10 Most Common HiSET Math Questions

E
The ratio of boys to girls is 2:3. Therefore, there are 2 boys out of 5 students. To find the answer, first, divide the total number of students by 5, then multiply the result by 2.
\(600 ÷ 5 = 120 ⇒ 120 × 2 = 240\)

C
Use percent formula:
\(part = \frac{percent}{100} × whole\)
\(25 = \frac{percent}{100} × 20 ⇒ 25 = \frac{percent ×20}{100}\)
\(⇒ 25 = \frac{percent ×2}{10}\)
multiply both sides by 10.
\(4250 = percent ×2, divide \space both \space sides \space by \space 2. \)
\(125 = percent\)

E
The perimeter of the trapezoid is 54.
Therefore, the missing side (height) is \(= 54 – 18 – 12 – 14 = 10\)
Area of the trapezoid:
\(A = \frac{1}{2}h (b_{1} + b_{2}) = \frac{1}{2}(10)(12 + 14) = 130\)

C
Let \(x\) be the number. Write the equation and solve for \(x\).
\(\frac{2}{3} ×18=\frac{2}{5} ⇒\frac{2×18}{3} = \frac{2x}{5} \)
use cross multiplication to solve for \(x\).
\(5×36=2x×3 ⇒180=6x ⇒ x=30\)

B
To find the discount, multiply the number by \((100\% – rate of discount)\).
Therefore, for the first discount we get: (D) \((100\% – 20\%) =\) (D) \((0.80) = 0.80\) D
For increase of \(10 \%:\) (0.85 D) \((100\% + 10\%) =\) (0.85 D) \((1.10) = 0.88\) D \(= 88\%\) of D

B
Use the formula of areas of circles.
\(Area = πr^2 ⇒ 64 π = πr^2 ⇒ 64 = r^2 ⇒ r = 8\)
The radius of the circle is 8. Now, use the circumference formula:
Circumference \(= 2πr = 2π (8) = 16 π\)

B
Use the formula for Percent of Change
\(\frac{New \space Value-Old \space Value}{Old \space Value}× 100 \%\)
\(\frac{28-40}{40}× 100 \% = –30 \%\)
(negative sign here means that the new price is less than the old price).

A
Let \(x\) be the number of years. Therefore, $2,000 per year equals \(2000x\).
starting from $24,000 annual salary means you should add that amount to \(2000x\).
Income more than that is:
\(I > 2000 x + 24000\)

C
The question is this: 1.75 is what percent of 1.25?
Use percent formula:
\(part =\frac{percent}{100}× whole\)
\(1.75 =\frac{percent}{100}× 1.25\)
\(1.75 =\frac{percent ×1.25}{100} \)
\(175 = percent ×1.25 ⇒\)
\(percent = \frac{175}{1.25}= 140\)

B
Use the information provided in the question to draw the shape.
Use Pythagorean Theorem: \(a^2 + b^2 = c^2\)
\(40^2 + 30^2 = c^2 ⇒ 1600 + 900 = c^2 ⇒ 2500 = c^2 ⇒ c = 50\)