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HSPT Math : Problem Solving

Study concepts, example questions & explanations for HSPT Math

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Example Questions

Example Question #72 : Use Parentheses, Brackets, Or Braces In Numerical Expressions And Evaluate These Expressions: Ccss.Math.Content.5.Oa.A.1

Solve:

$3\times(14+2)$ $\displaystyle 3\times(14+2)$

Possible Answers:

$\displaystyle 60$

$\displaystyle 24$

$\displaystyle 48$

$\displaystyle 44$

$\displaystyle 27$

Correct answer:

$\displaystyle 48$

Explanation:

$3\times(14+2)$ $\displaystyle 3\times(14+2)$

When solving this problem, remember order of operations PEMDAS. The parentheses come first followed by the multiplication.

14+2=16 $\displaystyle 14+2=16$

$3\times16=48$ $\displaystyle 3\times16=48$

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Example Question #192 : Problem Solving

Solve:

$4\times (27-19)\div8$ $\displaystyle 4\times (27-19)\div8$

Possible Answers:

$\displaystyle 8$

$\displaystyle 6$

$\displaystyle 5$

$\displaystyle 4$

$\displaystyle 7$

Correct answer:

$\displaystyle 4$

Explanation:

$4\times (27-19)\div8$ $\displaystyle 4\times (27-19)\div8$

When solving this problem, remember order of operations PEMDAS. The parentheses come first, followed by the multiplication, and then the division.

27-19=8 $\displaystyle 27-19=8$

$4\times8=32$ $\displaystyle 4\times8=32$

$32\div8=4$ $\displaystyle 32\div8=4$

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Example Question #73 : Use Parentheses, Brackets, Or Braces In Numerical Expressions And Evaluate These Expressions: Ccss.Math.Content.5.Oa.A.1

Solve:

$3\times(38-18)$ $\displaystyle 3\times(38-18)$

Possible Answers:

$\displaystyle 56$

$\displaystyle 46$

$\displaystyle 40$

$\displaystyle 52$

$\displaystyle 60$

Correct answer:

$\displaystyle 60$

Explanation:

$3\times(38-18)$ $\displaystyle 3\times(38-18)$

When solving this problem, remember order of operations PEMDAS. The parentheses come first followed by the multiplication.

$\displaystyle 38-18=20$

$3\times20=60$ $\displaystyle 3\times20=60$

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Example Question #194 : Problem Solving

Solve:

$45+(18-4)\div2$ $\displaystyle 45+(18-4)\div2$

Possible Answers:

$\displaystyle 48$

$\displaystyle 52$

$\displaystyle 44$

$\displaystyle 56$

$\displaystyle 40$

Correct answer:

$\displaystyle 52$

Explanation:

$45+(18-4)\div2$ $\displaystyle 45+(18-4)\div2$

When solving this problem, remember order of operations PEMDAS. The parentheses come first, followed by the division, and then the addition.

18-4=14 $\displaystyle 18-4=14$

$14\div2=7$ $\displaystyle 14\div2=7$

45+7=52 $\displaystyle 45+7=52$

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Example Question #81 : Use Parentheses, Brackets, Or Braces In Numerical Expressions And Evaluate These Expressions: Ccss.Math.Content.5.Oa.A.1

Solve:

$9\times(10-2)$ $\displaystyle 9\times(10-2)$

Possible Answers:

$\displaystyle 72$

$\displaystyle 79$

$\displaystyle 67$

$\displaystyle 81$

$\displaystyle 65$

Correct answer:

$\displaystyle 72$

Explanation:

$9\times(10-2)$ $\displaystyle 9\times(10-2)$

When solving this problem, remember order of operations PEMDAS. The parentheses come first followed by the multiplication.

10-2=8 $\displaystyle 10-2=8$

$9\times8=72$ $\displaystyle 9\times8=72$

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Example Question #82 : Use Parentheses, Brackets, Or Braces In Numerical Expressions And Evaluate These Expressions: Ccss.Math.Content.5.Oa.A.1

Solve:

$84\div(79-67)$ $\displaystyle 84\div(79-67)$

Possible Answers:

$\displaystyle 14$

$\displaystyle 12$

$\displaystyle 6$

$\displaystyle 7$

$\displaystyle 9$

Correct answer:

$\displaystyle 7$

Explanation:

$84\div(79-67)$ $\displaystyle 84\div(79-67)$

When solving this problem, remember order of operations PEMDAS. The parentheses come first followed by the division.

