Top 10 PSAT/NMSQT Math Practice Questions

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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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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