# 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. \(Area=\pi r^2⇒36\pi =\pi r^2⇒36=r^2⇒r=6\)

The 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 the 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 a 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:

The ladder is the hypotenuse. Therefore, the ladder is 24 ft.

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. 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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