HESI A2 Math Portion

HESI A2 Math Portion Related

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Relatively prime numbers share no common factors other than 1. Which of the following pairs of numbers are relatively prime?

  • A. 12 and 16
  • B. 15 and 17
  • C. 20 and 24
  • D. 28 and 36
Correct Answer: B

Rationale: Rationale:
- Relatively prime numbers are numbers that share no common factors other than 1.
- To determine if two numbers are relatively prime, we need to find the greatest common divisor (GCD) of the two numbers. If the GCD is 1, then the numbers are relatively prime.
- Let's calculate the GCD for each pair of numbers:
A) GCD(12, 16) = 4, not relatively prime
B) GCD(15, 17) = 1, relatively prime
C) GCD(20, 24) = 4, not relatively prime
D) GCD(28, 36) = 4, not relatively prime

Therefore, the pair of numbers 15 and 17 are relatively prime because their greatest common divisor is 1, meaning they share no common factors other than 1.

You may also like to solve these questions

Which numeric system was a base 20 system?

  • A. Mayan
  • B. Babylonian
  • C. Roman
  • D. Arabic
Correct Answer: A

Rationale: The Mayan numeric system was a base 20 system, known as vigesimal, as it used base 20 numerals. This system was unique and employed a combination of symbols and positional notation to represent numbers. The Babylonian system was a base 60 system, Roman numerals were based on combinations of letters, and Arabic numerals are in base 10, making choices B, C, and D incorrect.

Subtract and simplify: -5 - (-6) =

  • A. ½
  • B. 1â…œ
  • C. 1
  • D. 1â…”
Correct Answer: C

Rationale: To simplify the expression -5 - (-6), we can rewrite it as -5 + 6 (since subtracting a negative number is equivalent to adding its positive counterpart). This gives us -5 + 6 = 1. Therefore, the correct answer is 1. Choice A, ½, is incorrect because the subtraction of a negative number results in a positive number. Choices B and D are also incorrect as they do not match the simplified result of -5 - (-6), which is 1.

A lab needs 200ml of a 5% salt solution. They only have a 10% solution. How much 10% solution and water should be mixed?

  • A. 100ml 10% solution, 100ml water
  • B. 150ml 10% solution, 50ml water
  • C. 160ml 10% solution, 40ml water
  • D. 200ml 10% solution, 0ml water
Correct Answer: B

Rationale: Rationale:
1. Let x be the volume of the 10% solution needed and y be the volume of water needed.
2. The total volume of the final solution is 200ml, so x + y = 200.
3. The concentration of the final solution is 5%, so the amount of salt in the final solution is 0.05 * 200 = 10g.
4. The amount of salt in the 10% solution is 0.1x, and the amount of salt in the water is 0, so the total amount of salt in the final solution is 0.1x.
5. Since the total amount of salt in the final solution is 10g, we have 0.1x = 10.
6. Solving for x, we get x = 100ml.
7. Substituting x =

If she had $1,070 after spending $18, how much did she have initially?

  • A. $1,052
  • B. $1,060
  • C. $1,071
  • D. $1,075
Correct Answer: A

Rationale: To determine the initial amount she had, we subtract the amount spent ($18) from the total amount she had after spending. If she had $1,070 after spending, subtracting $18 gives us $1,052, which was the initial amount. Choices B, C, and D are incorrect as they do not consider the subtraction of the amount spent to find the initial amount.

A child's toy block is a cube with side lengths of 5cm. What is its total surface area?

  • A. 25 sq cm
  • B. 50 sq cm
  • C. 125 sq cm
  • D. 150 sq cm
Correct Answer: D

Rationale: The surface area of a cube is calculated using the formula: 6 * (side length)^2. Substituting the side length of 5cm into the formula, we get: 6 * (5cm)^2 = 6 * 25cm^2 = 150 sq cm. Therefore, the total surface area of the toy block is 150 sq cm. Choices A (25 sq cm), B (50 sq cm), and C (125 sq cm) are incorrect as they do not correctly calculate the total surface area of the cube.

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