Top 10 PSAT/NMSQT Math Practice Questions

Top 10 PSAT/NMSQT Math Practice Questions is a multiple-choice math challenge from Effortless Math. Read the problem, choose from the answer options below, then open the solution to see the full step-by-step working and check your reasoning against it.

B. 4.8

C. 7.2

D. 24

5- If a and b are solutions of the following equation, which of the following is the ratio (frac{a}{b})? ((a > b))
(2x^2-11x+8=-3x+18)

A. (frac{1}{5})

B. 5

C. (-frac{1}{5})

D. (-5)

6- How many tiles of 8 cm(^2) is needed to cover a floor of dimension 6 cm by 24 cm?

A. 6

B. 12

C. 18

D. 24

7- Which of the following is the solution to the following inequality?
(2x+4>11x-12.5-3.5x)

A. (x<3)

B. (x>3)

C. (x≤4)

D. (x≥4)

8- If a, b and c are positive integers and (3a = 4b = 5c), then the value of (a + 2b + 15c) is how many times the value of a?

A. 11.5

B. 12

C. 12.5

D. 15

9- A company pays its employer $7000 plus (2%) of all sales profit. If (x) is the number of all sales profit, which of the following represents the employer’s revenue?

A. (0.02x)

B. (0.98x-7000)

C. (0.02x+7000)

D. (0.98x+7000)

10- (frac{5x^2+75x-80}{x^2-1} = )?

A. (frac{5x+75}{ x-1} )

B. (frac{x+16}{ x+1} )

C. (frac{5x+80}{ x+1} )

D. (frac{x+15}{ x-1} )

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Answers:

2- D
Five years ago, Amy was three times as old as Mike. Mike is (10) years now. Therefore, (5) years ago Mike was (5) years.
Five years ago, Amy was: (A=3×5=15 )
Now Amy is (20) years old: (15 + 5 = 20)

3- D
(begin{cases}frac{-x}{2}+ frac{y}{4} = 1 \ frac{-5y}{6}+2x = 4 & end{cases})
Multiply the top equation by (4). then:
(-2x+y=4)
(frac{-5y}{6} + 2x = 4)
Add two equations.
( frac{1}{6}y=8→y=48 )
plug in the value of (y) into the first equation (→(x=22))

4- B
Two triangles ∆BAE and ∆BCD are similar. Then:
(frac{AE}{CD} = frac{AB}{BC})
(frac{4}{6} = frac{x}{12})
then:
(48-4x=6x→10x=48→x=4.8)

5- D
(2x^2-11x+8=-3x+18→2x^2-11x+3x+8-18=0→2x^2-8x-10=0)
(→2(x^2-4x-5)=0→) Divide both sides by (2). Then:
(x^2-4x-5=0), Find the factors of the quadratic equation.
(→(x-5)(x+1)=0→x=5) or ( x=-1)
(a>b), then: (a=5) and (b=-1)
(frac{a}{b} = frac{5}{-1}= -5 )

6- C
The area of the floor is: (6 cm × 24 cm = 144 cm)
The number is tiles needed (= 144 ÷ 8 = 18)

7- A
(2x+4>11x-12.5-3.5x→) Combine like terms:
(2x+4>7.5x-12.5$→) Subtract (2x) from both sides: (4>5.5x-12.5)
Add (12.5) both sides of the inequality.
(16.5>5.5x)
Divide both sides by (5.5).
(frac{16.5}{5.5}>x→x<3)

8- A
(3a=4b→b=frac{3a}{4}) and ( 3a=5c→c= frac{3a}{5})
(a+2b+15c=a+ (2× frac{3a}{4})+(15× frac{3a}{5})=a+1.5a+9a=11.5a)

9- C
(x) is the number of all sales profit and (2%) of it is:
(2%×x=0.02x)
Employer’s revenue: (0.2x+7000)

10- C
First, find the factors of numerator and denominator of the expression. Then simplify.
(frac{5x^2+75x-80}{x^2-1}=frac{5(x^2+15x-16)}{(x-1)(x+1)})
(frac{5(x+16)(x-1)}{ (x-1)(x+1)}=frac{5(x+16)}{ (x+1)} )
(=frac{(5x+80)}{ (x+1)})

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