$\displaystyle 79-67=12$

$84\div12=7$ $\displaystyle 84\div12=7$

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Example Question #197 : Problem Solving

Solve:

$8+(45-37)\times 11$ $\displaystyle 8+(45-37)\times 11$

Possible Answers:

$\displaystyle 96$

$\displaystyle 80$

$\displaystyle 94$

$\displaystyle 76$

$\displaystyle 88$

Correct answer:

$\displaystyle 96$

Explanation:

$8+(45-37)\times 11$ $\displaystyle 8+(45-37)\times 11$

When solving this problem, remember order of operations PEMDAS. The parentheses come first, followed by the multiplication, and then the addition.

45-37=8 $\displaystyle 45-37=8$

$8\times11=88$ $\displaystyle 8\times11=88$

8+88=96 $\displaystyle 8+88=96$

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Example Question #83 : Use Parentheses, Brackets, Or Braces In Numerical Expressions And Evaluate These Expressions: Ccss.Math.Content.5.Oa.A.1

Solve:

$18\div(5-2)$ $\displaystyle 18\div(5-2)$

Possible Answers:

$\displaystyle 6$

$\displaystyle 14$

$\displaystyle 8$

$\displaystyle 9$

$\displaystyle 12$

Correct answer:

$\displaystyle 6$

Explanation:

$18\div(5-2)$ $\displaystyle 18\div(5-2)$

When solving this problem, remember order of operations PEMDAS. The parentheses come first followed by the division.

5-2=3 $\displaystyle 5-2=3$

$18\div3=6$ $\displaystyle 18\div3=6$

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Example Question #199 : Problem Solving

Solve:

$16+3\times9+(42-10)$ $\displaystyle 16+3\times9+(42-10)$

Possible Answers:

$\displaystyle 82$

$\displaystyle 33$

$\displaystyle 75$

$\displaystyle 90$

$\displaystyle 48$

Correct answer:

$\displaystyle 75$

Explanation:

$16+3\times9+(42-10)$ $\displaystyle 16+3\times9+(42-10)$

When solving this problem, remember order of operations PEMDAS. The parentheses come first, followed by the multiplication, and then addition.

$\displaystyle 42-10=32$

$3\times9=27$ $\displaystyle 3\times9=27$

$\displaystyle 16+27+32=75$

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Example Question #1 : Word Problems

Mark is three times as old as his son Brian. In ten years, Mark will be $\displaystyle 43$ years old. In how many years will Mark be twice as old as Brian?

Possible Answers:

$\displaystyle 22$

$\displaystyle 20$

$\displaystyle 11$

$\displaystyle 17$

$\displaystyle 13$

Correct answer:

$\displaystyle 11$

Explanation:

In ten years, Mark will be $\displaystyle 43$ years old, so Mark is $\displaystyle 43-10 = 33$ years old now, and Brian is one-third of this, or $33 \div 3 = 11$ $\displaystyle 33 \div 3 = 11$ years old.

Let $\displaystyle N$ be the number of years in which Mark will be twice Brian's age. Then Brian will be N + 11 $\displaystyle N + 11$, and Mark will be N + 33 $\displaystyle N + 33$. Since Mark will be twice Brian's age, we can set up and solve the equation:

$\displaystyle 2 (N + 11) = N + 33$

$\displaystyle 2N + 22 = N + 33$

$\displaystyle 2N + 22-N - 22 = N + 33 -N - 22$

N = 11 $\displaystyle N = 11$

Mark will be twice Brian's age in $\displaystyle 11$ years.

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HSPT Math : Problem Solving

Study concepts, example questions & explanations for HSPT Math

All HSPT Math Resources

Example Questions

Example Question #72 : Use Parentheses, Brackets, Or Braces In Numerical Expressions And Evaluate These Expressions: Ccss.Math.Content.5.Oa.A.1

Example Question #192 : Problem Solving

Example Question #73 : Use Parentheses, Brackets, Or Braces In Numerical Expressions And Evaluate These Expressions: Ccss.Math.Content.5.Oa.A.1

Example Question #194 : Problem Solving

Example Question #81 : Use Parentheses, Brackets, Or Braces In Numerical Expressions And Evaluate These Expressions: Ccss.Math.Content.5.Oa.A.1

Example Question #82 : Use Parentheses, Brackets, Or Braces In Numerical Expressions And Evaluate These Expressions: Ccss.Math.Content.5.Oa.A.1

Example Question #197 : Problem Solving

Example Question #83 : Use Parentheses, Brackets, Or Braces In Numerical Expressions And Evaluate These Expressions: Ccss.Math.Content.5.Oa.A.1

Example Question #199 : Problem Solving

Example Question #1 : Word Problems

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