# Full-Length HiSET Math Practice Test-Answers and Explanations Did you take the HiSET Math Practice Test? If so, then it’s time to review your results to see where you went wrong and what areas you need to improve.

## HiSET Math Practice Test Answers and Explanations

1- Choice B is correct
The diagonal of the square is $$6$$. Let $$x$$ be the side.
Use Pythagorean Theorem: $$a^2 + b^2 = c^2$$
$$x^2+x^2= 62 ⇒ 2x^2= 6^2 ⇒ 2x^2=36 ⇒x^2 = 18 ⇒x= \sqrt{18}$$
The area of the square is: $$\sqrt{18}× \sqrt{18}= 18$$

2- Choice B is correct
Use Pythagorean Theorem: $$a^2 + b^2 = c^2, 5^2 + 12^2 = c^2 ⇒ 169 = c^2⇒ c = 13$$

3- Choice A is correct
If the score of Mia was 80, therefore the score of Ava is 40. Since, the score of Emma was half as that of Ava, therefore, the score of Emma is 20.

4- Choice D is correct
Add the first 5 numbers. 70 + 75 + 60 + 85 + 80 = 370
To find the distance traveled in the next 5 hours, multiply the average by number of hours.
Distance = Average × Rate = 60 × 5 = 300,    Add both numbers. 370 + 300 = 670

5- Choice B is correct
7.5% of 1,400 = 0.075 × 1400 = 105

6- Choice B is correct
Use distance formula:
Distance = Rate × time ⇒ 375 = 60 × T, divide both sides by 60.
375 / 60 = T ⇒ T = 6.25 hours.
Change hours to minutes for the decimal part. 0.25 hours = 0.25 × 60 = 15 minutes.

7- Choice D is correct
Use percent formula: $$part = \frac{percent}{100}×whole$$
$$45 = \frac{percent}{100} × 30 ⇒ 45 = \frac{percent ×30}{100} ⇒ 45 = \frac{percent ×3}{10}$$, multiply both sides by 10.
$$450 = percent ×3$$, divide both sides by 3. 150 = percent

8- Choice D is correct
$$x=40+95=135$$

9- Choice A is correct
Th ratio of boy to girls is 3:4. Therefore, there are 3 boys out of 7 students. To find the answer, first divide the total number of students by 7, then multiply the result by 3. $$350 ÷ 7 = 50 ⇒ 50 × 3 = 150$$

10- Choice D is correct
Let x be the number. Write the equation and solve for $$x$$.
$$\frac{2}{3}×15= \frac{4}{5}$$
$$x ⇒ \frac{2×15}{3}= \frac{4}{5}$$, use cross multiplication to solve for $$x$$.
$$5×30=4x×3 ⇒ 150=12x ⇒ x=12.5$$

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11- Choice E is correct
Simplify: $$3x-3-15=2x+8 ⇒ 3x-18=2x+8$$
Subtract 2x from both sides: $$x-18=8$$ , Add $$18$$ to both sides: $$x=26$$

12- Choice C is correct
Write the equation and solve for B:    0.50 A = 0.25 B, divide both sides by 0.25, then you will have 0.50/0.25 A = B, therefore: B = 2 A, and B is 2 times of A or it’s 200% of A.

13- Choice B is correct
Use FOIL (First, Out, In, Last) $$(3x + 4y)(2x- 5y) = 6x^2-15xy +8xy – 20y^2 = 6x^2- 7xy – 20^2$$

14- Choice D is correct
Use distributive property: $$-3x(2y-5) = -6xy + 15x = 15x-6xy$$

15- Choice B is correct
$$x = 2ab – 2b^3$$ Plug in the values of a and b in the equation: $$a = 5$$ and $$b = 2$$
$$x = 2 (5) (2) – 2 (2)^3 = 20 -2(8) = 20 -16 = 4$$

16- Choice C is correct
Let  be the original price.
If the price of a laptop is decreased by $$24\%$$ to $$285$$, then: ⇒$$76 % of x=285⇒ 0.76x=285 ⇒ x=285÷0.76=375$$

17- Choice A is correct
The perimeter of the trapezoid is $$45$$. So, the missing side (height) is = $$45 – 17 – 13 – 9 = 6$$ Area of the trapezoid: $$A =\frac{1}{2}h (b_1 + b_2) = \frac{1}{2}(6) (13 + 17) = 90$$

