| 1- Choice C is correct
The correct answer is \(9\)
\(2 \times\) M \(+\) N \(= 18\), then M \(+\) N \(= 9\). M \(> \ 0→\) N could not be \(9\)
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| 2- Choice C is correct
The correct answer is \(\frac{7}{2} \)
\(\frac{10}{6} = \frac{5}{3} = 3.33\), the only choice that is greater than \(3.33\) is \(\frac{7}{2}\).
(Recall that \(\frac{1}{32} = 0.5\)..)
\(\frac{7}{2}=3.5 \ ,3.5 \ > \ 3.33\)
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| 3- Choice C is correct
The correct answer is \(4\)
The closest to \(4.07\) is \(4\) in the choices provided.
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| 4- Choice D is correct
The correct answer is: Greater than \(24\)
If \(\frac{1}{4}\) of a number is greater than \(6\), the number must be greater than \(24\).
\(\frac{1}{4} \ x \ > \ 6 →\) multiply both sides of the inequality by \(4\), then: \(x \ > \ 24\)
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| 5- Choice A is correct
The correct answer is \(5\)
A represents digit \(5\) in the multiplication.
\(11 \times 456 = 5,016\)
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| 6- Choice B is correct
The correct answer is \(4.56\)
\(9.5 \ - \ 5.02 = 4.48\), which is closest to \(4.56\)
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| 7- Choice C is correct
The correct answer is \(57\)
The ratio of lions to tigers is \(8\) to \(6\) or \(4\) to \(3\) at the zoo.
Therefore, total number of lions and tigers must be divisible by \(7\).
\(4 \ + \ 3 = 7\)
From the numbers provided, only \(57\) is not divisible by \(7\)..
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| 8- Choice A is correct
The correct answer is \(40\)
Let \(x\) be the number. Then:
\(8 \ + \ x = 24 →\)
\(x = 16 →\)
\(16 \ + \ 24 = 40\)
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| 9- Choice D is correct
The correct answer is \((N \ + \ 3)\)
N is even. Let’s choose \(2\) and \(4\) for N.
Now, let’s review the choices provided.
A. \(\frac{N}{2} = \frac{2}{2} = 1, \ \frac{N}{2} = \frac{4}{2} = 2\), One result is odd and the other one is even.
B. \(N \ + \ 2 = 2 \ + \ 2 = 4 , \ 4 \ + \ 2 = 6\) Both results are even.
C. \(4 \ N = 4 \times 2 = 8, \ 4 \times 4=16\) Both results are even.
D. \(N \ + \ 3 = 2 \ + \ 3 = 5, \ 4 \ + \ 3 = 7\) Both results are odd.
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| 10- Choice C is correct
The correct answer is \(1\)
The value of digit \(4\) in both numbers \(x\) and \(y\) are in the tens place.
Therefore, they have the same value.
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| 11- Choice B is correct
The correct answer is \((3 \ x \ - \ 4)\)
\(15 = x \times 5 → x = 15 \div 5 = 3\)
\(x\) equals to \(3\). Let’s review the options provided:
A. \(x \ +\ 5 → 3 \ + \ 5 = 8\) \(15\) is not divisible by \(8\).
B. \(3 \ x\ - \ 4 → 3 \times 3 \ - \ 4 = 5\) \(15\) is divisible by \(5\).
C. \(10 \ - \ x → 10 \ - \ 3 = 7\) \(15\) is not divisible by \(7\).
D. \( x \times 2 → 3 \times 2 = 6\) \(15\) is not divisible by \(6\).
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| 12- Choice B is correct
The correct answer is \(\frac{10}{3}\)
\(\frac{3 \ + \ 4 \ + \ 2 \ \times \ 2 \ + \ 2}{2 \ + \ 4}=\frac{20}{6} = \frac{10}{3}\)
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| 13- Choice A is correct
The correct answer is \(\frac{5 \times 1}{3}\)
\(\frac{2}{3} \times \frac{5}{2} = \frac{10}{6} = \frac{5}{3}\)
\(\frac{5 \times 1}{3} = \frac{5}{3}\)
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| 14- Choice D is correct
The correct answer is \(9\)
\(x \ - \ 10 =14 → x = 4\)
\(12 \ + \ y = 17 → y= 5\)
\(x \ +\ y = 4 \ + \ 5 = 9\)
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| 15- Choice A is correct
The correct answer is \(16\)
\(4 \times 5 \times 8 \times 2\) is equal to the product of \(20\) and \(16\).
\((4 \times 5) \times (8 \times 2) = 20 \times 16\)
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| 16- Choice C is correct
The correct answer is (\(6\) degrees below zero)
\(16 \ -\ 22 = - \ 6\)
The temperature at midnight was \(6\) degrees below zero.
