| 1- Choice B is correct
The correct answer is 286
\(5 \ × \ 36 \ + \ 8 \ × \ 12 \ + \ 10 \ = \ 286\)
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| 2- Choice A is correct
The correct answer is \(33\)
Let x be the integer. Then:
\(3\ x \ + \ 7 \ = \ 106\)
reduce \(7\) both sides: \(3\ x \ = \ 99\)
Divide both sides by \(3\): \(x \ = \ 33\)
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| 3- Choice B is correct
The correct answer is \((200) \ (0.90) \ (0.75)\)
To find the discount, multiply the number by (\(100\)% – rate of discount).
Therefore, for the first discount we get: \((200) \ (100\)% \( – \ 10\)%) \( = \ (200) \ (0.90) \ = \ 180\)
For the next \(25%\) discount: \((200) \ (0.90) \ (0.75)\)
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| 4- Choice D is correct
The correct answer is \((5 \ , \ 3)\)
A. \((4 , 1)\) : \(3 \ (4) \ + \ 5 \ (1) \ = \ 17 \)
B. \((3 , 2)\) : \(3 \ (3) \ + \ 5 \ (2) \ = \ 19 \)
C. \((4 , 3)\) : \(3 \ (4) \ + \ 5 \ (3) \ = \ 27 \)
D. \((5 , 3)\) : \(3 \ (5) \ + \ 5 \ (3) \ = \ 30 \)
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| 5- Choice D is correct
The correct answer is \(-\ 25\)
Use PEMDAS (order of operation):
\(7 \ + \ 4 \ × \ (–\ 3) \ – \ [5 \ + \ 11 × \ 5] \ ÷ \ 3 \ = \ 7 \ + \ 4 \ × \ (–\ 3) \ – \ [4 \ + \ 55] \ ÷ \ 3 \ =\)
\( 7 \ + \ 4 \ × \ (–\ 3) \ – \ [60] \ ÷ \ 3 \ = \ 7 \ + \ (-\ 12) \ – \ 20 \ = \ –\ 5 \ –\ 20 = –\ 25\)
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| 6- Choice D is correct
The correct answer is \(30\)%
Use this formula: Percent of Change
\(\frac{New\ Value \ - \ Old \ Value}{Old \ Value}\) \(× \ 100\)%
\(\frac{21000 \ - \ 30000}{30000}\) \(× \ 100\)% \(= \ 30\)% and \(\frac{14700 \ - \ 21000}{21000}\) \(× \ 100\)% \(= \ 30\)%
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| 7- Choice A is correct
The correct answer is \(360\)
If the length of the box is \(30\), then the width of the box is one-fifth of it, \(6\)
and the height of the box is \(2\) (one-third of the width). The volume of the box is:
V \(=\) lwh \(=\) \((30) \ (6) \ (2) \ = \ 360\)
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| 8- Choice B is correct
The correct answer is \(25\)%
Write the equation and solve for B:
\(0.20 \ A \ = \ 0.80 \ B\), divide both sides by \(0.80\), then:
\(\frac{0.20}{0.80} A \ = \ B\), therefore:
\(B = \frac{1}{4} A\), and \(B\) is \(\frac{1}{4}\) times of \(A\) or it’s \(25\)% of \(A\).
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| 9- Choice D is correct
The correct answer is \(70\)
To find the number of possible outfit combinations, multiply the number of options for each factor:
\(7 \ × \ 2 \ × \ 5 \ = \ 70\)
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| 10- Choice A is correct
The correct answer is \(50\) feet
The relationship among all sides of special right triangle
\(30^\circ\ -\ 60^\circ\ -\ 90^\circ\) is provided in this triangle:
In this triangle, the opposite side of \(30^\circ\) angle is half of the hypotenuse.
Draw the shape for this question:
The latter is the hypotenuse. Therefore, the latter is \(50\) ft.
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| 11- Choice A is correct
The correct answer is \(8\)
Let \(x\) be the number. Write the equation and solve for \(x\).
\((48 \ – \ x) \ ÷ \ x \ = \ 5\)
Multiply both sides by x.
\((48 \ – \ x) \ = \ 5\ x\), then add x both sides:
\(48 \ = \ 6\ x\), now divide both sides by \(6\):
\(x \ = \ 8\)
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| 12- Choice D is correct
The correct answer is \(36\)
The sum of supplement angles is \(180\) . Let \(x\) be that angle.Therfore,
(\(x \ + \ 4\ x) \ = \ 180\)
\(5\ x \ = \ 180\), divide both sides by \(5\):
\(x \ = \ 36\)
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| 13- Choice B is correct
The correct answer is \(2 \ : \ 3\)
The average speed of john is: \(200 \ ÷ \ 5 \ = \ 40\) km
The average speed of Alice is: \(240 \ ÷ \ 4 \ = \ 60\) km
Write the ratio and simplify.
