Full-Length HiSET Math Practice Test-Answers and Explanations
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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