Full-Length TASC Math Practice Test-Answers and Explanations

36- Choice A is correct
Add the first 5 numbers. \(30 + 35 + 40 + 35 + 50 = 190\)
To find the distance traveled in the next 5 hours, multiply the average by the number of hours. Distance \(=\) Average \(×\) Rate \(= 45 × 5 = 225\)
Add both numbers. \(190 + 225 = 415\)

37- Choice C is correct
The question is this: 600 is what percent of 750?
Use the percent formula:
part\(=\frac{percent}{100}×\)whole
\(600=\frac{percent}{100}×750 ⇒ 600= \frac{percent ×750}{100} ⇒ 60000 =\)percent \(×75 ⇒\) percent\(=\frac{60000}{75}=80\)
600 is \(80 \%\) of 750. Therefore, the discount is: \(100\% –80\%=20\%\)

38- Choice D is correct
If 24 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 25. Therefore, the probability of not choosing a red ball is 24 out of 25, and the probability of not having a red ball after removing 24 balls is the same.

39- Choice B is correct
average \(=\frac{sum of terms }{number of terms}\)
The sum of the weight of all girls is: \(25×48=1200\) kg
The sum of the weight of all boys is: \(30×60=1800\) kg
The sum of the weight of all students is: \(1200+1800=3000\) kg
average\(=\frac{3000 }{55}=54.54\)

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40- Choice C is correct
Write the numbers in order:
\(5, 7, 11, 13, 15, 17, 21\)
Since we have 7 numbers (7 is odd), the median is the number in the middle, which is 13.

41- The answer is 8
average\(=\frac{sum of terms }{number of terms} ⇒ 15=\frac{12+17+23+x}{4}⇒60=52+x⇒x=8\)

42- The answer is 6
Use PEMDAS (order of operation):
\(-12-3×(–4)+[4-9×(-2)]÷2-5=-12+12+[4+18]÷2-5=[22]÷2-5=11-5=6\)

43- The answer is 5
\(-4x+7=19→-4x=19-7=12→x=\frac{12}{4}=3\)
Then; \(3x-4=3 (3)-4=9-4=5\)

44- The answer is 72
First, draw an isosceles triangle. Remember that the two sides of the triangle are equal.
Let’s put a for the legs. Then:
a\(=12⇒\) area of the triangle is \(=\frac{1}{2} (12×12)=\frac{144}{2}=72\)

45- The answer is 13.5
The rate of construction company\(=\frac{15 cm}{1 min}=15 \frac{cm}{min}\)
Height of the wall after 60 minutes \(= \frac{15 cm}{1 min}×60\) min\(=900\) cm
Let \(x\) be the height of wall, then \(\frac{2}{3} x=900 \)cm\(→x=\frac{3×900}{2}→x=1350\) cm\(=13.5\) m

46- The answer is 138
The question is this: 1.83 is what percent of 1.32?
Use percent formula: part \(=\frac{ percent}{100} ×\) whole
\(1.83 = \frac{percent}{100} × 1.32 ⇒ 1.83 = \frac{percent ×1.32}{100} ⇒183 =\) percent \(×1.32 ⇒\) percent \(= \frac{183}{1.32} = 138\)

47- The answer is 60
The relationship among all sides of a special right triangle
\(30^\circ-60^\circ- 90^\circ\) is provided in this triangle:

In this triangle, the opposite side of the 30\(^\circ\) angle is half of the hypotenuse.
Draw the shape of this question.
The ladder is the hypotenuse. Therefore, the ladder is 60 feet.

48- The answer is 3
Let x be the length of an edge of a cube, then the volume of a cube is: \(V=x^3\)
The surface area of a cube is: \(SA=6x^2\)
The volume of cube A is \(\frac{1}{2}\) of its surface area. Then:\( x^3=\frac{6x^2}{2}→x^3=3x^2\), divide both side of the equation by \(x^2\). Then: \(\frac{x^3}{x^2} =\frac{3x^2}{x^2} →x=3\)

49- The answer is 147
The perimeter of the trapezoid is 51.
Therefore, the missing side (height) is \(= 51 – 16 – 12 – 9 = 14 \)
Area of a trapezoid: A \(= \frac{1}{2} h (b_1 + b_2) = \frac{1}{2} (14) (9 + 12) = 147\)

50- The answer is 6
The input value is 3. Then: \(x=3, f(x)=-x^2+5x→ f(3)=-3^2+5(3)=-9+15=6\)

51- The answer is -12
Since N\(=3\), substitute 3 for N in the equation \(\frac{x+2}{4}=-\)N, which gives \(\frac{x+2}{4}=-3\). Multiplying both sides of \(\frac{x+2}{4}=-3\) by 4 gives \(x+2=-12\) and then subtract 2 from both sides of
\(x+2-2=-12-2\) then, \(x=-12\).

52- The answer is \(\frac{1}{3}\) or 0.33
Write the ratio of 6a to \(5b. \frac{6a}{5b}=\frac{2}{5}\)
Use cross multiplication and then simplify.
\(6a×5=5b×2→30a=10b→a=\frac{10b}{30}=\frac{b}{3}\)
Now, find the ratio of a to b. \(\frac{a}{b}=\frac{\frac{b}{3}}{b}→\frac{b}{3}÷b=\frac{b}{3}×\frac{1}{b}=\frac{b}{3b}=\frac{1}{3}=0.33\)

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