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18 Nov 2024, 01:30
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B
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Difficulty:
45%
(medium)
Question Stats:
67% (01:55) correct
33%
(02:06)
wrong
based on 152
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A container has 18 boxes containing 950 pebbles in total. The owner then puts 2 more boxes in the container. Is the average (arithmetic mean) number of pebbles per container for all 20 boxes greater than 52?
(1) Each of the extra box added to the container has more than 30 pebbles.
(2) Each of the extra box added to the container has less than 45 pebbles.
(1) Each of the extra box added to the container has more than 30 pebbles.
(2) Each of the extra box added to the container has less than 45 pebbles.
18 Nov 2024, 06:37
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Current Situation:
18 boxes; 950 pebbles => ~52.7 pebbles/box (Mean)
Now, 2 more boxes are added and the questions is
For mean to be greater than 52, the total pebbles in all boxes combined has to be >1040 (20*52). So, >90 pebbles would have to be added in the 2 extra boxes (1040 - 950). With that, lets see the statements:
St 1: (1) Each of the extra box added to the container has more than 30 pebbles.
This could be anything. If its 31 and 32 pebbles, for example, then the mean wouldn't go over 52. But if it is 60 and 61 pebbles, for example, then the mean would go over 52. So St 1 alone is not sufficient.
St 2: (2) Each of the extra box added to the container has less than 45 pebbles.
Now, for there to be >90 pebbles overall between the 2 extra added boxes, atleast one box needs to have >= 45 pebbles. Since both have lesser than 45 pebbles, the mean will not be >52.
So, St 2 alone is sufficient. Hence, B.
18 boxes; 950 pebbles => ~52.7 pebbles/box (Mean)
Now, 2 more boxes are added and the questions is
Quote:
For mean to be greater than 52, the total pebbles in all boxes combined has to be >1040 (20*52). So, >90 pebbles would have to be added in the 2 extra boxes (1040 - 950). With that, lets see the statements:
St 1: (1) Each of the extra box added to the container has more than 30 pebbles.
This could be anything. If its 31 and 32 pebbles, for example, then the mean wouldn't go over 52. But if it is 60 and 61 pebbles, for example, then the mean would go over 52. So St 1 alone is not sufficient.
St 2: (2) Each of the extra box added to the container has less than 45 pebbles.
Now, for there to be >90 pebbles overall between the 2 extra added boxes, atleast one box needs to have >= 45 pebbles. Since both have lesser than 45 pebbles, the mean will not be >52.
So, St 2 alone is sufficient. Hence, B.
18 Nov 2024, 10:39
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Question stem : decode -> 950/18 =52.777.. and now the owner put 2 additional boxes.. New count of boxes is 20.
what is asked : - is the new average (950 + New Sum of Pebbles /20) > 52.
When will the New Average be >=52; if New Sum = 950+ no. of pebbles in both the boxes are >= 190.. the owner has added 190 pebbles to the 950 count. 190 / 2 = 95 in each boxes.
St 1: > 30 pebbles.. if the owner could have added 31 pebbles per box.. New Sum (950 + 61) / 20.. New av <52.. It's NO
but if 95 or 96 or 98 or 100 pebbles are added.. New Av. >52 It's Yes.
St 2 : each box has <45 pebbles means the New Average is less than 950 + 190.. meaning each box contains < 95 pebbles..
This statement clear states that the count is less.. Always YES..
Answer is B.
what is asked : - is the new average (950 + New Sum of Pebbles /20) > 52.
When will the New Average be >=52; if New Sum = 950+ no. of pebbles in both the boxes are >= 190.. the owner has added 190 pebbles to the 950 count. 190 / 2 = 95 in each boxes.
St 1: > 30 pebbles.. if the owner could have added 31 pebbles per box.. New Sum (950 + 61) / 20.. New av <52.. It's NO
but if 95 or 96 or 98 or 100 pebbles are added.. New Av. >52 It's Yes.
St 2 : each box has <45 pebbles means the New Average is less than 950 + 190.. meaning each box contains < 95 pebbles..
This statement clear states that the count is less.. Always YES..
Answer is B.
