Choose the best answer. If necessary, use the paper you were given.
Of the following, which is closest to (2(12/15) - 1/10) / (16/6)?
- B. 1
- C. 2
- D. 3
Correct Answer & Rationale
Correct Answer: B
To evaluate the expression (2(12/15) - 1/10) / (16/6), we first simplify the numerator. Calculating 2(12/15) gives us 16/15. Next, we convert 1/10 to a common denominator of 30, resulting in 3/30. Thus, the numerator becomes (16/15 - 3/30). Converting 16/15 to a denominator of 30 yields 32/30, leading to (32/30 - 3/30) = 29/30. Now, simplifying the denominator, 16/6 reduces to 8/3. Dividing (29/30) by (8/3) is equivalent to multiplying by its reciprocal: (29/30) * (3/8) = 87/240, which approximates to 0.36, closest to 1. Options C (2) and D (3) are incorrect as they overshoot the calculated value, while option B (1) accurately reflects the result.
To evaluate the expression (2(12/15) - 1/10) / (16/6), we first simplify the numerator. Calculating 2(12/15) gives us 16/15. Next, we convert 1/10 to a common denominator of 30, resulting in 3/30. Thus, the numerator becomes (16/15 - 3/30). Converting 16/15 to a denominator of 30 yields 32/30, leading to (32/30 - 3/30) = 29/30. Now, simplifying the denominator, 16/6 reduces to 8/3. Dividing (29/30) by (8/3) is equivalent to multiplying by its reciprocal: (29/30) * (3/8) = 87/240, which approximates to 0.36, closest to 1. Options C (2) and D (3) are incorrect as they overshoot the calculated value, while option B (1) accurately reflects the result.
Other Related Questions
Which of the following is equal to 3 * 9?
- A. 6 * 6
- B. 9 * 3
- C. 3 * 3 * 6
- D. 3 * 3 * 3 * 3
Correct Answer & Rationale
Correct Answer: B
Option B, 9 * 3, is equal to 3 * 9 due to the commutative property of multiplication, which states that changing the order of factors does not change the product. Option A, 6 * 6, equals 36, which does not match 27 (the product of 3 * 9). Option C, 3 * 3 * 6, calculates to 54, also not equal to 27. Option D, 3 * 3 * 3 * 3, equals 81, further confirming it is not equivalent to 27. Thus, only option B accurately represents the value of 3 * 9.
Option B, 9 * 3, is equal to 3 * 9 due to the commutative property of multiplication, which states that changing the order of factors does not change the product. Option A, 6 * 6, equals 36, which does not match 27 (the product of 3 * 9). Option C, 3 * 3 * 6, calculates to 54, also not equal to 27. Option D, 3 * 3 * 3 * 3, equals 81, further confirming it is not equivalent to 27. Thus, only option B accurately represents the value of 3 * 9.
Of the following, which is greatest?
- A. -0.75
- B. 5/-2
- C. -3
- D. -2
Correct Answer & Rationale
Correct Answer: A
Option A, -0.75, is the greatest value among the choices since it is the least negative number. Option B, 5/-2, simplifies to -2.5, which is less than -0.75. Option C, -3, is clearly more negative than both -0.75 and -2. Option D, -2, is greater than -3 but still less than -0.75. In summary, -0.75 is the highest value among negative numbers, making it the greatest option in this comparison.
Option A, -0.75, is the greatest value among the choices since it is the least negative number. Option B, 5/-2, simplifies to -2.5, which is less than -0.75. Option C, -3, is clearly more negative than both -0.75 and -2. Option D, -2, is greater than -3 but still less than -0.75. In summary, -0.75 is the highest value among negative numbers, making it the greatest option in this comparison.
Marisol has 5 times as many books as Jerry. Jerry has 15 books. How many books does Marisol have?
- A. 10
- B. 20
- C. 75
- D. 225
Correct Answer & Rationale
Correct Answer: C
To determine how many books Marisol has, multiply the number of books Jerry has (15) by 5, since Marisol has 5 times as many. This calculation yields 15 x 5 = 75. Option A (10) is incorrect as it underestimates the multiplication factor. Option B (20) also miscalculates, suggesting a much lower total. Option D (225) overestimates the number of books, resulting from an incorrect multiplication. Thus, the only accurate answer is 75, reflecting Marisol's total based on Jerry's count.
To determine how many books Marisol has, multiply the number of books Jerry has (15) by 5, since Marisol has 5 times as many. This calculation yields 15 x 5 = 75. Option A (10) is incorrect as it underestimates the multiplication factor. Option B (20) also miscalculates, suggesting a much lower total. Option D (225) overestimates the number of books, resulting from an incorrect multiplication. Thus, the only accurate answer is 75, reflecting Marisol's total based on Jerry's count.
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 times n?
- A. 1.01
- B. 10.001
- C. 10.01
- D. 10.1
Correct Answer & Rationale
Correct Answer: C
When the decimal point in \( n \) is moved 2 places to the left, \( p \) becomes \( \frac{n}{100} \). Moving the decimal point 1 place to the right gives \( s \) as \( 10n \). Therefore, \( p + s = \frac{n}{100} + 10n \). To combine these, convert \( 10n \) to a fraction: \( 10n = \frac{1000n}{100} \). Thus, \( p + s = \frac{n}{100} + \frac{1000n}{100} = \frac{1001n}{100} \). This simplifies to \( 10.01n \). Option A (1.01) is too low, as it does not account for the large contribution from \( s \). Option B (10.001) and D (10.1) are also incorrect; they either underestimate or overestimate the sum of \( p \) and \( s \). Thus, the correct answer, \( 10.01 \), accurately reflects the relationship between \( p + s \) and \( n \).
When the decimal point in \( n \) is moved 2 places to the left, \( p \) becomes \( \frac{n}{100} \). Moving the decimal point 1 place to the right gives \( s \) as \( 10n \). Therefore, \( p + s = \frac{n}{100} + 10n \). To combine these, convert \( 10n \) to a fraction: \( 10n = \frac{1000n}{100} \). Thus, \( p + s = \frac{n}{100} + \frac{1000n}{100} = \frac{1001n}{100} \). This simplifies to \( 10.01n \). Option A (1.01) is too low, as it does not account for the large contribution from \( s \). Option B (10.001) and D (10.1) are also incorrect; they either underestimate or overestimate the sum of \( p \) and \( s \). Thus, the correct answer, \( 10.01 \), accurately reflects the relationship between \( p + s \) and \( n \).