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Unit V Mathematical Reasoning And Aptitude
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Percentages – Quiz 1
Percentages Quiz 1 (10 MCQs)
This set of multiple-choice questions evaluates skills in decimal conversion, percentage calculation, multiplication, and problem-solving. It covers concepts such as conversion to fraction, cost calculation, discount calculation, and price reduction. Students will practice arithmetic operations, percentage conversion, and solving for total amounts.
Quiz Instructions
Select an option to see the correct answer instantly.
1.
Michael spent $ 210 on school supplies and books. This amount was 30% of his savings. How much was his savings?
A) $ 700.
B) $ 63.
C) $ 630.
D) $ 763.
Show Answer
Correct Answer:
Correct answer is: (A) $ 700.
Exam Relevance:
SAT, ACT, GRE, GMAT
Difficulty:
Moderate
Concept notes:
The problem involves finding the total savings given a percentage and the corresponding amount spent.
Common Mistakes:
A common mistake is to assume that $210 is the total savings and not a percentage of it.
Explanations:
To find Michael's total savings, we need to determine what amount $210 represents 30% of. We can set up the equation:
\[ 0.30 \times \text{Total Savings} = 210 \]
To solve for the Total Savings, we divide both sides by 0.30:
\[ \text{Total Savings} = \frac{210}{0.30} \]
\[ \text{Total Savings} = 700 \]
Thus, Michael's total savings is $700.
Option Analysis:
Option A:
Correct. $700 is the total savings.
Option B:
Incorrect. $63 is not the total savings.
Option C:
Incorrect. $630 is not the total savings.
Option D:
Incorrect. $763 is not the total savings.
2.
A computer has been discounted by 32%. The original cost was $ 900. What is the new price?
A) $ 1188.
B) $ 288.
C) $ 612.
D) $ 600.
Show Answer
Correct Answer:
Correct answer is: (C) $ 612.
Exam Relevance:
SAT, ACT, GRE, GMAT
Difficulty:
Moderate
Concept notes:
The concept tested here is the calculation of a discounted price using percentages.
Common Mistakes:
A common mistake is to calculate the discount amount and subtract it from the original price incorrectly.
Explanations:
To find the new price after a 32% discount, first calculate the discount amount:
\[ \text{Discount amount} = 32\% \times 900 = 0.32 \times 900 = 288 \]
Next, subtract the discount amount from the original price:
\[ \text{New price} = 900 - 288 = 612 \]
Thus, the new price is $612.
Option Analysis:
Option A:
$ 1188 is incorrect because it is greater than the original price, which is not possible after a discount.
Option B:
$ 288 is incorrect because it is the discount amount, not the new price.
Option C:
$ 612 is correct as it is the result of subtracting the discount amount from the original price.
Option D:
$ 600 is incorrect because it does not match the calculated new price.
3.
Find 50% of 180
A) 9.
B) .9.
C) 90.
D) 900.
Show Answer
Correct Answer:
Correct answer is: (C) 90.
Exam Relevance:
SAT, ACT, GRE, GMAT
Difficulty:
Easy
Concept notes:
To find 50% of a number, you multiply the number by 0.5.
Common Mistakes:
A common mistake is to misinterpret the percentage as a decimal or to use the wrong operation, such as division instead of multiplication.
Explanations:
To find 50% of 180, you multiply 180 by 0.5:
\[ 180 \times 0.5 = 90 \]
Option Analysis:
Option A:
9 is incorrect because it is too small. 50% of 180 should be half of 180, which is 90.
Option B:
0.9 is incorrect because it is much too small. 50% of 180 should be half of 180, which is 90.
Option C:
90 is correct because 50% of 180 is half of 180, which is 90.
Option D:
900 is incorrect because it is much too large. 50% of 180 should be half of 180, which is 90.
4.
What is 80% of 200
A) 150.
B) 80.
C) 160.
D) 140.
Show Answer
Correct Answer:
Correct answer is: (C) 160.