18- Choice C is correct
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 $$15\%$$: (0.75 D) ($$100\% + 15\%) =$$ (0.75 D) (1.15) = 0.8625 D = $$86.25\%$$ of D

19- Choice C is correct
Surface Area of a cylinder = 2πr (r + h), The radius of the cylinder is 5 inches and its height is 11 inches.
Surface Area of a cylinder = 2 (π) (5) (5 + 11) = 160 π

20- Choice B is correct
$$average = \frac{sum \space of \space terms}{number \space of \space terms}⇒ 15 = \frac{11+16+21+x}{4}⇒60 = 48 + x ⇒ x = 12$$

21- Choice D is correct
Let x be the smallest number. Then, these are the numbers: $$x, x+1, x+2, x+3, x+4$$
average $$=\frac{sum \space of \space terms}{number \space of \space terms}⇒ 72 = \frac{x+(x+1)+(x+2)+(x+3)+(x+4)}{5}⇒72=\frac{5x+10}{5} ⇒ 360 = 5x+10 ⇒350 = 5x ⇒ x=70$$

22- Choice D is correct
Let $$x$$ be the original price.
If the price of the sofa is decreased by $$20\%$$ to $$240$$, then: $$80\%$$ of $$x=240 ⇒ 0.80=240 ⇒ x=240÷0.80=300$$

23- Choice C is correct
Frist factor the function: $$x (x+4)(x+5)$$
To find the zeros, $$f(x)$$ should be zero. $$f(x)=x (x+4)(x+5)=0$$
Therefore, the zeros are: $$x=0$$, $$(x+4)=0 ⇒ x= -4 , (x+5)=0 ⇒ x= -5$$

24- Choice C is correct
Use the formula of areas of circles. $$Area = πr^2 ⇒ 36 π = πr^2 ⇒ 36 = r^2 ⇒ r = 6$$
Radius of the circle is 6.
Now, use the circumference formula: $$Circumference= 2πr = 2π (6) = 12π$$

25- Choice B is correct
Write the numbers in order: $$3, 4, 6, 8, 11, 13, 17$$
Since we have $$7$$ numbers ($$7$$ is odd), then the median is the number in the middle, which is $$8$$.

26- Choice C is correct
Let $$x$$ be the number of years. Therefore, $$1,500$$ per year equals $$1500x$$.
starting from \$17,000 annual salary means you should add that amount to $$1500x$$. Income more than that is: $$I > 1500 x + 17000$$

27- Choice B is correct
The formula of the volume of pyramid is: $$V= \frac{l ×w ×h}{3}$$
The length and width of the pyramid is 4 cm and its height is $$15 \space cm$$. Therefore:
$$V= \frac{4×4 ×15}{3}=80 \space cm^3$$

28- Choice D is correct
The question is this: 1.8 is what percent of 1.2? Use percent formula: $$part = \frac{percent}{100}×whole$$
$$1.8 = \frac{percent}{100}×1.2 ⇒ 1.8 =\frac{percent ×1.2}{100} ⇒180 = percent ×1.2 ⇒ percent = 180/1.2 = 150$$

29- Choice D is correct
Some of prime numbers are: $$2, 3, 5, 7, 11, 13$$
Find the product of two consecutive prime numbers: $$2 × 3 = 6$$ (not in the options) $$3 × 5 = 15$$ (not in the options), $$5 × 7 = 35$$ (bingo!)

30- Choice C is correct
The question is this: 360 is what percent of 400?
Use percent formula: part $$= \frac{percent}{100}×$$ whole
$$360 = \frac{percent}{100}×400 ⇒ 360 =\frac{percent ×400}{100} ⇒ 36000 = percent ×400 ⇒$$
$$percent = 36000/400 = 90$$
$$360$$ is $$90\%$$ of $$400$$. Therefore, the discount is: $$100\% – 90\% = 10\%$$

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31- Choice C is correct
Use this formula: Percent of Change $$=\frac{New \space Value-Old \space Value}{Old \space Value}×100\%$$
$$\frac{25500-34000}{34000}× 100\% = 25\% and \frac{19125-25500}{25500}×100\% = 25\%$$

32- Choice D is correct
Use the information provided in the question to draw the shape.
Use Pythagorean Theorem: $$a^2 + b^2 = c^2$$
$$50^2 + 120^2 = c^2 ⇒ 2500 + 14400 = c^2 ⇒ 16900 = c^2 ⇒ c = 130$$

33- Choice C is correct
If the length of the box is 24, then the width of the box is one fourth of it, 6, and the height of the box is 2 (one third of the width). The volume of the box is: V = lwh = (24) (6) (2) = 288

34- Choice B is correct
Use the formula for Percent of Change: $$\frac{New \space Value-Old \space Value}{Old \space Value} × 100\%$$
$$\frac{60-80}{80}×100\% = –25\%$$ (negative sign here means that the new price is less than old price).

