Question:
Given \( x<y<z \), compare the following quantities:
\[
\frac{x + y + z}{3} \quad \text{and} \quad y
\]
Given \( x<y<z \), compare the following quantities:
\[
\frac{x + y + z}{3} \quad \text{and} \quad y
\]
Show Hint
When comparing averages and individual values, remember that the middle value (median) can be larger or smaller than the average depending on the values of the other numbers.
Updated On: Oct 7, 2025
- Quantity A is greater
- Quantity B is greater
- The two quantities are equal
- The relationship cannot be determined from the information given.
Show Solution
Verified By Collegedunia
The Correct Option is B
Solution and Explanation
Step 1: the given condition.
We are given \( x<y<z \), meaning \( y \) is the middle value. We are asked to compare the average \( \frac{x + y + z}{3} \) with \( y \).
Step 2: Try an example.
For example, let \( x = 1, y = 2, z = 3 \). Then: \[ \frac{x + y + z}{3} = \frac{1 + 2 + 3}{3} = 2 \] Thus, the two quantities are equal in this case. However, if \( x = 1, y = 2, z = 10 \), then: \[ \frac{x + y + z}{3} = \frac{1 + 2 + 10}{3} = 4.33 \] Here, Quantity A is greater than Quantity B.
Step 3: Conclusion.
Based on the analysis and the specific examples, the relationship between the quantities can be that Quantity B is greater.
Final Answer: \[ \boxed{\text{The correct answer is (2) Quantity B is greater.}} \]
We are given \( x<y<z \), meaning \( y \) is the middle value. We are asked to compare the average \( \frac{x + y + z}{3} \) with \( y \).
Step 2: Try an example.
For example, let \( x = 1, y = 2, z = 3 \). Then: \[ \frac{x + y + z}{3} = \frac{1 + 2 + 3}{3} = 2 \] Thus, the two quantities are equal in this case. However, if \( x = 1, y = 2, z = 10 \), then: \[ \frac{x + y + z}{3} = \frac{1 + 2 + 10}{3} = 4.33 \] Here, Quantity A is greater than Quantity B.
Step 3: Conclusion.
Based on the analysis and the specific examples, the relationship between the quantities can be that Quantity B is greater.
Final Answer: \[ \boxed{\text{The correct answer is (2) Quantity B is greater.}} \]
Was this answer helpful?
0
0
Top GRE Quantitative Aptitude Questions
One pen costs \(\$\)0.25 and one marker costs \(\$\)0.35. At those prices, what is the total cost of 18 pens and 100 markers?
- Working alone at its constant rate, machine A produces kkk liters of a chemical in 10 minutes. Working alone at its constant rate, machine B produces kkk liters of the chemical in 15 minutes. How many minutes does it take machines A and B, working simultaneously at their respective constant rates, to produce kkk liters of the chemical?
- If the dollar amount of sales at Store P was $800,000 for 2006, what was the dollar amount of sales at that store for 2008?
- At Store T, the dollar amount of sales for 2007 was what percent of the dollar amount of sales for 2008? Give your answer to the nearest 0.1%.
- If the ratio of A to B is 3:4 and the ratio of B to C is 5:6, what is the ratio of A to C?
View More Questions
Top GRE Averages Questions
- A group of five students averaged 85 points on an exam taken out of 100 total points. If the addition of two additional students raises the group average to 88 points, what is the minimum score that one of those two students can receive? Assume that 100 is the highest score for the exam.
- Sample Set A has 25 data points with an arithmetic mean of 50. Sample Set B has 75 data points with an arithmetic mean of 100. Quantity A: The arithmetic mean of the 100 data points encompassing A and B. Quantity B: 80
- Compare Quantity A and Quantity B, using additional information centered above the two quantities if such information is given, and select one of the four answer choices: The following table displays the income Jane's business earned and the percentage of that income she paid in taxes for the first half of the year. \[ \begin{array}{|c|c|c|} \hline \text{Month} & \text{Income earned ($ )} & \text{Percentage paid in taxes (%)}
\hline \text{January} & 10,000 & 10
\text{February} & 50,000 & 30
\text{March} & 20,000 & 20
\text{April} & 10,000 & 10
\text{May} & 30,000 & 20
\text{June} & 90,000 & 40
\hline \end{array} \] - The arithmetic mean of \( a, b, \) and \( c \) is 13.
Quantity A: The arithmetic mean of \( 2a + b, b + 3c, 39 - c \)
Quantity B: 39
- Product X costs $ 27 to manufacture at the rate of 50 per hour. Production can only be increased in groups of 10 units per hour. For each such increase, the production cost increases 30% of its previous amount. If the output is to be doubled, for how much must each unit be sold to make at least a 25% profit?
View More Questions
Top GRE Questions
One pen costs \(\$\)0.25 and one marker costs \(\$\)0.35. At those prices, what is the total cost of 18 pens and 100 markers?
- Working alone at its constant rate, machine A produces kkk liters of a chemical in 10 minutes. Working alone at its constant rate, machine B produces kkk liters of the chemical in 15 minutes. How many minutes does it take machines A and B, working simultaneously at their respective constant rates, to produce kkk liters of the chemical?
- If the dollar amount of sales at Store P was $800,000 for 2006, what was the dollar amount of sales at that store for 2008?
- At Store T, the dollar amount of sales for 2007 was what percent of the dollar amount of sales for 2008? Give your answer to the nearest 0.1%.
- If the ratio of A to B is 3:4 and the ratio of B to C is 5:6, what is the ratio of A to C?
View More Questions