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Question 1
Of the following, which is greatest?
Your Answer: Option(s)
Correct Answer: Option(s) A
Rationale
-0.75
When comparing numbers, the value closest to zero is considered the greatest in terms of magnitude. Since negative numbers are less than zero, the number closest to zero, in this case, -0.75, is the greatest among the options.
B) 5/-2
The division of 5 by -2 results in -2.5, which is further from zero compared to -0.75. Therefore, this choice is not the greatest.
C) -3
-3 is greater than -0.75 in terms of magnitude since it is further from zero on the number line. Thus, this choice is not the greatest.
D) -2
Similarly, -2 is greater than -0.75 in magnitude as it is farther from zero on the number line. Therefore, this option is not the greatest.
Conclusion
When comparing the options provided, -0.75 is the greatest number among them due to its proximity to zero on the number line. The negative sign indicates that these numbers are less than zero, making the number closest to zero the greatest in terms of magnitude.
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Question 2
Last year Joan's salary was $18,000. If she receives a $900 raise for this year, what percent of last year's salary is her raise?
Your Answer: Option(s)
Correct Answer: Option(s) B
Rationale
Choice B) 5%
To calculate the percentage increase in Joan's salary, divide the raise amount ($900) by her previous year's salary ($18,000), then multiply by 100 to express it as a percentage. In this case, ($900 / $18,000) * 100 = 5%, making B the correct choice.
A) 2%
This percentage represents the incorrect calculation of the raise. Dividing $900 by $18,000 yields 0.05, which when converted to a percentage equals 5%, not 2%.
C) 20%
This percentage overestimates the raise amount. If Joan's raise were 20% of her previous salary, it would amount to $3,600 ($18,000 * 0.20), which is four times higher than the actual raise of $900.
D) 50%
A 50% raise would mean Joan's salary increased by half of the previous year's amount, resulting in a raise of $9,000 ($18,000 * 0.50). This value greatly exceeds the $900 raise she actually received.
Conclusion
By correctly applying the percentage increase formula—dividing the raise amount by the initial salary and converting to a percentage—Joan's $900 raise for this year corresponds to 5% of her $18,000 salary from the previous year. This calculation accurately reflects the proportional increase in her earnings between the two consecutive years.
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Question 3
What is rounded to the nearest hundredth? 48/27
Your Answer: Option(s)
Correct Answer: Option(s) C
Rationale
1.78
When dividing 48 by 27, the result is approximately 1.77777777778. Rounding to the nearest hundredth means keeping two decimal places, resulting in 1.78 as the correct answer.
A) 1.7
1.7 is the result when the division is rounded to one decimal place, not two as required for rounding to the nearest hundredth.
B) 1.77
1.77 represents the result when the division is rounded to two decimal places but is not rounded correctly to the nearest hundredth.
C) 1.78
This is the correct answer. Rounding 1.77777777778 to the nearest hundredth results in 1.78.
D) 1.8
Rounding to the nearest tenth would yield 1.8, but rounding to the nearest hundredth requires two decimal places. Therefore, 1.8 is not the appropriate rounding for this calculation.
Conclusion
In this mathematical calculation, the division of 48 by 27 results in a decimal that can be rounded to the nearest hundredth by keeping two decimal places. The correct answer, 1.78, is obtained by correctly applying the rounding rule for this specific question.
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Question 4
If 40 is 20 percent of a number, then the number is what percent of 40?
Your Answer: Option(s)
Correct Answer: Option(s) A
Rationale
500%
To solve this problem, we can set up a proportion. If 40 is 20% of a number, that means 40 is equal to 20% of the unknown number. Therefore, 40 = 0.20x, where x is the unknown number. To find what percent x is of 40, we divide x by 40 and multiply by 100 to get the percentage. So, x/40 * 100 = (0.20x/40) * 100 = 0.005x * 100 = 0.5x * 100 = 50x = 500%.
B) 200%
If the number were 200% of 40, it would mean the number is twice the value of 40. However, in this scenario, we are looking for what percent the number is of 40, not how many times larger it is than 40.
C) 80%
If the number were 80% of 40, it would imply that the number is less than 40. However, the question asks for the percentage the number represents when compared to 40, not when compared to the number itself.
D) 20%
Choosing 20% as the answer would mean that the number is only 20% of 40, which is the opposite of what the question is asking. We need to find the percentage that the number represents concerning 40.
Conclusion
By setting up a proportion and solving for the unknown number, we determine that the number is 500% of 40. This means that the unknown number is five times larger than 40, fulfilling the conditions provided in the question.
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Question 5
The number p is obtained by moving the decimal point 2 places to the left in the positive number n. The number s is obtained by moving the decimal point 1 place to the right in the number n. The number p + s how many × n?
Your Answer: Option(s)
Correct Answer: Option(s) C
Rationale
Number n is multiplied by 10.
When the decimal point in a number is moved two places to the left, it is effectively multiplied by 10 twice, resulting in a factor of 100. Similarly, moving the decimal point one place to the right multiplies the number by 10. Therefore, the sum of these two operations, p + s, corresponds to multiplying n by 100 + 10 = 110.
A) 1.01
This choice represents a number slightly above 1, which does not align with the multiplication factor of 110 obtained by adding p and s to n. The value of 1.01 does not reflect the correct relationship between n, p, s, and their sum.
B) 10.001
The number 10.001 is notably higher than the expected result of multiplying n by 110. This value does not correspond to the sum of the two transformations applied to n and is not consistent with the arithmetic operation required to find p + s.
C) 10.01
Since p represents 100n and s represents 10n, adding these values together results in 110n, making the correct choice C, 10.01, the most suitable answer. This number reflects the operation of moving the decimal points in n as described in the question and sums them accurately.
D) 10.1
The value of 10.1 does not match the expected sum of 110n, which arises from moving the decimal point in n as specified in the question. This choice does not align with the multiplication factor associated with the transformations of n to obtain p and s.
Conclusion
In this scenario, the correct answer is option C, 10.01. By understanding how moving the decimal point in a number affects its value, we can deduce that p + s equals 110 times n. The sum of these two transformations results in a factor that multiplies the original number n to produce the final value of 10.01.
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