At a certain department store present-wrapping counter, each clerk will wrap no fewer than 20 and no more than 30 presents per hour. If seventy people are waiting in line, will all their presents be wrapped after one hour?
1) Each person in line has at least one present to be wrapped by one of the six clerks at the counter.
2) If each person in line had one more present to be wrapped, nine clerks would be required to guarantee that every gift would be wrapped in one hour.
Source: Kaplan
OA: C
How to interpret statement 2 correctly?
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Statement 1: Each person in line has at least one present to be wrapped by one of the six clerks at the counter.Mo2men wrote:At a certain department store present-wrapping counter, each clerk will wrap no fewer than 20 and no more than 30 presents per hour. If seventy people are waiting in line, will all their presents be wrapped after one hour?
1) Each person in line has at least one present to be wrapped by one of the six clerks at the counter.
2) If each person in line had one more present to be wrapped, nine clerks would be required to guarantee that every gift would be wrapped in one hour.
Since there are 6 clerks -- and each wraps between 20 and 30 presents per hour -- the total number of presents that can be wrapped in one hour is between 120 and 180.
Since each of the 70 customers has at least 1 present -- implying that the total number of presents could be any integer value greater than or equal to 70 -- we cannot determine whether all of the presents can be wrapped.
INSUFFICIENT.
Statement 2: If each person in line had one more present to be wrapped, nine clerks would be required to guarantee that every gift would be wrapped in one hour.
To GUARANTEE that all of the presents can be wrapped by the 9 sales clerks, we must consider the WORST-CASE SCENARIO.
Here, the worst-case scenario = all 9 sales clerks wrapping AS SLOWLY AS POSSIBLE.
If all 9 sales clerks wrap only 20 presents per hour, then the total number of presents that can be wrapped in one hour = 9*20 = 180.
Implication:
9 sales clerks are required to guarantee that 180 presents can be wrapped in 1 hour.
Since these 180 presents = (actual number of presents) + (1 additional present for each of the 70 customers), the actual number of presents = 180 - (1*70) = 110.
Since the actual number of clerks is unknown, we cannot determine whether the 110 presents can be wrapped.
Statements combined:
Since there are a total of 110 presents, and the 6 clerks are able to wrap at least 120 presents per hour, all of the presents can be wrapped.
SUFFICIENT.
The correct answer is C.
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Given: At a certain department store present-wrapping counter, each clerk will wrap no fewer than twenty and no more than thirty presents per hour.Mo2men wrote:At a certain department store present-wrapping counter, each clerk will wrap no fewer than 20 and no more than 30 presents per hour. If seventy people are waiting in line, will all their presents be wrapped after one hour?
1) Each person in line has at least one present to be wrapped by one of the six clerks at the counter.
2) If each person in line had one more present to be wrapped, nine clerks would be required to guarantee that every gift would be wrapped in one hour.
Target question: If seventy people are standing in line, will all of their presents be wrapped after one hour?
Statement 1: Each person in line has at least one present to be wrapped by one of the six clerks at the counter.
Since we aren't told the MAXIMUM number of presents each person has, there's no way to answer the target question.
To see what I mean, consider these two conflicting scenarios:
Case a: Each person in line has 1 present. So, there are 70 presents to be wrapped by 6 clerks. Since each clerk can wrap AT LEAST 20 presents (for a total of 120 presents), the answer to the target question is YES, all of the presents will be wrapped after 1 hour
Case b: Each person in line has 1 trillion presents. Here, the answer to the target question is NO, all of the presents will NOT be wrapped after 1 hour
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: If each person in line had one more present to be wrapped, nine clerks would be required to guarantee that every present would be wrapped in one hour.
Here, we aren't given any information about the actual number of clerks.
Consider these two conflicting scenarios:
Case a: There are 9 clerks available. If 9 clerks can wrap all of the presents in the hypothetical situation in which everyone has 1 EXTRA present, then 9 clerks will definitely be enough to wrap the presents. In other words, the answer to the target question is YES, all of the presents will be wrapped after 1 hour
Case b: There is are ZERO clerks available (all on lunch break). Here, the answer to the target question is NO, all of the presents will NOT be wrapped after 1 hour
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined
Let T = the TOTAL number of presents to be wrapped
IF each of the 70 people in line had one more present, then there WOULD be T + 70 presents to be wrapped
Since each of the 9 clerks can wrap AT LEAST 20 presents per hour, they can wrap AT LEAST 180 presents.
So, we can write: T + 70 < 180
Subtract 70 from both sides to get: T < 110
So, statement 2 is telling us (indirectly) that there are fewer than 110 presents to be wrapped
Statement 1 tells there are 6 clerks.
Since each clerk can wrap AT LEAST 20 presents in one hour, they can can wrap AT LEAST 120 presents in total.
Since statement 2 tells us that there are FEWER THAN 110 presents, the answer to the target question is YES, all of the presents will be wrapped after 1 hour
Since we can answer the target question with certainty, the combined statements are SUFFICIENT
Answer: C
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