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| 17- Choice C is correct
The correct answer is (side \(\times\) side)
area of a square \(=\) side \(\times\) side
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| 18- Choice B is correct
The correct answer is \(7\)
\(4 \ + \ 3 \ N = 25 →\)
\(3 \ N = 25 \ - \ 4 = 21 →\)
\(N = 7\)
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| 19- Choice A is correct
The correct answer is \(21\) cm\(^2\)
Area of a triangle \(= \frac{1}{2} \times\) (base) \(\times\) (heiht)
\(= \frac{1}{2} \times 6 \times 7= 21\)
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| 20- Choice D is correct
The correct answer is \(28\)
First, find the pattern,
\(3 \ +\ 3 = 6 →\)
\(6 \ +\ 4 = 10 →\)
\(10 \ + \ 5 = 15 →\)
\(15 \ + \ 6 = 21\)
The difference of two consecutive numbers increase by \(1\).
The difference of \(15\) and \(21\) is \(6\).
So, the next number should be \(28\).
\(21 \ +\ 7 = 28\)
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| 21- Choice A is correct
The correct answer is \(3\)
An equilateral triangle has \(3\) lines of symmetry.
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| 22- Choice B is correct
The correct answer is (\(2 \ + \ 3 ) \times 2 = 12\)
Let’s review the options provided:
A. \(3 \times 5 = 15\) This is true!
B. \((2 \ + \ 3) \times 2 = 12→2 \ + \ 3 \times 2 = 10\) This is not true!
C. \(10 \div (7 \ - \ 2) = 2\) This is true!
D. \(5 \times (6 \ -\ 2) = 20 → 5 \times 4 = 20\) This is true!
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| 23- Choice A is correct
The correct answer is \(\frac{3}{8}\)
There are \(6\) red ball and \(16\) are total number of balls.
Therefore, probability that Ann will pick out a red ball from the basket is \(6\) out of \(16\) or \(\frac{6}{6 \ + \ 10} = \frac{6}{16} = \frac{3}{8}\).
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| 24- Choice B is correct
The correct answer is \(0.14\)
\(\frac{3}{7} \ - \ \frac{2}{7} = \frac{1}{7} = 0.14\)
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| 25- Choice C is correct
The correct answer is \(17.8\)
average \(= \frac{sum \ of \ all \ numbers}{number \ of \ numbers} = \frac{5 \ + \ 8 \ + \ 11\ + \ 27 \ + \ 38}{5} = 17.8\)
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| 26- Choice D is correct
The correct answer is \(45\)
\(15\) percent of \(300 = 15\%\) of \(300 = \frac{15}{100} \times 300=45\)
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| 27- Choice A is correct
The correct answer is \(36\)
The shape has \(6\) equal sides.
And is side is \(6\).
Then, the perimeter of the shape is:
\(6 \times 6 = 36\)
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| 28- Choice C is correct
The correct answer is \(16\)
Four people can paint \(4\) houses in \(10\) days.
It means that for painting \(8\) houses in \(10\) days we need \(8\) people.
To paint \(8\) houses in \(5\) days, \(16\) people are needed.
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| 29- Choice C is correct
The correct answer is \(19\)
\(N = 3\), then: \(\frac{42}{3} \ +\ 5 = 14 \ + \ 5 = 19\)
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| 30- Choice A is correct
The correct answer is \(12\)
Write the numbers in order:
\(2, \ 6, \ 9, \ 12, \ 14, \ 17, \ 19\)
Median is the number in the middle.
Therefore, the median is \(12\).
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| 31- Choice C is correct
The correct answer is \(4,352.5\)
\(4,352.47546\) rounded to the nearest tenth is \(4,352.5\)
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| 32- Choice C is correct
The correct answer is (\(160\) Pounds)
\(142 \ + \ 12 \ + \ 6 = 160\)
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| 33- Choice C is correct
The correct answer is \(400\)
The biggest city is city C and the smallest city is city B.
Number of men in city A is \(700\) and number of men in city C is \(300\).
Then: \(700 \ –\ 300 = 400\)
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| 34- Choice D is correct
The correct answer is \(2\)
\(15 \ a \ +\ 25 = 55\)
\(15 \ a = 55 \ -\ 25\)
\(15 \ a = 30\)
\(a = 2\)
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| 35- Choice B is correct
The correct answer is \(72\)
There are equal numbers of four types of cards.
Therefore, the total number of cards must be divisible by \(4\).
Only choice C \((72)\) is divisible by \(4\).
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| 36- Choice A is correct
The correct answer is \(65\)
All angles in a triangle sum up to \(180\) degrees.
Two angles of a triangle measure \(40\) and \(75\).
