Choose the best answer. If necessary, use the paper you were given.
1,500 / (15 + 5) =
- A. 75
- B. 130
- C. 315
- D. 400
Correct Answer & Rationale
Correct Answer: A
To solve the expression 1,500 / (15 + 5), first calculate the sum in the parentheses: 15 + 5 equals 20. Next, divide 1,500 by 20. Performing the division gives 1,500 รท 20 = 75, confirming option A as the correct answer. Option B (130) results from an incorrect division or miscalculation. Option C (315) likely stems from misunderstanding the order of operations, possibly miscalculating the sum before division. Option D (400) may arise from mistakenly multiplying instead of dividing. Understanding the correct order of operations is crucial for accurate calculations.
To solve the expression 1,500 / (15 + 5), first calculate the sum in the parentheses: 15 + 5 equals 20. Next, divide 1,500 by 20. Performing the division gives 1,500 รท 20 = 75, confirming option A as the correct answer. Option B (130) results from an incorrect division or miscalculation. Option C (315) likely stems from misunderstanding the order of operations, possibly miscalculating the sum before division. Option D (400) may arise from mistakenly multiplying instead of dividing. Understanding the correct order of operations is crucial for accurate calculations.
Other Related Questions
Which of the following is equivalent to 1.04?
- A. 52/51
- B. 51/50
- C. 27/25
- D. 26/25
Correct Answer & Rationale
Correct Answer: D
To determine which option is equivalent to 1.04, we convert each fraction to a decimal. A: 52/51 equals approximately 1.0196, which is less than 1.04. B: 51/50 equals 1.02, also below 1.04. C: 27/25 equals 1.08, exceeding 1.04. D: 26/25 calculates to 1.04 exactly, matching the target value. Thus, option D accurately represents 1.04, while the other options do not meet the requirement.
To determine which option is equivalent to 1.04, we convert each fraction to a decimal. A: 52/51 equals approximately 1.0196, which is less than 1.04. B: 51/50 equals 1.02, also below 1.04. C: 27/25 equals 1.08, exceeding 1.04. D: 26/25 calculates to 1.04 exactly, matching the target value. Thus, option D accurately represents 1.04, while the other options do not meet the requirement.
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 \( n \).
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.
2(1/2 + 1/3) =
- A. 1(2/3)
- B. 1(5/6)
- C. 2(1/6)
- D. 2(5/6)
Correct Answer & Rationale
Correct Answer: A
To solve 2(1/2 + 1/3), first find a common denominator for the fractions 1/2 and 1/3, which is 6. Rewrite the fractions: 1/2 becomes 3/6 and 1/3 becomes 2/6. Adding these gives 5/6. Now, multiply by 2: 2 * 5/6 equals 10/6, which simplifies to 1(2/3). Option B, 1(5/6), results from miscalculating the addition. Option C, 2(1/6), misinterprets the multiplication step. Option D, 2(5/6), incorrectly applies the multiplication to the wrong sum. Each incorrect option reflects a misunderstanding of the operations involved.
To solve 2(1/2 + 1/3), first find a common denominator for the fractions 1/2 and 1/3, which is 6. Rewrite the fractions: 1/2 becomes 3/6 and 1/3 becomes 2/6. Adding these gives 5/6. Now, multiply by 2: 2 * 5/6 equals 10/6, which simplifies to 1(2/3). Option B, 1(5/6), results from miscalculating the addition. Option C, 2(1/6), misinterprets the multiplication step. Option D, 2(5/6), incorrectly applies the multiplication to the wrong sum. Each incorrect option reflects a misunderstanding of the operations involved.