 5y = 100. Divide by 5 on both sides toisolate the y and you get y = 20. Ta-da (more information)

5 Not

Answered

If y = 4, what does |1-y| = ?

a) -5

b) -3

c) 3

d) 4

e) 5Your answer is wrong! The correct answer is "c". Remember, those two lines indicate absolute value. So,
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3/9

it must always be greater than or equal to zero, you can get rid of choices A and B. Substitute y = 4 intothe expression and you get this: |1-y| = |1-4| =|-3| =3 (more information)

6 Not

Answered

Two similar triangles have perimeters in the ratio of 5:6. The sides of the larger triangle measure 12 in, 7 inand 5 in. What is the perimeter, in inches of the smaller triangle?

a) 18

b) 20

c) 22

d) 24

e) 32Your answer is wrong! The correct answer is "b". First, find the perimeter of the first triangle by addingup the sides = 24 inches. Since you know the ratio, you can set up this ratio and solve for x: 5/6 = x/24. x= 20. (more information)

7 Not

Answered

In triangle XYZ, angle Y is a right angle and angle Z measures less than 52 degrees. Which of the followingphrases best describes the measure of angle X?

a) Greater than 38 degrees

b) Equal to 38 degrees

c) Equal to 45 degrees

d) Equal to 142 degrees

e) Less than 38 degreesYour answer is wrong! The correct answer is "a". The sum of the measures of all angles in a triangle is180 degrees. If Y, a right angle is 90 degrees (by definition), The other two angles must add up to 90degrees to total 180. If angle Z measures less than 52, then angle X has to be greater than 90-52. It can't

be equal to 38 degrees because angle Z is described as less than 52 degrees. Get it? (more information)

8 Not

Answered

A 16-piece orchestra wants to choose one of its members to speak at performances. They decide that thismember CANNOT be one of the 4 soloists in the group. What is the probability that Jonah, who is NOT asoloist, will be chosen as the speaker?

a) 0

b) 1/16

c) 1/12

d) 1/4

e) 1/3Your answer is wrong! The correct answer is "c". Basic probability laws indicate that you have to figureout the part to whole ratio. The question you have to ask yourself is "How many people have a shot as thespeaker?" The answer = 12, because the 4 soloists weren't included in those with a shot. So Jonah, being1 of those 12 people with a shot has a 1 in 12 chance of being selected. Hence, 1/12. ( more information)

9 Not

Answered

For what value of q is the equation 9/q = 6/10 true?

a) 3

b) 5

c) 13

d) 15

e) 19
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4/9

Your answer is wrong! The correct answer is "d". Basic cross-multiplication gets you to 90 = 6q. Divideboth sides by 6 to isolate the q and you get 15. Easy cheesy. (more information)

10 Not

Answered

For the imaginary number i, which of the following is a possible value of i to the nth power if n is an integerless than 5?

a) 0

b) -1

c) -2

d) -3

e) -4Your answer is wrong! The correct answer is "b". Because i is defined as the square root of negative 1, itsrange of possibility when raised to certain powers is limited, and B is the only possibility if you figureout the square root of i to every power under 5. (more information)

11 Not

Answered

What is the sum of the two solutions of the equation xsquared +5x minus 24 = 0?

a) -24

b) -8

c) -5

d) 0

e) 5Your answer is wrong! The correct answer is "c". First, simplify the expression, and you get (x + 8)(x -3). Now, find the solutions by setting each of them equal to 0. If x + 8 = 0, then x = -8. If x3 = 0, thenx = 3. 8 + 3 = -5, or answer C. (more information)

12 Not

Answered

Point X is located at negative 15 on the real number line. If point Y is located at negative 11, what is themidpoint of line segment XY?

a) -13

b) -4

c) -2

d) 2

e) 13Your answer is wrong! The correct answer is "a". The midpoint of the line is the average of the twonumbers, so add them up and divide by two. negative 15 + -11/2 = -13. Or in this case, you could simplydraw out the line and plot the numbers on it, counting toward the middle. ( more information)

13 Not

Answered

While working on a lengthy problem on his calculator, Matt had meant to multiply a number by 3, butaccidentally divided the number 3 instead. Which of the following calculations could he do on his calculatorto obtain the result he originally wanted?