35- Choice D is correct
To find the number of possible outfit combinations, multiply number of options for each factor: $$5 × 2 × 7 = 70$$

36- Choice D is correct
Let  be the number. Write the equation and solve for : $$(18 –x ) ÷ x= 2$$
Multiply both sides by : $$(18 – x) = 2x$$ , then add x both sides:  $$18 = 3x$$ , now divide both sides by 3.  $$x= 6$$

37- Choice C is correct
The sum of supplement angles is $$180$$. Let $$x$$ be that angle. Therefore, $$x + 4x = 180$$.
$$5x = 180$$, divide both sides by $$5$$: $$x = 36$$

38- Choice D is correct
The average speed of john is: $$180 ÷ 3 = 60$$, The average speed of Alice is: $$350 ÷ 7 = 50$$, Write the ratio and simplify. $$60: 50 ⇒ 6: 5$$

39- Choice B is correct
The percent of girls playing tennis is: $$65\% × 20\% = 0.65 × 0.20 = 0.13 = 13 \%$$

40- Choice B is correct
Solving Systems of Equations by Elimination
$$\begin{cases}-2x+5y= 9 \\ x-2y=-6 \end{cases}$$
Add second equation to the first equation.
$$\begin{cases}-x+3y= 3 \\ x-2y=-6 \end{cases}$$ $$\begin{cases}x=3y -3 \\ (3y-3)-2y=-6 \end{cases}$$ ⇒ $$y=-3$$

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41- Choice D is correct
The area of the floor is: $$180 cm × 240 cm = 43200$$ cm$$^2$$
The number is tiles needed $$= 43200 ÷ 60 = 720$$

42- Choice B is correct
The weight of 15.8 meters of this rope is: 15.8 × 700 g = 11060 g
1 kg = 1000 g, therefore, 11060 g ÷ 1000 = 11.06 kg

43- Choice D is correct
$$16\%$$ of the volume of the solution is alcohol. Let $$x$$ be the volume of the solution.
Then: $$16\%$$ of $$x = 60$$ ml ⇒ $$0.16 x= 60 ⇒x = 60 ÷ 0.16 = 375$$

44- Choice A is correct
$$average =\frac{sum \space of \space terms}{number \space of \space terms}$$
The sum of the weight of all girls is: $$38 × 50 = 1900$$ kg
The sum of the weight of all boys is: $$22 × 68 = 1496$$ kg
The sum of the weight of all students is: $$1900 + 1496 = 3396$$ kg
$$average =\frac{3396}{60} = 56.6$$

45- Choice D is correct
Use simple interest formula: $$I=prt$$ (I = interest, p = principal, r = rate, t = time)
$$I=(17,000)(0.036)(5)=3,060$$

46- Choice C is correct
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 of this question:

47- Choice C is correct
$$(4.7 × 10^8) × (3.4 × 10^{−4}) = (4.7 × 3.4) × (10^8 × 10^{−4}) = 15.98 × (10^{8 + (−4)} ) = 15.98 × 104$$

48- Choice A is correct
Since the triangle ABC is reflected over the $$y$$-axis, then all values of $$y$$’s of the points don’t change and the sign of all $$x$$’s change. (remember that when a point is reflected over the $$y$$-axis, the value of $$y$$ does not change and when a point is reflected over the $$x$$-axis, the value of $$x\0 does not change). Therefore: \((−1,4)$$ changes to (1, 4), (5, 1) changes to $$(-5, 1), (1, -6)$$ changes to $$(−1, -6)$$

49- Choice C is correct
Use Pythagorean theorem: $$a^2 + b^2 = c^2, 6^2 + 8^2 = x^2$$, $$36 + 64 = x^2$$
$$100 = x^2 x = 10$$

50- Choice C is correct
If 13 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 14. Therefore, the probability of not choosing a red ball is 13 out of 14 and the probability of having not a red ball after removing 13 balls is the same.

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