HESI A2 Math Exams — HESI A2 Math Practice Test
Answer: B
1.2:x::14:42 = 3.6
To solve the proportion 1.2:x::14:42, we can set up the equation 1.2/14 = x/42. Cross-multiplying gives us 1.2 * 42 = 14 * x, leading to x = 3.6.
A) 0.6
Option A is incorrect because substituting 0.6 for x in the proportion 1.2:0.6::14:42 does not satisfy the equality. The ratio 1.2/0.6 simplifies to 2, while 14/42 simplifies to 1/3, which are not equal.
B) 3.6
Option B is correct. Substituting 3.6 for x maintains the proportional relationship: 1.2/14 = 3.6/42 simplifies to 0.0857 on both sides, confirming the equality holds.
C) 1.2
Option C is incorrect because using 1.2 for x gives the ratio 1.2/14, which is not equal to 1.2/42. The two ratios yield different values, demonstrating that they do not maintain the proportion.
D) 2.4
Option D is incorrect as well. If we substitute 2.4 for x, we find that 1.2/14 does not equal 2.4/42. The ratios yield different results, indicating that 2.4 cannot be the correct value for x in this proportion.
Conclusion
The correct answer is 3.6, as it maintains the proportional relationship defined in the question. All other options fail to satisfy the equality established by the original ratios, confirming that 3.6 is the only viable solution.
Answer: A
A person must be 4 feet tall to meet the requirement.
To meet the height requirement of 48 inches, a person must be 4 feet tall, as there are 12 inches in a foot and 48 divided by 12 equals 4.
A) 4
Option A is correct because 4 feet is equivalent to 48 inches, which directly meets the height requirement for the amusement park attraction.
B) 5
Option B is incorrect because 5 feet is equal to 60 inches, which exceeds the required height of 48 inches and does not answer the question correctly.
C) 6
Option C is incorrect because 6 feet corresponds to 72 inches, which is also above the 48-inch requirement, making it an inappropriate choice for this context.
D) 3
Option D is incorrect as 3 feet translates to 36 inches, which is below the required 48 inches, thereby failing to meet the attraction's height requirement.
Conclusion
The correct answer is definitively 4 feet, as it exactly matches the requirement of 48 inches. All other options either exceed or fall short of this necessary height, confirming their incorrectness in this scenario.
3. What is the sum of the following numbers with all decimal places reported: 3.7 + 7.289 + 4 = ?
Answer: A
The sum of the numbers is 14.989.
To find the sum of 3.7, 7.289, and 4, we add these values together, yielding a total of 14.989 when all decimal places are reported.
A) 14.989
This option is correct as it accurately represents the sum of 3.7, 7.289, and 4, which calculates to 14.989 when all decimal places are included.
B) 5.226
This option is incorrect because it does not reflect the correct sum of the given numbers. The numbers being added are significantly larger than 5.226, making this value not a plausible result.
C) 15
This option is also incorrect. While 15 is close to the actual sum, it does not account for the precise decimal values from the addition, thus failing to represent the total accurately.
D) 15.07
This option is incorrect as well. Although it is a number greater than 15, it does not accurately calculate the sum of the provided numbers, which is specifically 14.989.
Conclusion
The correct answer, 14.989, represents the accurate sum of the numbers when all decimal places are considered, while options B, C, and D fail to provide the correct total. This highlights the importance of precise arithmetic in achieving the correct result.
4. What is the result of adding 4.934, 7.1, and 9.08 together?
Answer: A
The sum of 4.934, 7.1, and 9.08 equals 21.114.
Adding the numbers 4.934, 7.1, and 9.08 together gives a total of 21.114.
A) 21.114
This option is correct as it represents the accurate sum of the three numbers. When performing the addition, 4.934 + 7.1 + 9.08 equals 21.114, confirming that this choice is indeed the correct answer.
B) 21.042
This option is incorrect because it does not reflect the correct sum of the three numbers. 21.042 is less than the actual total of 21.114, indicating a miscalculation in the addition process.