\(40 \ + \ 75 = 115\)
Then, the third angle is:
\(180 \ – \ 115 =65 \)
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| 37- Choice B is correct
The correct answer is \(\frac{7}{21}\)
There are equal
From the choice provided, only choice B is not equal to \(\frac{3}{5}\).
\(\frac{7}{21} = \frac{1}{3}\)
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| 38- Choice B is correct
The correct answer is \(50\)
\(30\) seconds is one second of a minute.
One second of \(100\) is \(50\).
\(100 \div 2 = 50\)
Mary types \(50\) words in \(30\) seconds.
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| 38- Choice B is correct
The correct answer is \(50\)
\(30\) seconds is one second of a minute.
One second of \(100\) is \(50\).
\(100 \div 2 = 50\)
Mary types \(50\) words in \(30\) seconds.
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| 39- Choice A is correct
The correct answer is \(56\)
least common multiple (LCM) of \(8\) and \(14\) is the smallest number that is divisible by both \(8\) and \(14\). LCM \(= 56\)
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| 40- Choice C is correct
The correct answer is \(6\) Times
\(8\) hour \(= 480\) minutes.
Write a proportion and solve.
\(\frac{80}{1} = \frac{480}{x} →\)
\(x = \frac{480}{80} = 6\)
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| 41- Choice A is correct
The correct answer is \(\frac{13}{5}\)
Find common denominator and solve.
\(\frac{4}{2} \ + \ \frac{3}{5} = \frac{20}{10} \ +\frac{6}{10} = \frac{26}{10}→\frac{13}{5}\)
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| 42- Choice C is correct
The correct answer is \(12\)
The factors of \(30\) are:
\(\left\{ 1, \ 2,\ 3 , \ 5, \ 6 , \ 10, \ 15, \ 30\right\}\)
\(12\) is not a factor of \(30\).
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| 43- Choice D is correct
The correct answer is \(\frac{6}{7}\)
One method to compare fractions is to convert them to decimals.
A. \(\frac{1}{2} = 0.5\)
B. \(\frac{2}{3} = 0.66\)
C. \(\frac{4}{5} = 0.8\)
D. \(\frac{6}{7} = 0.85\)
\(0.85\) or \(\frac{6}{7}\) is the largest number.
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| 44- Choice A is correct
The correct answer is \(130\%\)
The question is this:
\(1.50\) is what percent of \(1.15\)?
Use percent formula:
part \(= \frac{percent}{100} \times\) whole
part \(= \frac{percent}{100} \times 1.15 ⇒\)
\(1.50 = \frac{percent \ \times 1.15}{100} ⇒\)
\(150 =\) percent \(\times 1.15 ⇒\)
percent \(= \frac{150}{1.15} = 130\)
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| 45- Choice A is correct
The correct answer is \(80\) cm\(^2\)
Area of a triangle \(= \frac{1}{2}\) (base)(height)
A \(= \frac{1}{2} \ (20) \ (8) = 80\)
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| 46- Choice C is correct
The correct answer is \(648\)
Perimeter \(= 2\) ( width \(+\) length)
A \(=\) width \(\times\) length
First, find the length of the rectangle.
Perimeter \(= 2\) ( width \(+\) length) \(\rightarrow 108= 2 ( 18\ +\) length) \(\rightarrow\)
\(108 = 36 \ + \ 2\) (length) \(\rightarrow\)
\(72= 2\) (length) \(\rightarrow\)
length \(=36 \)
A \(= 18 \times 36 =648 \)
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| 47- Choice A is correct
The correct answer is \(7,459.4\) Times
\(7,459.3256\) rounded to the nearest tenth is \(7,459.4\)
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| 48- Choice C is correct
The correct answer is \(\frac{14}{15}\)
If \(14\) balls are removed from the bag at random, there will be one ball in the bag.
The probability of choosing a red ball is \(1\) out of \(15\).
Therefore, the probability of not choosing a brown ball is \(14\) out of \(15\) and the probability of having not a red ball after removing \(14\) balls is the same.
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| 49- Choice C is correct
The correct answer is \(3\%\)
The question is this:
\(650.20\) is what percent of \(670\)?
Use percent formula:
part \(= \frac{percent}{100} \times\) whole
\(650.20 = \frac{percent}{100} \times 670 ⇒\)
\(650.20 = \frac{percent \times 670}{100} ⇒\)
\(65020 =\) percent \(\times 670 ⇒\)
percent \(= \frac{65020}{670} = 97\)
\(650.20\) is \(97\%\) of \(670\).
Therefore, the discount is:
\(100\% \ – \ 97\% = 3\%\)
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| 50- Choice D is correct
The correct answer is \(76\)
All angles in a triangle add up to \(180\) degrees.
