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Karen goes to the grocery store with $40. She buys a carton of milk for $1.85, a loaf of bread for $3.20, and a bunch of bananas for $3.05. How much money does she have left?
- A. $31.90
- B. $31.90
- C. $32.10
- D. $34.95
Correct Answer: B
Rationale: To determine how much money Karen has left, we need to subtract the total cost of her purchases from the amount she started with. The total cost of her purchases is calculated by adding the prices of the carton of milk, loaf of bread, and bunch of bananas: $1.85 + $3.20 + $3.05 = $8.10. By subtracting $8.10 from the $40 Karen started with, we get $31.90. Therefore, Karen has $31.90 left after buying the items.
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1.2:x::14:42 =
- A. 0.6
- B. 3.6
- C. 1.2
- D. 2.4
Correct Answer: B
Rationale: To solve this proportion, we use the property that the product of the means is equal to the product of the extremes. In this case, we have 1.2 * 42 = 14 * x. Simplifying, we get 50.4 = 14x. To find the value of x, we divide both sides by 14, giving x = 50.4 / 14 = 3.6. Therefore, the correct answer is 3.6, which corresponds to option B. This means that the relationship between 1.2 and x is the same as the relationship between 14 and 42, following a proportional logic where the ratios are equivalent.
Solve for x: 3:2 :: 24:x
- A. 16
- B. 12
- C. 2
- D. 22
Correct Answer: A
Rationale: To solve this proportion, we use the property that in a proportion, the product of the means is equal to the product of the extremes. So, 3 * x = 2 * 24. By solving for x, we find x = 16. Therefore, the correct answer is A. In this analogy, the relationship between the first pair of numbers (3 and 2) must hold true for the second pair of numbers (24 and x). By setting up the proportion, we can find the missing value x. This type of problem is common in mathematics and helps test your understanding of proportional relationships.
What is the result of adding the fractions 2/3 + 1/6 + 2/5?
- A. 2/5
- B. 1 7/30
- C. 1/3
- D. 1 1/15
Correct Answer: B
Rationale: To add fractions with different denominators, first, find a common denominator. In this case, the common denominator is 30. Convert each fraction to have a denominator of 30: 2/3 = 20/30, 1/6 = 5/30, and 2/5 = 12/30. Now, add the numerators: 20/30 + 5/30 + 12/30 = 37/30. Simplifying 37/30 gives 1 7/30 as the final result.
What is 32 divided by 8/9?
- A. 36
- B. 4 & 1/9
- C. 28 & 4/9
- D. 4
Correct Answer: A
Rationale: To divide by a fraction, you can multiply by its reciprocal. In this case, 32 divided by 8/9 is equivalent to 32 multiplied by 9/8. Multiplying 32 by 9/8 gives 288/8, which simplifies to 36. Therefore, the correct answer is A, 36. When dividing by a fraction, remember to multiply by the reciprocal to find the result. In this case, multiplying 32 by the reciprocal of 8/9, which is 9/8, gives the final answer of 36.
Divide: 41.2 ÷ 0.2 =
- A. 206
- B. 2.06
- C. 0.206
- D. 2.06
Correct Answer: A
Rationale: Correct Answer: A
Rationale:
1. Divide 41.2 by 0.2:
41.2 ÷ 0.2 = 412 ÷ 2 = 206.
Explanation:
To divide a decimal by another decimal, first, move the decimal point in both numbers to make the divisor a whole number. Then, divide as usual. The correct answer is 206.
Summary:
- Choice B (2.06) is incorrect as the decimal point was not moved correctly for division.
- Choice C (0.206) is incorrect as the decimal point was not moved correctly for division.
- Choice D (2.06) is incorrect as it doesn't reflect the correct result of dividing 41.2 by 0.2.