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27 Oct 2024, 10:59
Kudos
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
65%
(hard)
Question Stats:
55% (01:52) correct
45%
(01:54)
wrong
based on 119
sessions
History
Date
Time
Result
Not Attempted Yet
The average price of three stocks is $25 per share. Is the stock that costs $30 per share the highest priced of the three stocks?
(1) The highest-priced stock costs $1 more per share than the next-highest-priced stock.
(2) The lowest-priced stock costs $14 per share.
(1) The highest-priced stock costs $1 more per share than the next-highest-priced stock.
(2) The lowest-priced stock costs $14 per share.
11 Mar 2025, 00:42
Kudos
Bookmarks
We are given that the average price of three stocks is $25 per share. This means the total price of all three stocks is:
\( \frac{x + y + z}{3} = 25 \)
Multiplying both sides by 3:
\( x + y + z = 75 \)
where \( x, y, \) and \( z \) represent the prices of the three stocks in ascending order, i.e.,
\( x \leq y \leq z. \)
We need to determine whether the $30 per share stock is the highest-priced one, meaning we want to check
\( z =? 30. \)
### Analyzing the Statements
**Statement (1):** The highest-priced stock costs $1 more per share than the next-highest-priced stock.
This means:
\( y = z - 1 \)
Substituting this into the total price equation:
\( x + z - 1 + z = 75 \)
\( x + 2z - 1 = 75 \)
\( x + 2z = 76 \)
\( 26 \leq z \leq 38 \)
This alone does not tell us whether \( z = 30 \) or not.
**Insufficient.**
---
**Statement (2):** The lowest-priced stock costs $14 per share.
This gives:
\( x = 14 \)
Substituting this into the total price equation:
\( 14 + y + z = 75 \)
\( y + z = 61 \)
\( 14 \leq y \leq z \)
\( 30.5 \leq z \leq 47 \)
Since \( z = 30 \) does not satisfy this inequality, we conclude that \( z \) must be **equal or greater than 30.5**.
**Sufficient.**
Option B
\( \frac{x + y + z}{3} = 25 \)
Multiplying both sides by 3:
\( x + y + z = 75 \)
where \( x, y, \) and \( z \) represent the prices of the three stocks in ascending order, i.e.,
\( x \leq y \leq z. \)
We need to determine whether the $30 per share stock is the highest-priced one, meaning we want to check
\( z =? 30. \)
### Analyzing the Statements
**Statement (1):** The highest-priced stock costs $1 more per share than the next-highest-priced stock.
This means:
\( y = z - 1 \)
Substituting this into the total price equation:
\( x + z - 1 + z = 75 \)
\( x + 2z - 1 = 75 \)
\( x + 2z = 76 \)
\( 26 \leq z \leq 38 \)
This alone does not tell us whether \( z = 30 \) or not.
**Insufficient.**
---
**Statement (2):** The lowest-priced stock costs $14 per share.
This gives:
\( x = 14 \)
Substituting this into the total price equation:
\( 14 + y + z = 75 \)
\( y + z = 61 \)
\( 14 \leq y \leq z \)
\( 30.5 \leq z \leq 47 \)
Since \( z = 30 \) does not satisfy this inequality, we conclude that \( z \) must be **equal or greater than 30.5**.
**Sufficient.**
Option B
11 Mar 2025, 04:11
Kudos
Bookmarks
Bunuel
Average of three = 25
Question: Is highest cost = 30?
Given: 30 is price of one stock
Statement 1: The highest-priced stock costs $1 more per share than the next-highest-priced stock.
Highest = x
Second highest = x-1
Third = Anything is possible
Case 1: Prices are 30, 29 and 16
Case 2: Prices are 31, 30 and 14
NOT SUFFICIENT
Statement 2:The lowest-priced stock costs $14 per share.
i.e. Prices are 14, 30 and 31
i.e. Highest is NOT 30
SUFFICIENT
Answer: Option B
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