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28 Nov 2024, 01:30
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D
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Difficulty:
55%
(hard)
Question Stats:
55% (01:25) correct
45%
(01:18)
wrong
based on 166
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A survey was conducted to find out how many TV show viewers voted for a movie which will be aired in 4 days. Was the average number of votes cast per day for this 4-day period greater than 6000?
(1) For the two days with the greatest number of votes cast, the average (arithmetic mean) number of votes cast was 12492.
(2) The minimum number of votes cast on a single day was 6156.
(1) For the two days with the greatest number of votes cast, the average (arithmetic mean) number of votes cast was 12492.
(2) The minimum number of votes cast on a single day was 6156.
ajain31
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30 Nov 2024, 17:32
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To determine if the average number of votes cast per day during the 4-day period was greater than 6000, we need to evaluate whether the total number of votes over the 4 days exceeds
4 × 6000 = 24,000
4×6000=24,000. The average number of votes per day is:
Average votes per day = Total votes over 4 days/ 4
Statement (1): The two days with the greatest number of votes cast had an average of 12,492.
This means that the total number of votes for the two highest-voting days is:
2 × 12,492 = 24,984.
2×12,492=24,984.
If there were no votes on the other two days, the total number of votes for the 4 days would still be:
24,984+0=24,984.
The average number of votes per day in this case would be:
24,984/4 = 6,246.
Since this exceeds 6,000, the condition is satisfied regardless of the number of votes cast on the other two days (as additional votes would only increase the average).
Statement (2): The minimum number of votes cast on a single day was 6,156.
This tells us that every day had at least 6,156 votes. Over the 4 days, the total number of votes must be at least:
4×6,156 = 24,624.
Since 24,624 > 24,000
24,624>24,000, the average number of votes per day is guaranteed to be greater than 6,000.
Statement (2) alone is sufficient.
4 × 6000 = 24,000
4×6000=24,000. The average number of votes per day is:
Average votes per day = Total votes over 4 days/ 4
Statement (1): The two days with the greatest number of votes cast had an average of 12,492.
This means that the total number of votes for the two highest-voting days is:
2 × 12,492 = 24,984.
2×12,492=24,984.
If there were no votes on the other two days, the total number of votes for the 4 days would still be:
24,984+0=24,984.
The average number of votes per day in this case would be:
24,984/4 = 6,246.
Since this exceeds 6,000, the condition is satisfied regardless of the number of votes cast on the other two days (as additional votes would only increase the average).
Statement (2): The minimum number of votes cast on a single day was 6,156.
This tells us that every day had at least 6,156 votes. Over the 4 days, the total number of votes must be at least:
4×6,156 = 24,624.
Since 24,624 > 24,000
24,624>24,000, the average number of votes per day is guaranteed to be greater than 6,000.
Statement (2) alone is sufficient.
01 Dec 2024, 11:14
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Correct Answer - D
To find: whether average number of votes cast per day for this 4-day period greater than 6000 i.e. (sum of votes of all 4 days)/4 > 6000 ?
This means, we need to find where (sum of votes of all 4 days) > 24000 ?
Stmt1: Average of greatest 2 days i.e. (x+y)/2 = 12492. This means, Sum of votes of those 2 days = 12492*2 = 24984. Now, even if 0 votes were cast on other 2 days, sum of all 4 days would still be > 24000 (from above) and so, avg votes per day would be greater than 6000. Sufficient
Stmt2: min votes cast = 6156 i.e. on other 3 days, either same or more than 6156 were cast. In any case, the sum would be > 24000 and so, avg votes per day would be greater than 6000. Sufficient.
To find: whether average number of votes cast per day for this 4-day period greater than 6000 i.e. (sum of votes of all 4 days)/4 > 6000 ?
This means, we need to find where (sum of votes of all 4 days) > 24000 ?
Stmt1: Average of greatest 2 days i.e. (x+y)/2 = 12492. This means, Sum of votes of those 2 days = 12492*2 = 24984. Now, even if 0 votes were cast on other 2 days, sum of all 4 days would still be > 24000 (from above) and so, avg votes per day would be greater than 6000. Sufficient
Stmt2: min votes cast = 6156 i.e. on other 3 days, either same or more than 6156 were cast. In any case, the sum would be > 24000 and so, avg votes per day would be greater than 6000. Sufficient.