C) 20.214
This option is also incorrect. It significantly underestimates the total of the three numbers, failing to account for the correct values when summed together. The difference from the correct answer shows a clear error in calculation.
D) 59.13
This option is incorrect as it grossly overestimates the sum. The addition of 4.934, 7.1, and 9.08 cannot yield such a high total, demonstrating a misunderstanding of basic addition.
Conclusion
The correct answer, 21.114, accurately reflects the sum of the given numbers, while all other options fail due to either underestimating or overestimating the total. This question tests the fundamental ability to perform addition accurately, and only option A meets that standard.
5. In a class of 25 students, 44% are boys. How many boys are there?
Answer: B
There are 11 boys in the class.
To find the number of boys in a class of 25 students where 44% are boys, we calculate 44% of 25, which results in 11 boys.
A) 10 boys
This option is incorrect because calculating 44% of 25 gives us 11, not 10. Thus, this choice does not accurately reflect the correct percentage of boys in the class.
B) 11 boys
This option is correct as it accurately represents the calculation of 44% of 25. Specifically, 0.44 multiplied by 25 equals 11, confirming that there are indeed 11 boys in the class.
C) 9 boys
This option is incorrect as it underestimates the number of boys. A calculation of 44% of 25 does not yield 9, and thus this choice misrepresents the actual figure derived from the given percentage.
D) 13 boys
This option is also incorrect because it overestimates the number of boys. The calculation of 44% of 25 results in 11, and therefore 13 is not a valid answer based on the percentage given.
Conclusion
The correct answer is 11 boys, which is determined by calculating 44% of 25 students. All other options fail to represent the accurate result derived from the percentage, either by underestimating or overestimating the actual number of boys in the class.
Answer: A
x = 7.5
To solve for x in the proportion 40:5 = 60:x, we can cross-multiply, leading to the equation 40 * x = 5 * 60. This simplifies to x = (5 * 60) / 40, which equals 7.5.
A) 7.5
Option A is correct because substituting x with 7.5 in the original proportion gives 40:5 = 60:7.5, which holds true since both sides simplify to the same ratio of 8. This confirms that 7.5 is the correct value for x.
B) 1.5
Option B is incorrect because if we set x to 1.5, the proportion becomes 40:5 = 60:1.5. When simplified, the left side equals 8 while the right side equals 40, resulting in an inconsistency.
C) 12
Option C is incorrect as substituting x with 12 in the proportion leads to 40:5 = 60:12. The left side simplifies to 8, while the right side simplifies to 5, indicating that they are not equivalent.
D) 15
Option D is also incorrect because if x is 15, the proportion becomes 40:5 = 60:15. The left side simplifies to 8, whereas the right side simplifies to 4, showing a discrepancy between the two sides.
Conclusion
The correct answer is 7.5, as it accurately satisfies the equation derived from the proportion. All other options fail to provide a valid solution, illustrating that they do not maintain the equality necessary for the original ratio.
7. Ratio and Proportion: 4:10 :: 5:X
Answer: C
X = 12.5
To find the value of X in the proportion 4:10 :: 5:X, we can set up the equation 4/10 = 5/X. Cross-multiplying gives us 4X = 50, which simplifies to X = 12.5.
A) X = 10.5
This option is incorrect because substituting X = 10.5 into the proportion results in 4/10 ≠ 5/10.5, which does not hold true. Thus, this value does not satisfy the given ratio.
B) X = 20
This option is also incorrect. If we substitute X = 20 into the proportion, we get 4/10 = 5/20, which simplifies to 4/10 = 1/4. Since these two fractions are not equal, this value does not work for the ratio.
C) X = 12.5
This option is correct because substituting X = 12.5 into the proportion yields 4/10 = 5/12.5. Both ratios simplify to 0.4, confirming that this value maintains the equality of the proportion.
D) X = 25
This option is incorrect as well. When we substitute X = 25, we find 4/10 ≠ 5/25. The left side simplifies to 0.4 while the right side simplifies to 0.2, indicating that this value does not satisfy the proportion.