\(40 \ : \ 60\) ⇒ \(2 \ : \ 3\)
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| 14- Choice A is correct
The correct answer is \(18\%\)
The percent of girls playing tennis is: \(30\%\) × \(60\%\) = \(0.30\) × \(0.60\) = \(0.18\) = \(18\%\)
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| 15- Choice D is correct
The correct answer is \(0\)
Solving Systems of Equations by Elimination
\(2\ x \ - \ y \ = \ -\ 3\)
\(4\ x \ + \ 2\ y \ = \ 6\)
Multiply the first equation by \(2\), then add it to the second equation.
\(2\ (2\ x \ - \ y \ = -\ 3\))
\(4\ x \ + \ 2\ y \ = \ 6\)
\(⇒\)
\(4\ x \ - \ 2\ y \ = -\ 6\)
\(4\ x \ + \ 2\ y \ = 6⇒8\ x = 0 ⇒ x = 0\)
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| 16- Choice A is correct
The correct answer is \(310\)
Add the first \(5\) numbers. \(20\) + \(45\) + \(40\) + \(35\) + \(50\) = \(190\)
To find the distance traveled in the next \(2\) hours, multiply the average by the number of hours.
Distance = Average \(×\) Rate = \(60\) \(×\) \(2\) = \(120\)
Add both numbers. \(120\) + \(190\) = \(310\)
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| 17- Choice A is correct
The correct answer is \(6\) hours and \(24\) minutes
Use the distance formula:
Distance \(=\) Rate \(×\) time \(⇒\) \(320\) = \(50\) \(×\) T , divide both sides by \(50\) . \(320\) \(÷\) \(50\) \(=\) T \(⇒\) T \(=\) \(6.4\) hours.
Change hours to minutes for the decimal part. \(0.4\) hours \(=\) \(0.4\) \(×\) \(60\) \(=\) \(24\) minutes
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| 18- Choice B is correct
The correct answer is \(9899\)
Smallest \(3\)–digit number is \(100\) and biggest \(4\)–digit number is : \(9999\)
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| 19- Choice D is correct
The correct answer is \(1024\)
\(4^5\) \(=\) \(4\) \(×\) \(4\) \(×\) \(4\) \(×\) \(4\) \(×\) \(4\) \(=\) \(1024\)
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| 20- Choice C is correct
The correct answer is \(5\)
Use Pythagorean Theorem: \(a^2\) \(+\) \(b^2\) \(=\) \(c^2\)
\(3^2\) \(+\) \(4^2\) \(=\) \(c^2\) \(⇒\) \(25\) \(=\) \(c^2\) \(⇒\) \(c\) \(=\) \(5\)
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| 21- Choice D is correct
The correct answer is \(300\)
The ratio of boy to girls is \(3\):\(5\) .
Therefore, there are \(3\) boys out of \(8\) students.
To find the answer, first divide the total number of students by \(8\), then multiply the result by \(3\)
\(800\) \(÷\) \(8\) \(=\) \(100\) \(⇒\) \(100\) \(×\) \(3\) \(=\) \(300\)
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| 22- Choice A is correct
The correct answer is \(200\)
Use percent formula\(:\)
Part \(=\) \(\frac{percent}{100}\) \(×\) whole
\(30\) \(=\) \(\frac{percent}{100}\) \(×\) \(15\) \(⇒\) \(30\) \(=\) \(\frac{percent × 15}{100}\) multiply both sides by \(100\)
\(3000\) \(=\) percent \(×\) \(15\), divide both sides by \(15\)
percent \(=\) \(200\)
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| 23- Choice D is correct
The correct answer is \(260\)
Therefore, the missing side (height) is \(=\) \(64\) \(-\) \(18\) \(-\) \(12\) \(-\) \(14\) \(=\) \(20\)
Area of a trapezoid: A \(=\frac{1}{2} \ h \ (b_1 \ +\ b_2) = \frac{1}{2}\ (20)\ (12\ +\ 14) = 260\)
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| 24- Choice B is correct
The correct answer is \(64\)
Let \(x\) be the number. Write the equation and solve for \(x\)
\(\frac{2}{3}\) \(×\) \(24\) \(=\) \(\frac{1}{4}\) . \(x\) \(⇒\) \(\frac{2
× 24}{3}\) \(=\) \(\frac{x}{4}\)
use cross multiplication to solve for \(x\).
\(4\) \(×\) \(48\) \(=\) \(3\ x\) \(⇒\) \(192\) \(=\) \(3\ x\) \(⇒\) \(x\) \(=\) \(64\)
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| 25- Choice A is correct
The correct answer is \(78\)%
To find the discount, multiply the number by (\(100\)% – rate of discount).
