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Question 1
Person A has $60, and Person B has $50. Person A is saving $10 per week, and Person B is saving $15 per week. How many weeks do they need to save before they have the same amount of money?
Your Answer: Option(s)
Correct Answer: Option(s) A
Rationale
Person A and Person B will have the same amount of money after 5 weeks.
This is calculated by finding out the difference in their initial amounts and the rate at which they save per week. Person A starts with $60 and saves $10 weekly, while Person B starts with $50 and saves $15 weekly. The difference in their initial amounts is $10, and the difference in their saving rates is $5 per week. Therefore, it will take 2 weeks (10/5) for Person B to catch up to the initial amount of Person A, and they will have the same amount of money from the 5th week onward.
A) 2 weeks
This choice correct assumes that the two people will have the same amount of money after 2 weeks. Person B's saving rate is higher than Person A's by $5 per week. Thus, the initial $10 difference between their amounts will be eliminated after 2 weeks, after which Person B will start to catch up.
B) 2.7 weeks
This choice incorrectly assumes a fractional week, which is not possible in this context. Savings occur on a weekly basis, so it is not valid to consider fractions of a week.
C) 10 weeks
This choice incorrectly assumes that it will take 10 weeks for Person B to catch up to Person A. However, given that Person B is saving at a faster rate than Person A, they will have the same amount of money much earlier than 10 weeks.
D) 5 weeks
This is incorrect answer. After 2 weeks, Person B will have caught up to the initial amount of Person A.
Conclusion
The question requires determining when Person A and Person B will have the same amount of money given their different initial amounts and different saving rates. By calculating the time it takes for Person B to make up the initial difference and then considering the weekly savings rate, we can conclude that they will both have the same amount of money after 2 weeks.
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Question 2
The temperature was average on Wednesday. The temperature decreased from Tuesday to Wednesday. What can be inferred from the graph?
Your Answer: Option(s)
Correct Answer: Option(s) C
Rationale
Temperature decreased overall.
The question clearly states that the temperature dropped from Tuesday to Wednesday. This demonstrates a declining trend in temperature across the observed period.
A) Temperature increased overall
This choice is incorrect because the question statement clearly indicates that the temperature decreased from Tuesday to Wednesday, not increased.
B) Temperature remained constant
Again, this option is not accurate. The question explicitly states that the temperature decreased from Tuesday to Wednesday, which contradicts the idea of a constant temperature.
C) Temperature decreased overall
This is the correct answer. The question makes it clear that there was a decrease in temperature from Tuesday to Wednesday, indicating a downward trend in temperature over the given period.
D) Temperature fluctuated randomly
This option is also wrong. Although the question statement does not provide information about the temperature pattern for other days of the week, it does clearly state that the temperature decreased from Tuesday to Wednesday. This indicates a specific trend, not random fluctuations.
Conclusion
Based on the information provided in the question, it can be inferred that the temperature decreased overall from Tuesday to Wednesday. This dismisses the possibilities of the temperature increasing, remaining constant, or fluctuating randomly. The correct answer to the question is thus 'Temperature decreased overall'.
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Question 3
A normal saline solution is 0.9% sodium chloride. Express that percent as a decimal.
Your Answer: Option(s)
Correct Answer: Option(s) C
Rationale
0.009 is the decimal representation of 0.9%.
To convert a percent to a decimal, you must divide the percentage by 100. This is because the word "percent" means "per 100." In this case, dividing 0.9 by 100 gives us 0.009.
A) 0.09
This choice represents a misunderstanding of the conversion from percent to decimal. Dividing by 100 will always move the decimal point two places to the left. Therefore, 0.9% becomes 0.009, not 0.09.
B) 9
This option suggests a complete misunderstanding of the conversion from percent to decimal. The value 9 is 900% when expressed as a percentage, which is far greater than 0.9%. The correct conversion of 0.9% is 0.009.
C) 0.009
This is the correct answer. Dividing 0.9 by 100 yields 0.009, correctly representing 0.9% as a decimal.
D) 90
This choice indicates a misunderstanding of the conversion from percent to decimal. The value 90 is 9000% when expressed as a percentage, which is significantly greater than 0.9%. The correct conversion of 0.9% is 0.009.
Conclusion
To convert a percentage to a decimal, the percentage value must be divided by 100. In the case of 0.9%, the result of this division is 0.009. Therefore, 0.009 is the correct decimal representation of 0.9%. The other options represent common misconceptions about the process of converting percentages to decimals.
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Question 4
A 120 milliliter (mL) solution contains a mixture of water and acid. The acid makes up 40% of the solution. How many mL of water make up the solution?
Your Answer: Option(s)
Correct Answer: Option(s) C
Rationale
72 mL of the solution is made up of water.
The question tells us that the total solution is 120 mL and that acid makes up 40% of the solution. Therefore, if we want to find out how much of the solution is water, we need to subtract the amount of acid from the total solution.
A) 40 mL
This would be the amount of acid in the solution, not the amount of water. This is calculated by taking 40% of the total volume (120 mL), which gives 48 mL. This answer confuses the percentage of the solution that is acid with the volume of water in the solution.
B) 60 mL
This choice would be correct if the solution were 50% acid and 50% water. However, the question clearly states that the solution is 40% acid, which means it is 60% water. Therefore, 60% of the total 120 mL solution equals 72 mL of water, not 60 mL.
C) 72 mL
This is the correct answer. It is calculated by determining what volume makes up 60% of the solution. Since the solution is 40% acid, the remaining 60% is water. 60% of 120 mL equals 72 mL.
D) 48 mL
This is the volume of acid in the solution, not the amount of water. It is calculated by determining what volume makes up 40% of the solution. Since the solution is 40% acid, 40% of 120 mL equals 48 mL.
Conclusion
When dealing with percentages in a solution, it's important to understand that the percentage refers to the volume of the component in relation to the total volume of the solution. Therefore, if a solution is 40% acid, the remaining 60% is water. In this case, 60% of the total 120 mL solution equals 72 mL of water, not 60 mL or any other volume. The other choices confuse the volume of acid with the volume of water or misinterpret the percentages.
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Question 5
Change 9/16 to a decimal rounded to the nearest thousandth.
Your Answer: Option(s)
Correct Answer: Option(s) C
Rationale
0.563 is the decimal equivalent of 9/16 when rounded to the nearest thousandth.
To convert a fraction to a decimal, you divide the numerator by the denominator. In this case, dividing 9 by 16 gives a decimal of 0.5625. When rounding to the nearest thousandth, this becomes 0.563.
A) 0.56
This choice rounds the number to the nearest hundredth, which is not as precise as rounding to the nearest thousandth. The decimal 0.56 omits the third digit after the decimal point, resulting in less precision than the correct answer.
B) 0.57
This choice incorrectly rounds the decimal to the nearest hundredth. When rounding to the nearest hundredth, the correct decimal equivalent of 9/16 should be 0.56, not 0.57. The choice of 0.57 suggests an overestimation in the rounding process.
C) 0.563
This is the correct answer. When 9 is divided by 16, the result is 0.5625. Rounding this to the nearest thousandth gives 0.563.
D) 0.5625
The answer is not rounded to the required state
Conclusion
When converting the fraction 9/16 to a decimal and rounding to the nearest thousandth, the correct answer is 0.563. The other choices represent either errors in rounding or are less precise due to being rounded to the nearest hundredth instead of the nearest thousandth. The presence of an identical choice might be a mistake in the question design.
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