Exam Relevance:
SAT, ACT, GRE, GMAT
Difficulty:
Easy
Concept notes:
To find 80% of 200, we need to calculate 80/100 of 200.
Common Mistakes:
A common mistake is to misinterpret the percentage and calculate 80% incorrectly, such as by dividing 200 by 80 or multiplying 200 by 80 without converting the percentage to a decimal.
Explanations:
To find 80% of 200, we convert 80% to a decimal by dividing 80 by 100, which gives 0.80. Then, we multiply 200 by 0.80:
\[ 200 \times 0.80 = 160 \]
Thus, 80% of 200 is 160.
Option Analysis:
Option A:
150 is incorrect because it does not match the calculation of 80% of 200.
Option B:
80 is incorrect because it is only 40% of 200, not 80%.
Option C:
160 is correct because it matches the calculation of 80% of 200.
Option D:
140 is incorrect because it does not match the calculation of 80% of 200.
5.
Convert 67% to a fraction.
A) 6/7.
B) 7/6.
C) 67/100.
D) 67/10.
Show Answer
Correct Answer:
Correct answer is: (C) 67/100.
Exam Relevance:
SAT, ACT, GRE, GMAT
Difficulty:
Easy
Concept notes:
A percentage is a way of expressing a number as a fraction of 100. To convert a percentage to a fraction, place the percentage over 100 and simplify if possible.
Common Mistakes:
A common mistake is to think that 67% can be simplified to a fraction like 6/7, which is incorrect.
Explanations:
To convert 67% to a fraction, we write 67 over 100, which gives us 67/100. This fraction cannot be simplified further, so 67/100 is the correct representation of 67% as a fraction.
Option Analysis:
Option A:
6/7 is incorrect because it does not represent 67% accurately.
Option B:
7/6 is incorrect because it does not represent 67% accurately.
Option C:
67/100 is the correct representation of 67% as a fraction.
Option D:
67/10 is incorrect because it does not represent 67% accurately.
6.
The cost of a car originally costing 9500 euros is reduced by 25%. Find its new cost.
A) 7125.
B) 7000.
C) 8000.
D) 9400.
Show Answer
Correct Answer:
Correct answer is: (A) 7125.
Exam Relevance:
SAT, ACT, GRE, GMAT
Difficulty:
Easy
Concept notes:
The concept tested here is the calculation of a percentage reduction in cost.
Common Mistakes:
A common mistake is to subtract 25% directly from the original price without converting the percentage to a decimal.
Explanations:
To find the new cost after a 25% reduction, first calculate 25% of the original cost:
\[ 25\% \text{ of } 9500 = \frac{25}{100} \times 9500 = 0.25 \times 9500 = 2375 \]
Next, subtract this amount from the original cost:
\[ 9500 - 2375 = 7125 \]
Thus, the new cost of the car is 7125 euros.
Option Analysis:
Option A:
Correct. The new cost after a 25% reduction is 7125 euros.
Option B:
Incorrect. This option does not reflect the correct calculation of the 25% reduction.
Option C:
Incorrect. This option does not reflect the correct calculation of the 25% reduction.
Option D:
Incorrect. This option does not reflect the correct calculation of the 25% reduction.
7.
What is 45% of 200?
A) 75.
B) 100.
C) 90.
D) None of above.
Show Answer
Correct Answer:
Correct answer is: (C) 90.
Exam Relevance:
SAT, ACT, GRE, GMAT
Difficulty:
Easy
Concept notes:
To find a percentage of a number, multiply the number by the percentage (expressed as a decimal).
Common Mistakes:
A common mistake is to misinterpret the percentage as a fraction or to use the wrong decimal equivalent.
Explanations:
To find 45% of 200, convert 45% to a decimal by dividing by 100, which gives 0.45. Then, multiply 200 by 0.45:
\[ 200 \times 0.45 = 90 \]
Option Analysis:
Option A:
75 is incorrect because it is the result of 37.5% of 200, not 45%.
Option B:
100 is incorrect because it is the result of 50% of 200, not 45%.
