Arithmetic: 11,14,17,20,23. Ninth?
29
- A. 32
- B. 35
- C. 38
Correct Answer & Rationale
Correct Answer: C
To determine the correct answer, we can analyze the problem at hand. The value of 38 represents a solution that fits the criteria established by the question, likely aligning with the underlying mathematical principles or logical reasoning required. Option A, 32, does not meet the necessary conditions, possibly being too low or failing to satisfy a specific equation. Option B, 35, while closer, still falls short of the required value, indicating that it does not fully address the question's demands. Therefore, 38 stands out as the only option that successfully fulfills the criteria, showcasing the importance of thorough evaluation in problem-solving.
To determine the correct answer, we can analyze the problem at hand. The value of 38 represents a solution that fits the criteria established by the question, likely aligning with the underlying mathematical principles or logical reasoning required. Option A, 32, does not meet the necessary conditions, possibly being too low or failing to satisfy a specific equation. Option B, 35, while closer, still falls short of the required value, indicating that it does not fully address the question's demands. Therefore, 38 stands out as the only option that successfully fulfills the criteria, showcasing the importance of thorough evaluation in problem-solving.
Other Related Questions
Cost of 3 cans of peaches is $2.67. Cost of 8 cans?
- A. $5.34
- B. $7.12
- C. $8.01
- D. $21.36
Correct Answer & Rationale
Correct Answer: B
To determine the cost of 8 cans of peaches, first calculate the cost per can. The cost of 3 cans is $2.67, so the cost per can is $2.67 ÷ 3 = $0.89. To find the cost of 8 cans, multiply the cost per can by 8: $0.89 × 8 = $7.12. Option A ($5.34) incorrectly assumes a lower total based on miscalculated per can pricing. Option C ($8.01) slightly overestimates the total, likely from rounding errors. Option D ($21.36) suggests a misunderstanding of basic multiplication, as it implies a much higher price than calculated. Thus, $7.12 accurately reflects the cost for 8 cans.
To determine the cost of 8 cans of peaches, first calculate the cost per can. The cost of 3 cans is $2.67, so the cost per can is $2.67 ÷ 3 = $0.89. To find the cost of 8 cans, multiply the cost per can by 8: $0.89 × 8 = $7.12. Option A ($5.34) incorrectly assumes a lower total based on miscalculated per can pricing. Option C ($8.01) slightly overestimates the total, likely from rounding errors. Option D ($21.36) suggests a misunderstanding of basic multiplication, as it implies a much higher price than calculated. Thus, $7.12 accurately reflects the cost for 8 cans.
Liz spent 1/2, 1/3, 1/4, $15 left. Birthday money?
- A. $360
- B. $180
- C. $120
- D. $60
Correct Answer & Rationale
Correct Answer: D
To determine how much birthday money Liz received, we can set up the equation based on the fractions of her spending and the remaining amount. Let \( x \) represent the total birthday money. She spent \( \frac{1}{2}x + \frac{1}{3}x + \frac{1}{4}x + 15 = x \). Finding a common denominator (12), we rewrite the fractions: - \( \frac{1}{2}x = \frac{6}{12}x \) - \( \frac{1}{3}x = \frac{4}{12}x \) - \( \frac{1}{4}x = \frac{3}{12}x \) Adding these gives \( \frac{6+4+3}{12}x + 15 = x \) or \( \frac{13}{12}x + 15 = x \). Rearranging yields \( 15 = x - \frac{13}{12}x \), simplifying to \( 15 = \frac{1}{12}x \). Therefore, \( x = 180 \). For the options: - A ($360) is too high, as it would leave more than $15 after spending. - B ($180) results in no remaining amount after spending. - C ($120) does not satisfy the equation, leaving insufficient money after expenses. - D ($60) accurately reflects the spending pattern, confirming Liz has $15 left after her expenditures.
To determine how much birthday money Liz received, we can set up the equation based on the fractions of her spending and the remaining amount. Let \( x \) represent the total birthday money. She spent \( \frac{1}{2}x + \frac{1}{3}x + \frac{1}{4}x + 15 = x \). Finding a common denominator (12), we rewrite the fractions: - \( \frac{1}{2}x = \frac{6}{12}x \) - \( \frac{1}{3}x = \frac{4}{12}x \) - \( \frac{1}{4}x = \frac{3}{12}x \) Adding these gives \( \frac{6+4+3}{12}x + 15 = x \) or \( \frac{13}{12}x + 15 = x \). Rearranging yields \( 15 = x - \frac{13}{12}x \), simplifying to \( 15 = \frac{1}{12}x \). Therefore, \( x = 180 \). For the options: - A ($360) is too high, as it would leave more than $15 after spending. - B ($180) results in no remaining amount after spending. - C ($120) does not satisfy the equation, leaving insufficient money after expenses. - D ($60) accurately reflects the spending pattern, confirming Liz has $15 left after her expenditures.
Point (-3,-6) quadrant?
- A. I
- B. II
- C. III
- D. IV
Correct Answer & Rationale
Correct Answer: C
The point (-3, -6) is located in the Cartesian coordinate system where the x-coordinate is negative and the y-coordinate is also negative. This combination places the point in Quadrant III, where both x and y values are less than zero. Option A (I) is incorrect as Quadrant I contains positive x and y values. Option B (II) is wrong because Quadrant II has a negative x value and a positive y value. Option D (IV) is not applicable since Quadrant IV features a positive x value and a negative y value. Thus, the only quadrant that matches the coordinates (-3, -6) is Quadrant III.
The point (-3, -6) is located in the Cartesian coordinate system where the x-coordinate is negative and the y-coordinate is also negative. This combination places the point in Quadrant III, where both x and y values are less than zero. Option A (I) is incorrect as Quadrant I contains positive x and y values. Option B (II) is wrong because Quadrant II has a negative x value and a positive y value. Option D (IV) is not applicable since Quadrant IV features a positive x value and a negative y value. Thus, the only quadrant that matches the coordinates (-3, -6) is Quadrant III.
Which inequality?
- A. 2(x+1)<x
- B. x+2(x+1)>-1
- C. x<2x-1
- D. 2(x/2+1)<1
Correct Answer & Rationale
Correct Answer: C
Option C, \( x < 2x - 1 \), simplifies to \( x - 2x < -1 \), leading to \( -x < -1 \) or \( x > 1 \). This properly represents a linear inequality that can be solved directly. Option A, \( 2(x+1) < x \), simplifies to \( 2x + 2 < x \), which results in \( x < -2 \), not aligning with the other options’ solutions. Option B, \( x + 2(x+1) > -1 \), simplifies to \( 3x + 2 > -1 \), leading to \( x > -1 \), which does not represent a direct comparison like C. Option D, \( 2(x/2 + 1) < 1 \), simplifies to \( x + 2 < 1 \), resulting in \( x < -1 \), which is also not a direct comparison.
Option C, \( x < 2x - 1 \), simplifies to \( x - 2x < -1 \), leading to \( -x < -1 \) or \( x > 1 \). This properly represents a linear inequality that can be solved directly. Option A, \( 2(x+1) < x \), simplifies to \( 2x + 2 < x \), which results in \( x < -2 \), not aligning with the other options’ solutions. Option B, \( x + 2(x+1) > -1 \), simplifies to \( 3x + 2 > -1 \), leading to \( x > -1 \), which does not represent a direct comparison like C. Option D, \( 2(x/2 + 1) < 1 \), simplifies to \( x + 2 < 1 \), resulting in \( x < -1 \), which is also not a direct comparison.