| 1- Choice B is correct
The correct answer is \(38\)
The sum of numbers divided by \(7\) give the average of numbers. Then:
\(\frac{210}{7} \ < \ x \ < \ \frac{280}{7}\)
\(30 \ < \ x \ < \ 40\)
From choices provided, only \(38\) is correct.
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| 2- Choice C is correct
The correct answer is \(81\)
\(3^4 = 3 \times 3 \times 3 \times 3 =81 \)
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| 3- Choice A is correct
The correct answer is \( 32\)
Use PEMDAS (order of operation):
\(- \ 20 \ + \ 5 \times (– \ 4) \ – \ \left[ \ 6 \ + \ 25 \ \times (- \ 6) \ \right] \div 2 =\)
\(- \ 20 \ -\ 20 \ - \ \left[\ 6 \ - \ 150 \ \right] \div 2 =\)
\(- \ 40 \ - \ \left[ \ - \ 144 \ \right] \div 2 =\)
\(- \ 40 \ + \ 144 \div 2 = - \ 40 \ + \ 72 = 32\)
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| 4- Choice D is correct
The correct answer is \(\frac{5}{3}\)
A. \(\frac{4}{5} = 0.8\)
B. \(\frac{3}{2} = 1.5\)
C. \(\frac{7}{9} = 0.77\)
D. \(\frac{5}{3} = 1.66\)
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| 5- Choice A is correct
The correct answer is \(200\)
\(50 \times 4 = 200\)
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| 6- Choice C is correct
The correct answer is \(13\)
The difference of each number and the next number is \(4\).
\(\left\{29, \ 25, \ 21, \ 17, \ 13\right\}\)
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| 7- Choice D is correct
The correct answer is \(9\)
\(15 \ a \ + \ 25 = 160 →\)
\(15 \ a = 160 \ - \ 25 →\)
\(15 \ a = 135 →\)
\(a = 9\)
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| 8- Choice C is correct
The correct answer is \(84\)
A. \(\frac{52}{7} = 7.42\)
B. \(\frac{32}{7} = 4.57\)
C. \(\frac{84}{7} = 12\)
D. \(\frac{13}{7} =1.85 \)
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| 9- Choice B is correct
The correct answer is \(56\)
The smallest number that is divisible by both \(8\) and \(14\) is \(56\). LCM \(= 56\)
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| 10- Choice A is correct
The correct answer is \(90\)
\(15 \times 6 = 90\)
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| 11- Choice C is correct
The correct answer is \(18\)
Each worker can walk \(3\) dogs: \(12 \div 4 = 3\)
\(6\) workers can walk \(18\) dogs. \(6 \times 3 = 18\)
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| 12- Choice C is correct
The correct answer is approximately \(42\) hours
Speed \(= \frac{distance }{time}\)
\(60 = \frac{2,500 }{time} →\)
time \(= \frac{2,500 }{60} = 41.66\)
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| 13- Choice B is correct
The correct answer is \(3\)
The factors of \(21\) are: \(\left\{ 1, \ 3, 7 \ , \ 21\right\}\)
The factors of \(30\) are: \(\left\{ 1, \ 2,\ 3 , \ 4 , \ 5 , \ 6 , \ 10 \ , \ 15, \ 30\right\}\)
GCF \(= 3\)
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| 14- Choice B is correct
The correct answer is \(75\)
\(25 \div \frac{1}{3} = 75\)
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| 15- Choice B is correct
The correct answer is \(2\)
The factors of \(12\) are: \(\left\{1, \ 2, \ 3, \ 4, \ 6, \ 12\right\}\)
The factors of \(18\) are: \(\left\{1, \ 2, \ 3, \ 6, 9 ,\ 18\right\}\)
The factors of \(32\) are: \(\left\{1, \ 2, \ 4, 8 ,16 , \ 32\right\}\)
GCF \(= 2\)
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| 16- Choice D is correct
The correct answer is \(30\)
Write a proportion and solve.
\(\frac{5}{25} = \frac{x}{150} →\)
\(x = \frac{5 \times 150}{25} = 30\)
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| 17- Choice A is correct
The correct answer is \(5\)
Ashly \(=\) Billy, Ashly \(= 4\) (Kevin)
Billy \(= 15 \ +\) Kevin
Ashly \(=\) Billy \(→\) Ashly \(= 15 \ +\) Kevin
Ashly \(= 4\) (Kevin) \(→ 4\) (Kevin) \(= 15 \ +\) Kevin \(→ 4\) (Kevin) \(–\) Kevin \(= 15\)
\(3\) (Kevin) \(= 15\), Kevin \(= 5\)
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| 18- Choice C is correct
The correct answer is \(256\)
\(\frac{4^5}{4} = 4^4 = 256\)
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| 19- Choice B is correct
The correct answer is \(21\)
A. \(\frac{12}{6} = 2\)
B. \(\frac{21}{6} = 3.5\)
C. \(\frac{36}{6} = 6\)
D. \(\frac{24}{6} = 4\)
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| 20- Choice C is correct
The correct answer is \(p^5\)
\((p^2) \ . \ (p^3) = p^{2 \ +\ 3} = p^5\)
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| 21- Choice C is correct
The correct answer is \(13\)