Therefore, for the first discount we get: (D) (\(100\% – (25)\%) \)= (D) (\(0.75) = (0.75\) D)
For increase of \(5\%: (0.75\) D) (\(100\% \ + \ 5\%)= (0.75\)D) (\(1.05\)D) \(=0.78\)D \(= (78\%) \)of D
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| 26- Choice C is correct
The correct answer is \(14\ π\)
Use the formula of area of circles.
Area \(=\) \(π\)\(r^2\) \(⇒\) \(49\)\(π\) \(=\) \(π\)\(r^2\) \(⇒\) \(49\) \(=\) \(r^2\) \(⇒\) \(r\) \(=\) \(7\)
Radius of the circle is \(7\). Now, use the circumference formula\(:\)
Circumference\(=\) \(2\ π\ r\) \(=\) \(2\ π\ (7)\) \(=\) \(14\ π\)
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| 27- Choice B is correct
The correct answer is \(30\)%
Use the formula for Percent of Change:
Part \(=\) \(\frac{New Value - Old Value}{Old Value}\) \(×\) \(100\)%
\(\frac{35 - 50}{50}\) \(×\) \(100\)% \(=\) \(-30\)% (negative sign here means that the new price is less than old price).
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| 28- Choice B is correct
The correct answer is: \( I >\) \(1900\ x\) \(+\) \(25000\)
Let \(x\) be the number of years. Therefore, \($1900\) per year equals \(1900x\).
starting from \($25000\) annual salary means you should add that amount to \(1900x\).
Income more than that is:
\(I >\) \(1900\ x\) \(+\) \(25000\)
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| 29- Choice D is correct
The correct answer is \(150\)
The question is this: \(1.5\) is what percent of \(1\)\(?\)
Use percent formula:
\(Part\) \(=\) \(\frac{percent}{100}\) \(×\) whole
\(1.5\) \(=\) \(\frac{percent × 1 }{100}\) \(⇒\) \(150\) \(=\) percent \(×\) 1 \(⇒\) percent = \(\frac{150}{1}\) = \(150\)
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| 30- Choice B is correct
The correct answer is \(100\)
Use the information provided in the question to draw the shape.
Use Pythagorean Theorem: \(a^2\) \(+\) \(b^2\) = \(c^2\)
\(80^2\) \(+\) \(60^2\) \(=\) \(C^2\) \(⇒\) \(6400\) \(+\) \(3600\) \(=\) \(C^2\) \(⇒\) \(10000\) \(=\) \(C^2\) \(⇒\) \(C\) \(=\) \(100\)
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| 31- Choice B is correct
The correct answer is \(6\)
Some of prime numbers are: \(2\), \(3\), \(5\), \(7\), \(11\), \(13\)
Find the product of two consecutive prime numbers:
\(2\) \(×\) \(3\) = \(6\) (bingo!)
\(3\) \(×\) \(5\) = \(15\) (not in the options)
\(13\) \(×\) \(11\) \(=\) \(143\) (not in the options)
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| 32- Choice A is correct
The correct answer is \(26.2\%\)
The question is this: \($620\) is what percent of \($840\) ?
Use percent formula:
\(Part\) \(=\) \(\frac{percent}{100}\) \(×\) whole
\(620\) \(=\) \(\frac{percent}{100}\) \(×\) \(840\) \(⇒\) \(620\) \(=\) \(\frac{percent × 840}{100}\) \(⇒\) \(62000\) \(=\) percent \(×\) \(840\) \(⇒\)
percent \(=\) \(\frac{62000}{840}\) \(=\) \(73.8\)
\(620\) is \(73.8\)% of \(840\). Therefore, the discount is: \(100\)% \(-\) \(73.8\)% \(=\) \(26.2\)%
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| 33- Choice C is correct
The correct answer is \(20\)
If the score of Mia was \(80\), therefore the score of Ava is \(40\).
Since the score of Emma was half that of Ava, therefore, the score of Emma is \(20\).
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| 34- Choice A is correct
The correct answer is \(\frac{23}{24}\)
If \(23\) balls are removed from the bag at random, there will be one ball in the bag.
The probability of choosing a brown ball is \(1\) out of \(24\). Therefore, the probability of not choosing a brown ball is
\(23\) out of \(24\) and the probability of having not a brown ball after removing \(23\) balls is the same.
