Joe’s age 4 more than 3x Amy’s. Equation?
- A. A=J/3+4
- B. A=3J+4
- C. J=3A+4
- D. J=3(A+4)
Correct Answer & Rationale
Correct Answer: C
To find the equation representing Joe's age in relation to Amy's, we start with the statement: Joe's age (J) is 4 more than 3 times Amy's age (A). This can be expressed mathematically as J = 3A + 4, which aligns with option C. Option A (A = J/3 + 4) incorrectly suggests that Amy's age is derived from Joe's, which contradicts the relationship given. Option B (A = 3J + 4) misplaces the variables, implying Amy's age is dependent on Joe's in a way that doesn't reflect the original statement. Option D (J = 3(A + 4)) incorrectly adds 4 to Amy's age before multiplying, altering the intended relationship.
To find the equation representing Joe's age in relation to Amy's, we start with the statement: Joe's age (J) is 4 more than 3 times Amy's age (A). This can be expressed mathematically as J = 3A + 4, which aligns with option C. Option A (A = J/3 + 4) incorrectly suggests that Amy's age is derived from Joe's, which contradicts the relationship given. Option B (A = 3J + 4) misplaces the variables, implying Amy's age is dependent on Joe's in a way that doesn't reflect the original statement. Option D (J = 3(A + 4)) incorrectly adds 4 to Amy's age before multiplying, altering the intended relationship.
Other Related Questions
Quickly multiply 24x16?
- A. 20x20-4x4
- B. 20x20
- C. 20x10+4x6
- D. 25x10+4x15
Correct Answer & Rationale
Correct Answer: A
Option A, 20x20 - 4x4, effectively utilizes the difference of squares method. It simplifies the multiplication by recognizing that 24 can be expressed as 20 + 4 and 16 as 20 - 4, leading to a calculation of (20+4)(20-4). Option B, 20x20, underestimates the value of 24 and 16, yielding only 400 instead of the correct 384. Option C, 20x10 + 4x6, inaccurately breaks down the multiplication, leading to 200 + 24, which totals 224. Option D, 25x10 + 4x15, misrepresents the factors, resulting in 250 + 60, totaling 310. Thus, option A is the most accurate approach for this multiplication.
Option A, 20x20 - 4x4, effectively utilizes the difference of squares method. It simplifies the multiplication by recognizing that 24 can be expressed as 20 + 4 and 16 as 20 - 4, leading to a calculation of (20+4)(20-4). Option B, 20x20, underestimates the value of 24 and 16, yielding only 400 instead of the correct 384. Option C, 20x10 + 4x6, inaccurately breaks down the multiplication, leading to 200 + 24, which totals 224. Option D, 25x10 + 4x15, misrepresents the factors, resulting in 250 + 60, totaling 310. Thus, option A is the most accurate approach for this multiplication.
Measure changed?
- A. Mean
- B. Median
- C. Mode
- D. Range
Correct Answer & Rationale
Correct Answer: A
The mean is sensitive to changes in data values, as it considers all values in a dataset. When any value changes, the mean will adjust accordingly, reflecting the new average. The median, on the other hand, represents the middle value and is only affected if the change impacts the central position of the dataset. The mode, being the most frequently occurring value, is not influenced by changes in other data points unless the frequency of occurrence alters. Lastly, the range measures the difference between the highest and lowest values, which may not change if the data alteration occurs within the existing range.
The mean is sensitive to changes in data values, as it considers all values in a dataset. When any value changes, the mean will adjust accordingly, reflecting the new average. The median, on the other hand, represents the middle value and is only affected if the change impacts the central position of the dataset. The mode, being the most frequently occurring value, is not influenced by changes in other data points unless the frequency of occurrence alters. Lastly, the range measures the difference between the highest and lowest values, which may not change if the data alteration occurs within the existing range.
d=rt, triple d, same t, new rate?
- A. 3dt
- B. (3d)/t
- C. t/(3d)
- D. d/(3t)
Correct Answer & Rationale
Correct Answer: B
In the equation d = rt, if distance (d) is tripled while time (t) remains constant, the new distance becomes 3d. To find the new rate (r'), we can rearrange the formula to r' = d/t. Substituting the new distance gives r' = (3d)/t, which is option B. Option A (3dt) incorrectly suggests multiplying distance by time, which does not represent rate. Option C (t/(3d)) misplaces the variables, implying time is divided by distance, which does not align with the rate formula. Option D (d/(3t)) incorrectly divides distance by three times the time, again misrepresenting the relationship between distance, rate, and time.
In the equation d = rt, if distance (d) is tripled while time (t) remains constant, the new distance becomes 3d. To find the new rate (r'), we can rearrange the formula to r' = d/t. Substituting the new distance gives r' = (3d)/t, which is option B. Option A (3dt) incorrectly suggests multiplying distance by time, which does not represent rate. Option C (t/(3d)) misplaces the variables, implying time is divided by distance, which does not align with the rate formula. Option D (d/(3t)) incorrectly divides distance by three times the time, again misrepresenting the relationship between distance, rate, and time.
3 in 321,745 vs 4,631?
- A. 100
- B. 1000
- C. 10000
- D. 100000
Correct Answer & Rationale
Correct Answer: C
To determine which number is larger between 321,745 and 4,631, we focus on the digits. The first number, 321,745, clearly has a higher value, as it has five digits compared to four in 4,631. Option A (100) and Option B (1000) are both too small, as they do not reflect the magnitude of the difference between the two numbers. Option D (100,000) is also incorrect, as it exceeds the value of 321,745. Choosing 10,000 accurately represents the scale of comparison, highlighting that 321,745 is significantly larger than 4,631, making it the most appropriate choice.
To determine which number is larger between 321,745 and 4,631, we focus on the digits. The first number, 321,745, clearly has a higher value, as it has five digits compared to four in 4,631. Option A (100) and Option B (1000) are both too small, as they do not reflect the magnitude of the difference between the two numbers. Option D (100,000) is also incorrect, as it exceeds the value of 321,745. Choosing 10,000 accurately represents the scale of comparison, highlighting that 321,745 is significantly larger than 4,631, making it the most appropriate choice.