A. \(9 → 9\) is not prime. It is divisible by \(3\).
B. \(6 → 6\) is not prime. It is divisible by \(2\).
C. \(13 → 13\) is prime!
D. \(45 → 45\) is not prime. It is divisible by \(3\).
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| 22- Choice B is correct
The correct answer is \(2\)
\(6 \ a \ – \ 3 = 9\)
\(6 \ a = 9 \ + \ 3\)
\(6 \ a = 12\)
\(a = 2\)
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| 23- Choice C is correct
The correct answer is \(9\) feet
\(\frac{(15 \ feet \ + \ 7 \ yards) }{4} = \frac{(15 \ feet \ + \ 21 \ feet ) }{4} = \frac{(36 \ feet ) }{4} = 9\) feet
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| 24- Choice A is correct
The correct answer is \(0\)
\((5.2 \ + \ 3.3 \ + \ 2.5) \ x = x\)
\(11 \ x = x\)
Then \(x = 0\)
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| 25- Choice C is correct
The correct answer is \(2 \ (X \ - \ 7)\)
\(A \ + \ B = X\)
\(A \ + \ 7 = X\)
\(A = X \ -\ 7\)
\(2 \ A = 2 \ (X \ - \ 7)\)
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| 26- Choice B is correct
The correct answer is \(>\)
\(0.325\) is bigger than \(0.0452\).
\(0.325 \ > \ 0.0452\)
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| 27- Choice C is correct
The correct answer is \(26\)
Susy \(=\) Mary \(+ \ 8\)
Mary \(=\) Jimmy \(– \ 4 →\) Jimmy \(=\) Mary \(+ \ 4\)
Jimmy \(+\) Mary \(+\) Sylvia \(= 90\)
(Mary \(+ \ 4) \ +\) Mary \(+\) (Mary \(+ \ 8) = 90\)
\(3\) Mary \(+ \ 12 = 90\)
\(3\) Mary \(= 78\), Mary \(= 26\)
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| 28- Choice D is correct
The correct answer is \(5\) Times
\(5\) hours \(= 300\) minutes
\(\frac{60}{1} = \frac{300}{x} →\)
\(x = \frac{300}{60} = 5\)
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| 29- Choice A is correct
The correct answer is \(18.84\)
Diameter \(= 6\), then: Radius \(= 3\)
C \(= 2 \ π \ r\) , C \(= 6 \ π →\) C \(= 18.84\)
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| 30- Choice C is correct
The correct answer is \(<\)
\(0.632\) is bigger than \(0.0540\).
\(0.524 \ < \ 0.0234\)
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| 31- Choice A is correct
The correct answer is \( \frac{3}{4}\)
\(\frac{1}{x} = \frac{\frac{1}{1}}{\frac{4}{3}} = \frac{3}{4}\)
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| 32- Choice C is correct
The correct answer is \(16\)
The factors of \(40\) are:
\(\left\{ 1, \ 2, \ 4 , \ 5, \ 8 , \ 10, 20 , \ 40\right\}\)
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| 33- Choice A is correct
The correct answer is \(5.5\%\)
\(0.055 \times 100 = 5.5\%\)
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| 34- Choice B is correct
The correct answer is \(6,598.5\)
The number in the tenth place is \(4\).
The number \(6,598.44\) is closer to \(6,598.5\) than \(6,598.4\)
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| 35- Choice C is correct
The correct answer is thousandths
\(3\) is in the thousandths place.
