Five volunteers signed up to work a bake sale. George signed up for the 9:00 a.m.-10:00 a.m. slot, and Juan signed up for the 10:00 a.m.-11:00 a.m. slot. The start of Cora's time slot begins with an even number. Which time slot does Cora work? (1) Cora's time slot is not immediately before George's time slot. (2) Cora's time slot is later in the day than George's time slot.
Rationale
Cora's time slot must begin with an even hour and cannot be immediately before George's slot, which runs from 9:00 a.m. to 10:00 a.m. Since the only even-numbered hour after George's is 10:00 a.m., her possible slot can only be the 11:00 a.m.-12:00 p.m. slot, making each statement alone sufficient to conclude Cora's time.
A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. Statement (1) indicates that Cora's time slot is not immediately before George's, but it does not provide information on the even-numbered requirement. Therefore, while it suggests a later time, it cannot assure Cora's time slot, making this statement insufficient on its own.
B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. Statement (2) reveals that Cora's time slot is later than George's, which does imply she works in the 10:00 a.m.-11:00 a.m. or 11:00 a.m.-12:00 p.m. slots. However, it does not confirm the even-numbered requirement for her time slot. Thus, this statement alone is also insufficient.
C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. Combining both statements does help establish Cora's time slot, as neither can independently provide the solution. The first rules out the slot before George, while the second confirms it must be later, making them jointly sufficient but not independently so.
D) EACH statement ALONE is sufficient. This is correct because both statements independently clarify Cora's time slot. Statement (1) confirms she is not in the 10:00 a.m. slot, while statement (2) confirms she must be in the 11:00 a.m. slot, fulfilling both the even and time slot requirements alone.
Conclusion Each statement can independently determine Cora's time slot as 11:00 a.m.-12:00 p.m. Statement (1) confirms she cannot be in George's time slot, while statement (2) establishes she works later in the day. Hence, both statements are sufficient on their own.
For each of the following products, select Sufficient if the information provided is sufficient to determine whether the unit price of the product is less than €3. Otherwise, select Insufficient.
Rationale
For both Product A and Product D, the subtotals in the table can be divided by an integer number of units purchased to determine the unit price. If the subtotal is less than €3 multiplied by the number of units, we can conclude that the unit price is indeed less than €3.
A) Product A The information for Product A allows us to calculate the unit price by using the subtotal and the integer number of units purchased. If the subtotal is less than €3 multiplied by the number of units, we can confirm that the unit price is less than €3, making the information sufficient.
B) Product B For Product B, while we have a subtotal, we do not have enough information about the number of units purchased relative to the subtotal to definitively ascertain whether the unit price is less than €3. Therefore, the information is insufficient.
C) Product C Similar to Product B, the information for Product C does not provide enough clarity regarding the relationship between the subtotal and the number of units bought. Without this, we cannot determine if the unit price is less than €3, leading to insufficient information.
D) Product D The information for Product D is sufficient because the subtotal can be divided by the integer number of units purchased to determine the unit price. If the resulting unit price is less than €3, we have the necessary conclusion, thus making the information sufficient.
Conclusion The determination of whether the unit price is less than €3 can be definitively made for Products A and D given the provided subtotals and integer units. In contrast, Products B and C lack sufficient information to arrive at a conclusion regarding their unit prices, highlighting the importance of the relationship between subtotal and quantity in making price assessments.
Company T's business model predicted the company's revenue for the years 2001 through 2006, based on the company's revenue for the year 2000. For each of the years 2001 through 2006, the predicted revenue was 10% more than the predicted revenue for the preceding year. What was the first year for which the predicted revenue was more than $16,000,000? (1) The predicted revenue for 2001 was $11,000,000. (2) The predicted revenue for 2004 was $4,641,000 more than the revenue for 2000.
Rationale
The first statement provides the initial revenue for 2001, allowing us to calculate subsequent years' revenues based on a consistent 10% increase. In contrast, the second statement lacks the necessary initial revenue figure to determine the revenue for the years in question.
A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. Statement (1) indicates that the predicted revenue for 2001 is $11,000,000. From this, we can calculate the revenues for the following years, applying the 10% increase successively until we exceed $16,000,000. This calculation shows that by 2005, the predicted revenue surpasses $16,000,000, making statement (1) sufficient.
B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. Statement (2) claims that the predicted revenue for 2004 is $4,641,000 more than the revenue for 2000. However, without knowing the revenue for 2000, we cannot infer the actual revenue for 2004 or any subsequent years. Hence, statement (2) is insufficient on its own.
C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. While combining both statements might provide additional information, statement (1) alone is sufficient to determine the first year the revenue exceeds $16,000,000. Therefore, this option is incorrect, as statement (1) stands alone.
D) EACH statement ALONE is sufficient. This option is false as statement (2) does not provide enough information to determine the revenue for the required years, while statement (1) does.
E) Statements (1) and (2) TOGETHER are NOT sufficient. This option is incorrect because statement (1) alone is sufficient to find the answer, rendering the combination unnecessary.
Conclusion In this scenario, statement (1) gives a clear starting point for revenue calculations, enabling us to determine the first year that revenue exceeds $16,000,000. Statement (2) lacks the essential initial revenue data, making it insufficient for solving the problem on its own. Thus, the analysis confirms that statement (1) is the key to resolving the question.
Lynn was born on February 29th. She celebrates her birthday every year on the last day of February. Lynn's cousin, Pete, whose date of birth is the same as that of Lynn, celebrated his birthday today. Is it February 28th today? (1) Lynn had a birthday party exactly four years ago. (2) Pete turned exactly 24 years old today.
Rationale
Both statements provide enough information to determine that today is February 28th. Since Lynn was born on February 29th and only celebrates her birthday every year on the last day of February, if Pete is celebrating his birthday today and he is also born on February 29th, today must be the day before a leap year, making it February 28th.
A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. Statement (1) indicates that Lynn had a birthday party exactly four years ago, which suggests she has had at least one birthday on February 28th, but it does not explicitly confirm the current date.
B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. Statement (2) states that Pete turned exactly 24 years old today. While this implies a leap year context, it does not provide enough information on its own to confirm that today is February 28th.
C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. While both statements contribute valuable information, each statement alone is indeed sufficient to determine that today is February 28th, making this choice incorrect.
E) Statements (1) and (2) TOGETHER are NOT sufficient. This option is incorrect because both statements independently confirm that today is February 28th, making them sufficient.
Conclusion Both statements alone offer sufficient information to conclude that today is February 28th. Statement (1) implies Lynn's birthday celebration context, while statement (2) clarifies Pete's age, reinforcing the leap year scenario. Therefore, the answer is that each statement alone is sufficient to answer the question accurately.
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