Quant Practice Questions for ACT - 1 | Mathematics for ACT PDF Download

Ans: (d)
The relationship among all sides of special right triangle 30^∘ -60^∘ - 90^∘ is provided in this triangle:
In this triangle, the opposite side of 30∘ angle is half of the hypotenuse. Draw the shape of this question: The latter is the hypotenuse. Therefore, the latter is 60 ft.

Ans: (c)
40% of 60 equals to: 0.40 × 60 = 24
12% of 600 equals to: 0.12 × 600 = 72
40% of 60 is added to 12% of 600: 24 + 72 = 96

Ans: (c)
Use distance formula:
𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒 = 𝑅𝑎𝑡𝑒 × 𝑡𝑖𝑚𝑒 ⇒ 420=50×𝑇, divide both sides by 50. 420/50 = 𝑇 ⇒ 𝑇 = 8.4 hours.
Change hours to minutes for the decimal part. 0.4 hours  = 0.4 × 60 = 24  minutes.

Ans: (b)
By definition, the sine of an acute angle is equal to the cosine of its complement.
Since angle A and B are complementary angles, therefore:
sin A = cos B

Ans: (b)
The diagonal of the square is 8. Let 𝑥  be the side.
Use Pythagorean Theorem: 𝑎²+𝑏² = 𝑐²
𝑥² + 𝑥² = 82 ⇒ 2𝑥² = 82 ⇒ 2𝑥² = 64 ⇒ 𝑥² = 32 ⇒ 𝑥 = √32
The area of the square is:
√32 × √32 = 32

Ans: (b)
𝑥 = 20 + 125 = 145

Ans: (d) Solve the system of equations by elimination method.
3𝑥−4𝑦 = −20
−𝑥+2𝑦 = 10
Multiply the second equation by 3, then add it to the first equation.
3𝑥−4𝑦 = −20
3(−𝑥+2𝑦 = 10)
⇓
3𝑥 − 4𝑦 = −20
−3𝑥 + 6𝑦 = 30)
⇒ add the equations
2𝑦 = 10 ⇒ 𝑦 = 5