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| 35- Choice D is correct
The correct answer is \(38\)
Let \(x\) be the smallest number. Then, these are the numbers:
\(x\) , \(x\) \(+\) \(1\) , \(x\) \(+\) \(2\) , \(x\) \(+\) \(3\) , \(x\) \(+\) \(4\)
average = \(\frac{sum \ of \ terms }{number \ of \ terms}\) \(⇒\) \(40\) = \(\frac{sum \ of \ terms }{5}\) \(⇒\) \(40\) = \(\frac{5\ x \ +\ 10 }{5}\) \(⇒\)
\(200 = 5\ x+ 10 ⇒ 190 = 5\ x ⇒ x = 38\)
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| 36- Choice C is correct
The correct answer is \(16\)
The area of the floor is: \(8\) cm × \(32\) cm = \(256\) cm\(^2\)
The number of tiles needed = \(256\) \(÷\) \(16\) = \(16\)
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| 37- Choice C is correct
The correct answer is \(11.52\) kg
The weight of \(14.4\) meters of this rope is: \(14.4\ ×\ 800\) \(= 11520\)g
\(1\) kg \(= 1000\) g, therefore, \(11520\) g \(÷\ 1000 = 11.52\) kg
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| 38- Choice A is correct
The correct answer is \(400\)
\(10\)% of the volume of the solution is alcohol. Let \(x\) be the volume of the solution.
Then: \(10\)% of \(x = 40\) ml \(⇒\) \(0.1\ x= 40\) \(⇒\) \(40\) \(÷\) \(0.1= 400\)
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| 39- Choice B is correct
The correct answer is \(63.2\)
average = \(\frac{sum \ of \ terms }{number \ of \ terms}\)
The sum of the weight of all girls is: \(24\) \(×\) \(56\) = \(1344\)
The sum of the weight of all boys is: \(36\) \(×\) \(68\) = \(2448\)
The sum of the weight of all students is: \(2448\) \(+\) \(1344\) = \(3792\)
average = \(\frac{3792 }{60}\)= = \(63.2\)
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| 40- Choice C is correct
The correct answer is : \(500\)
Let\(x\) be the original price.
If the price of a laptop is decreased by \(20\)% to $\(400\), then:
\(80\)% of \(x\) = \(400\) \(⇒\) \(0.8\ x\) = \(400\) \(⇒\) \(x\) = \(400\) \(÷\) \(0.8\) = \(500\)
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| 41- Choice A is correct
The correct answer is : \(11\)
Write the numbers in order:
\(3\),\(10\),\(11\),\(14\),\(20\)
Since we have \(5\) numbers (\(5\) is odd), then the median is the number in the middle, which is \(11\).
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| 42- Choice D is correct
The correct answer is : \(2813.44\)
Surface Area of a cylinder \(= 2\ π\ r \ (r \ + \ h)\) ,
The radius of the cylinder is \(14\) inches and its height is \(18\) inches. \(π\) is about \(3.14\). Then:
Surface Area of a cylinder = \(( 2) \ (π) (14\)) (\(14 \ + \ 18) = 896 \ π = 2813.44\)
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| 43- Choice D is correct
The correct answer is: \(46\)
average = \(\frac{sum \ of \ terms}{number \ of\ terms}\) \(⇒\) \(24\) \(=\) \(\frac{13 + 15 + 22 + x}{4}\) \(⇒\) \(96\) \(=\) \(50 + x\)
\(⇒\) \(x =46 \)
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| 44- Choice C is correct
The correct answer is :\(1440\)
Let \(x\) be the original price.
If the price of the shoe is decreased by \(50\%\) to \($720\), then:
\(50\)% of \(x\) \(=\) \(720\) ⇒ \(0.5\ x= 720\) \(⇒\) \(x\) \(=\) \(720\ ÷ \ 0.5= 1440\)
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| 45- Choice A is correct
\(y\ ≤\ x\ +\ 4\)
\(2\ x\ +\ y\ ≤\ -\ 4\)
A.Point \((–\ 4,\ –\ 4)\) is in the solution section. Let’s check the point in both inequalities.
\(–\ 4\ ≤\ –\ 4\ +\ 4\), It works
\(2\ (–\ 4)\ +\ (–\ 4)\ ≤\ –\ 4 ⇒ –\ 12\ ≤\ –\ 4\), it works (this point works in both)
B.Let’s choose this point \((0,\ 0)\)
\(0\ ≤\ 0\ +\ 4\), It works
\(2\ (0)\ +\ (0)\ ≤\ –\ 4\), That’s not true!
C. Let’s choose this point \((–\ 5,\ 0)\)
\(0\ ≤\ –\ 5\ +\ 4\), That’s not true!
D.Let’s choose this point \((0,\ 5)\)
\(5\ ≤\ 0\ +\ 4\), That’s not true!
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| 46- Choice D is correct
The correct answer is: \(3000\)
Use simple interest formula:
\(I =p\ r\ t\)
(\(I = \)interest, \(p =\) principal, \(r =\) rate, \(t =\) time)
\(I =\) \((20000)\)(\(0.03)( 5)= 3000\)
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