\(68 \ +\ 36 = 104\)
\(180 \ –\ 104 = 76\)
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| 51- Choice A is correct
The correct answer is \(4.5\%\)
\(0.045 \times 100 = 4.5\%\)
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| 52- Choice C is correct
The correct answer is \(3\) Hours
Since Mary running at \(4\) miles per hour and Mary is running at the speed of \(7\) miles per hour, each hour their distance decreases by \(3\) mile.
So, it takes \(15\) hours to cover distance of \(9\) miles.
\(9 \div 3 = 3\)
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| 53- Choice B is correct
The correct answer is \(360\)
Since Susan gives \(6\) pieces of candy to each of her friends, then, then number of pieces of candies must be divisible by \(6\).
A. \(214 \div 6 = 35.66\)
B. \( 360 \div 6 = 60\)
C. \(325 \div 6 = 54.16\)
D. \( 157\div 6 = 26.16\)
Only choice B \((360)\) gives a whole number.
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| 54- Choice A is correct
The correct answer is \(\frac{5}{1000}\)
\(\frac{5}{1000} = 0.005\)
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| 55- Choice C is correct
The correct answer is \($32\)
\($8 \times 8 = $64\)
Petrol use: \(8 \times 2 = 16\) liters
Petrol cost: \(16 \times $2 = $32\)
Money earned: \($64 \ - \ $32 = $32\)
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| 56- Choice A is correct
The correct answer is \(1500\) m\(^3\)
If the length of the box is \(30\), then the width of the box is one third of it, \(10\), and the height of the box is \(5\) (one second of the width).
The volume of the box is:
V \(=\) (length)(width)(height) \(= (30) \ (10) \ (5) = 1500\) m\(^3\)
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| 57- Choice C is correct
The correct answer is \(13 \ hr. \ \ 47 \ min\)
\(\cfrac{\begin{align} 37 \ hr. \ \ 25 \ min \\ - \ 23 \ hr. \ \ 38 \ min \end{align}}{} \)
\(13 \ hr. \ \ 47 \ min\)
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| 58- Choice C is correct
The correct answer is \(5\)
Let \(x\) be the number of raptors Daniel saw on Monday.
Then:
Mean \(= \frac{x \ + \ 7 \ + \ 18 \ + \ 11 \ + \ 9}{5} = 10 →\)
\(x \ + \ 45 = 50 →\)
\(x = 50 \ – \ 45 = 5\)
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| 59- Choice A is correct
The correct answer is \(80\%\)
The failing rate is \(25\) out of \(125 = \frac{25}{125}\)
Change the fraction to percent:
\(\frac{25}{125} \times 100\% = 20\%\)
\(20\) percent of students failed.
Therefore, \(80\) percent of students passed the exam.
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| 60- Choice C is correct
The correct answer is \(135^{◦}\)
An obtuse angle is an angle of greater than \(90\) degrees and less than \(180\) degrees.
Only choice C (\(135\) degrees) is an obtuse angle
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| 61- Choice A is correct
The correct answer is \(\frac{3}{4}\)
There are \(8\) squares and \(6\) of them are shaded.
Therefore, \(6\) out of \(8\) or \(\frac{6}{8} = \frac{3}{4}\) are shaded.
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| 62- Choice A is correct
The correct answer is \((300)(0.75)(0.85)\)
To find the discount, multiply the number by (\(100\% \ – \) rate of discount).
Therefore, for the first discount we get:
\((300)(100\% \ – \ 25\%) = (300)(0.75)\)
For the next \(15\%\) discount:
\((300)(0.75)(0.85)\)
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| 63- Choice A is correct
The correct answer is A \( \times \ 2 = 28\)
Plug in \(14\) for A in the equation.
Only choice A works.
A \( \times \ 2 = 28\)
\(14 \ \times \ 2 = 28\)
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| 64- Choice C is correct
The correct answer is \(75\)
Write a proportion and solve.
\(\frac{3}{5} = \frac{x}{45}\)
Use cross multiplication:
\(3 \ x = 225 → x =75 \)
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| 65- Choice D is correct
The correct answer is trapezoid
A quadrilateral with one pair of parallel sides is a trapezoid.
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| 66- Choice A is correct
The correct answer is \($19.5\)
\(1\) hour: \($3.25\)
\(6\) hours: \(6 \times $3.25 = $19.5\)
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| 67- Choice B is correct
The correct answer is \(96\)
\(1\) pizza has \(8\) slices.
\(12\) pizzas contain \((12 \times 8) \ 96\) slices.
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| 68- Choice C is correct
The correct answer is \(62.5\%\)
There are \(40\) students in the class.
\(15\) of the are male and \(25\) of them are female.
\(25\) out of \(40\) are female. Then:
\(\frac{25}{40} = \frac{x}{100} →\)
\(2,500 = 40 \ x →\)
\(x=2,500\div 40 =62.5 \%\)
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