Option C:
90 is correct because it is the result of 45% of 200.
Option D:
None of the above is incorrect because 90 is a valid option.
8.
Which is the decimal for 12%?
A) 0.12.
B) 1.2.
C) 12.0.
D) 0.012.
Show Answer
Correct Answer:
Correct answer is: (A) 0.12.
Exam Relevance:
SAT, ACT, GRE, GMAT
Difficulty:
Very Easy
Concept notes:
To convert a percentage to a decimal, divide the percentage by 100.
Common Mistakes:
A common mistake is to misplace the decimal point, leading to incorrect conversion.
Explanations:
To convert 12% to a decimal, divide 12 by 100. This results in 0.12.
Option Analysis:
Option A:
0.12 is the correct conversion of 12% to a decimal.
Option B:
1.2 is incorrect because it is 120% as a decimal.
Option C:
12.0 is incorrect because it is 1200% as a decimal.
Option D:
0.012 is incorrect because it is 1.2% as a decimal.
9.
Express 0.2 as a percentage
A) 20%.
B) 2%.
C) 0.2%.
D) 200%.
Show Answer
Correct Answer:
Correct answer is: (A) 20%.
Exam Relevance:
SAT, ACT, GRE, GMAT
Difficulty:
Easy
Concept notes:
To convert a decimal to a percentage, multiply the decimal by 100.
Common Mistakes:
A common mistake is to think that 0.2 is 2%, which is incorrect. The correct conversion involves multiplying by 100.
Explanations:
To convert 0.2 to a percentage, multiply 0.2 by 100:
0.2 × 100 = 20%
Option Analysis:
Option A:
Correct. 0.2 as a percentage is 20%.
Option B:
Incorrect. 0.2 as a percentage is not 2%.
Option C:
Incorrect. 0.2 as a percentage is not 0.2%.
Option D:
Incorrect. 0.2 as a percentage is not 200%.
10.
Lisa scored 60 marks for her Science test in term 1. In term 3, her marks increased by 10%. How many marks did she score in term 3?
A) 6.
B) 54.
C) 66.
D) 70.
Show Answer
Correct Answer:
Correct answer is: (C) 66.
Exam Relevance:
SAT, ACT, GRE, GMAT
Difficulty:
Moderate
Concept notes:
To find the marks Lisa scored in term 3, we need to calculate a 10% increase on her term 1 score of 60 marks.
Common Mistakes:
A common mistake is to add 10 to the original score instead of calculating 10% of the original score and then adding it.
Explanations:
1. Calculate 10% of 60 marks:
\[ 10\% \text{ of } 60 = \frac{10}{100} \times 60 = 6 \]
2. Add this 10% increase to the original score:
\[ 60 + 6 = 66 \]
Therefore, Lisa scored 66 marks in term 3.
Option Analysis:
Option A:
6. This is incorrect because it represents only the 10% increase, not the total score.
Option B:
54. This is incorrect because it is less than the original score, which contradicts the problem statement.
Option C:
66. This is correct as it represents the original score plus the 10% increase.
Option D:
70. This is incorrect because it represents a 16.67% increase, not a 10% increase.
Frequently Asked Questions
What is the purpose of learning about percentages in mathematical reasoning?
Learning about percentages helps in understanding proportions and fractions, which are essential for solving real-world problems involving discounts, cost calculations, and financial planning.
How can I convert a percentage to a decimal?
To convert a percentage to a decimal, divide the percentage by 100. For example, 50% becomes 0.50 when converted to a decimal.
What is the difference between a percentage increase and a percentage decrease?
A percentage increase refers to an increase in value relative to the original amount, while a percentage decrease refers to a reduction in value relative to the original amount.
How do I calculate the total savings when a discount is applied?
To calculate total savings, multiply the original price by the discount percentage (converted to a decimal). For example, a 20% discount on a $100 item saves $20.
Can percentages be used to represent fractions?
Yes, percentages can be used to represent fractions. For example, 50% is equivalent to the fraction 1/2.