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| 36- Choice C is correct
The correct answer is \(\frac{3}{4}\)
\(\frac{15}{20} = \frac{3}{4}\)
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| 37- Choice D is correct
The correct answer is \(9\)
\(- \ 3 \ + \ 9 = 6\)
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| 38- Choice C is correct
The correct answer is \(0.36\)
\(\frac{8}{22} = 0.36\)
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| 39- Choice B is correct
The correct answer is \(5\)
\(\sqrt{25} = 5\)
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| 40- Choice A is correct
The correct answer is \(81\)
\(a^a \ . \ a = (3)^3 \ . \ 3 = 27\ . \ 3 =81 \)
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| 41- Choice C is correct
The correct answer is \(7.5\)
\(4.5 \ < \ x \ ≤ \ 7.0\), then cannot be equal to \(7.5\)
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| 42- Choice C is correct
The correct answer is \(3\)
\(9 \ + \ 3 \ x \ ≤ \ 18\)
\(3 \ x \ ≤ \ 18 \ – \ 9\)
\(3 \ x \ ≤ \ 9\)
\(x \ ≤ \ 3\)
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| 43- Choice A is correct
The correct answer is \(1 \ \frac{1}{2}\)
The reduced fraction equal to \(1.5\) is \(1 \ \frac{1}{2}\)
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| 44- Choice C is correct
The correct answer is \(0.4\)
\(\frac{2}{5} = 0.4\)
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| 45- Choice D is correct
The correct answer is \(159\) inches
\(1\) feet \(= 12\) inches
\(5\) feet, \(5\) inches \(=65 \) inches
\(7\) feet, \(10\) inches \(= 94\) inches
\(65 \ + \ 94 =159 \) inches
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| 46- Choice A is correct
The correct answer is \(18\)
\(50 \ – \ 32 =18 \)
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| 47- Choice A is correct
The correct answer is \(2\)
\(\frac{1}{6} \ + \ \frac{1}{3} \ + \ \frac{3}{2} =\)
\(\frac{1 \ + \ 2 \ + \ 9}{6} = \frac{12}{6} =2\)
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| 48- Choice D is correct
The correct answer is \(58\)
\(72 \ – \ 14 = 58\)
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| 49- Choice C is correct
The correct answer is \(2\)
Write a proportion and solve.
\(\frac{8}{20} = \frac{x}{5} →\)
\(x = \frac{8 \times 5}{20} = 2\)
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| 50- Choice A is correct
The correct answer is \(1 \ \frac{3}{10}\) Miles
\(\frac{1}{5}\) of the distance is \(6 \ \frac{1}{2}\) miles. Then:
\(\frac{1}{5} \times 6 \ \frac{1}{2} = \frac{1}{5} \times \frac{13}{2} = \frac{13}{10}\)
Converting \(\frac{13}{10}\) to a mixed number gives: \(\frac{13}{10} = 1 \ \frac{3}{10}\)
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| 51- Choice A is correct
The correct answer is \(90\)
\(3\) lab \(= 3 \ (3) \ (2) \ (5) =90 \)
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| 52- Choice B is correct
The correct answer is \(6^{3}\)
\(6 \times 6 \times 6 = 6^{3}\)
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| 53- Choice C is correct
The correct answer is \(\frac{5}{6}\)
\(2 \ \frac{2}{3} \ − \ 1 \ \frac{5}{6} =\)
\(2 \ \frac{4}{6} \ − \ 1 \ \frac{5}{6} =\)
\(\frac{16}{6} \ − \ \frac{11}{6} = \frac{5}{6}\)
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| 54- Choice D is correct
The correct answer is \($32\)
Use interest rate formula:
Interest \(=\) principal \(\times\) rate\( \times\) time
\(= 800 \times 0.04 \times 1= 32\)
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| 55- Choice C is correct
The correct answer is \(16\) years old
Cristina \(= 32\)
Cristina \(= 2\) Ashly
Ashly \(= \frac{32}{2} = 16\)
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| 56- Choice C is correct
The correct answer is \(135\) degrees
Angle \(x\) and angle \(45\) degrees are supplementary angles.
Then: \(180^{◦} \ – \ 45^{◦} = 135^{◦}\)
\(x = 135^{◦}\)
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| 57- Choice C is correct
The correct answer is \(6,864\)
\(312 \times 22 = 6,864\)
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| 58- Choice A is correct
The correct answer is \(77\) cm\(^2\)
A \(= \frac{1}{2} \ b \ h\)
A \(= \frac{1}{2} \ (22) \ (7) = 77\)
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| 59- Choice D is correct
The correct answer is \(720\)
\(6! = 6 \times 5 \times \ 4 \times 3 \times 2 \times 1 = 720\)
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| 60- Choice A is correct
The correct answer is \(1 \times 2 \times 3 \times 4 \times 5\)
\(5! = 5 \times 4 \times 3 \times 2 \times 1\)
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| 61- Choice A is correct
The correct answer is \(\frac{2}{100}\)
\(\frac{2}{100} = 0.02\)
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| 62- Choice D is correct
The correct answer is \(3\)
Oven \(1 = 3\) oven \(2\)
If Oven \(2\) burns \(3\) then oven \(1\) burns \(9\) pizzas.
\(3 \ + \ 9 = 12\)
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| 63- Choice A is correct
The correct answer is \(\frac{1}{6}\)
\(6\) children, \(1\) liter of orange juice
Then each child gets \(\frac{1}{6}\) of litter.
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| 64- Choice C is correct
The correct answer is \(11\)
A. \(12 → 12\) is not prime. It is divisible by \(2\).
B. \(8 → 8\) is not prime. It is divisible by \(2\).
C. \(17 → 17\) is prime!
D. \(33 → 33\) is not prime. It is divisible by \(3\).
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