Digit 1 in ten thousands 9 in ones? Select ALL.
- A. 12,679
- B. 12,769
- C. 12,796
- D. 21,679
- E. 21,769
Correct Answer & Rationale
Correct Answer: A,B: 1 ten thousands, 9 ones. C: 6 ones. D,E,F: 2 ten thousands. Place values must match both conditions.
To identify numbers with 1 in the ten thousands place and 9 in the ones place, we analyze each option. - **A (12,679)**: The digit 1 is in the ten thousands place, and 9 is in the ones place, meeting both criteria. - **B (12,769)**: Here, 1 is again in the ten thousands place, and 9 is in the ones place, satisfying the conditions. - **C (12,796)**: The digit in the ones place is 6, not 9, which disqualifies it. - **D (21,679)**: The digit in the ten thousands place is 2, failing to meet the first condition. - **E (21,769)**: Similarly, 2 is in the ten thousands place, not 1. - **F (21,796)**: Again, 2 is in the ten thousands place, disqualifying this option. Only options A and B fulfill both requirements, confirming their validity.
To identify numbers with 1 in the ten thousands place and 9 in the ones place, we analyze each option. - **A (12,679)**: The digit 1 is in the ten thousands place, and 9 is in the ones place, meeting both criteria. - **B (12,769)**: Here, 1 is again in the ten thousands place, and 9 is in the ones place, satisfying the conditions. - **C (12,796)**: The digit in the ones place is 6, not 9, which disqualifies it. - **D (21,679)**: The digit in the ten thousands place is 2, failing to meet the first condition. - **E (21,769)**: Similarly, 2 is in the ten thousands place, not 1. - **F (21,796)**: Again, 2 is in the ten thousands place, disqualifying this option. Only options A and B fulfill both requirements, confirming their validity.
Other Related Questions
3/4 as sum of unit fractions?
- A. 1/8 + 1/8 + 1/8 + 1/4 + 1/4
- B. 2/8 + 1/4 + 4/16
- C. 5/8 + 2/16
- D. 1/2 + 1/4
Correct Answer & Rationale
Correct Answer: D
To express \( \frac{3}{4} \) as a sum of unit fractions, each option must be evaluated for its total. Option A totals \( \frac{3}{8} + \frac{1}{2} = \frac{3}{8} + \frac{4}{8} = \frac{7}{8} \), which exceeds \( \frac{3}{4} \). Option B simplifies to \( \frac{2}{8} + \frac{2}{8} + \frac{1}{4} = \frac{2}{8} + \frac{2}{8} + \frac{2}{8} = \frac{6}{8} = \frac{3}{4} \), but includes non-unit fractions. Option C simplifies to \( \frac{5}{8} + \frac{1}{4} = \frac{5}{8} + \frac{2}{8} = \frac{7}{8} \), again exceeding \( \frac{3}{4} \). Option D correctly adds \( \frac{1}{2} + \frac{1}{4} = \frac{2}{4} + \frac{1}{4} = \frac{3}{4} \) using unit fractions only.
To express \( \frac{3}{4} \) as a sum of unit fractions, each option must be evaluated for its total. Option A totals \( \frac{3}{8} + \frac{1}{2} = \frac{3}{8} + \frac{4}{8} = \frac{7}{8} \), which exceeds \( \frac{3}{4} \). Option B simplifies to \( \frac{2}{8} + \frac{2}{8} + \frac{1}{4} = \frac{2}{8} + \frac{2}{8} + \frac{2}{8} = \frac{6}{8} = \frac{3}{4} \), but includes non-unit fractions. Option C simplifies to \( \frac{5}{8} + \frac{1}{4} = \frac{5}{8} + \frac{2}{8} = \frac{7}{8} \), again exceeding \( \frac{3}{4} \). Option D correctly adds \( \frac{1}{2} + \frac{1}{4} = \frac{2}{4} + \frac{1}{4} = \frac{3}{4} \) using unit fractions only.
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.
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.