a) Multiply by 3

b) Multiply by 9

c) Divide by 3

d) Divide by 9

e) Add the original numberYour answer is wrong! The correct answer is "b". Matt needs to get back to his original place bycanceling the division by multiplying by 3. Then, he needs to multiply by 3 again to get the correct


5/9

answer, which in essence, is just multiplying by 9, answer B. (more information)

14 Not

Answered

All the following statements about rational and/or irrational numbers must be true EXCEPT:

a) the sum of any two rational numbers is rational

b) the product of any two rational numbers is rational

c) the sum of any two irrational numbers is irrational

d) the product of a rational and an irrational number may be rational or irrational

e) the product of any two irrational numbers is irrational.Your answer is wrong! The correct answer is "e". Remember ona "Must be" type of question, therelationships must be true in all cases. If there is one case in which a relationship is not true, that answerchoice my be wrong. In this case, that one wrong instance is what you're looking for, and since answer Eis often true, but not always, it's the one you'd choose. (more information)

15 Not

Answered

Elvis, the hamster, is running on his wheel when the wheel breaks free of its axis due to a mechanical error.Elvis remains in the wheel, running in a straight line until the weheel has rotated exactly 15 times. If thediameter of the wheel is 10 inches, how many inches has the wheel rolled?

a) 75

b) 150

c) 75pi

d) 150pi

e) 1,500piYour answer is wrong! The correct answer is "d". Since the wheel's diameter is 10, you can find thecircumference of Elvis' wheel C = pi x d = 10pi. This means Elvis' wheel travels 10pi inches in onerotation. Since her wheel rotated 15 times, multiply it by 15. 150pi.y 15. 150pi. ( more information)

16 Not

Answered

If the first day of the year is a Monday, what is the 260th day?

a) Monday

b) Tuesday

c) Wednesday

d) Thursday

e) FridayYour answer is wrong! The correct answer is "a". Here, draw out a mini-calendar until you see a patterndevelop: Day 1 is Mon. 2 is Tues, all the way until you realize that Sundays fall on multiples of 7. So,

pick a multiple of 7 close to 260, such as 259. If Day 259 has to be a Sunday because it's a multiple of 7,then day 260 has to be a Monday. (more information)

17 Not

Answered

Janie has 5 novels and 7 memoirs on the bookshelf in her dorm room. As she collapses on her bed at the endof the night and randomly grabs a book to read, what is the probability that the book she selects is a novel?

a) 1/5

b) 5/7

c) 1/12

d) 5/12

e) 7/12Your answer is wrong! The correct answer is "d". Here, you just make a fraction. The total number of


6/9

novels goes on top and the total number of books goes on the bottom: 5/12, choice D ( moreinformation)

18 Not

Answered

In the Cartesian plane, a line runs through points (1,-5) and (5,10). What is the slope of that line?

a) 4/15

b) 4/5

c) 1

d) 5/4

e) 15/4Your answer is wrong! The correct answer is "e". Don't panic the Cartesian plane is the same old(x,y) plane you're used to. Slope = rise/run, so use the two points given in the slope formula: y2 minusy1/x2 minus x1 = 10 minus (-5) / 5-1 = 10 + 5 / 4 = 15/4 (more information)

19 Not

Answered

Which of the following expressions must be an even integer if x is an integer?

a) x + 5

b) x/4

c) x to the fourth power

d) 4x

e) 5 to the x powerYour answer is wrong! The correct answer is "d". Only D can be correct because the product of an evennumber multiplied by either an even or an odd number will always be even. That's the only instance inthe above samples where it will be true. Don't believe me? Plug in a smattering of numbers in the otherequations and see what you get. (more information)

20 Not

Answered

In the fall semester of her math class, Alissa's test scores were 108, 81, 79, 99, 85, and 82. What was heraverage test score?

a) 534

b) 108

c) 89

d) 84

e) 80Your answer is wrong! The correct answer is "c". To find the average test score, add up all the numbersand divide by the total, which would be 534/6 = 89, choice C. You could immediately eliminate choicesA and B because the average score has to be less than the highest test score. ( more information)

Your Score:You got 0 right out of 20 questions, for a score of 0 percent.Keep Trying

Thanks for taking the ACT Math Test 1!.If you were not ready to take the ACt Math Test, learn more about the ACT first!

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