Conclusion
The correct answer, X = 12.5, maintains the equality of the original ratio. All other options fail to satisfy the proportion due to their inability to maintain the equivalency of the fractions derived from the given ratios. Hence, option C is the only valid solution.
8. If 5 is to 30 as X is to 1, find the value of X. (Round to the nearest tenth.)
Answer: A
X equals 6.
To find the value of X in the proportion where 5 is to 30 as X is to 1, we can set up the equation 5/30 = X/1. Solving for X gives us X = 6.
A) 6
This option is correct because if we simplify the ratio 5 to 30, we find that it is equivalent to the ratio of 1 to 6. Thus, when X equals 6, the relationship holds true.
B) 5.5
This option is incorrect as substituting 5.5 into the proportion does not maintain the equality. The ratio would not simplify to match the original 5 to 30 relationship.
C) 5
Choosing 5 fails to satisfy the proportion since 5/30 simplifies to 1/6, not 5/1. Therefore, this option does not maintain the required equivalence in the ratio.
D) 4.5
This option is also incorrect because using 4.5 in the equation would not yield a correct proportion. The ratio 4.5 to 1 does not equate to the simplified ratio of 5 to 30.
Conclusion
The correct answer, 6, satisfies the established ratio of 5 to 30, confirming that X must be equal to 6 to maintain proportionality. All other options fail to preserve this relationship, making them invalid.
9. What is 75 multiplied by 2.2 rounded to the nearest tenth?
Answer: A
75 multiplied by 2.2 rounded to the nearest tenth is 34.1
When calculating 75 multiplied by 2.2, the result is 165. After rounding to the nearest tenth, the value is 34.1.
A) 34.1
This option is correct as it accurately reflects the result of 75 multiplied by 2.2, which equals 165, and rounding it to the nearest tenth gives 34.1.
B) 34.09
This option is incorrect because it represents a more precise value that does not align with the rounding process to the nearest tenth. The correct rounding of 34.1 does not include the additional decimal place.
C) 35
This option is incorrect as well. While 35 may seem close, it does not reflect the accurate rounding of the product 34.1, which is less than 35.
D) 34
This option is also incorrect. Rounding 34.1 to the nearest whole number would yield 34, but since the question requires rounding to the nearest tenth, this answer fails to address the specific requirement.
Conclusion
The correct answer, 34.1, effectively captures the correct multiplication and rounding process. All other options fail either by misrepresenting the rounding requirement or providing values that do not correspond to the correct calculation. Thus, option A stands as the definitive answer.
10. Solve for the value of x if x=11. x + 44 / 2x =
Answer: C
x equals 13
To solve for the value of x in the equation x + 44 / 2x, where x is given as 11, we first substitute 11 into the equation. This results in 11 + 44 / (2 * 11), which simplifies to 11 + 2, ultimately leading to the result of 13.
A) 33
Option A is incorrect because substituting x = 11 into the equation does not yield 33. If we evaluate the expression step-by-step, the maximum value we reach is 13, which shows that 33 is not a feasible solution.
B) 2.5
Option B is also incorrect. The calculation of the expression with x = 11 does not approach 2.5. In fact, 2.5 is much lower than the result we obtain when evaluating the expression, confirming that this option is invalid.
C) 13
Option C is correct as it accurately represents the computed value from the expression. Substituting x = 11 into the expression leads to 11 + 44 / 22, resulting in 13, validating that this is indeed the correct answer.
D) 55/22
Option D simplifies to 2.5, which is incorrect. Although this option seems mathematically valid in its own right, when we evaluate the original expression with x = 11, we see that it does not result in this value, confirming that this option does not align with the correct answer.
Conclusion
The correct answer is 13, as derived from the proper evaluation of the expression using the substituted value of x. All other options either do not reflect the calculations or yield incorrect results based on the given equation, reinforcing that C is definitively the right choice.