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14 May 2017, 10:51
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D
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Difficulty:
95%
(hard)
Question Stats:
44% (02:19) correct
56%
(02:32)
wrong
based on 271
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At a bakery, cakes are sold every day for a certain number of days. If 6 or more cakes were sold for 20% of the total number of days, is the median number of cakes sold less than 4?
(1) On 75% of the days that less than 6 cakes were sold, the number of cakes sold each day was less than 4.
(2) On 50% of the days that 4 or more cakes were sold, the number of cakes sold each day was 6 or more.
(1) On 75% of the days that less than 6 cakes were sold, the number of cakes sold each day was less than 4.
(2) On 50% of the days that 4 or more cakes were sold, the number of cakes sold each day was 6 or more.
14 May 2017, 10:53
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17 Jun 2017, 03:31
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Let the total number of days be x,
Given that 6+ cakes are sold on x/5 days
(1) On 75% of the days that less than 6 cakes were sold, the number of cakes sold each day was less than 4.
From this statement, on 75%(of remaining days) * \(\frac{4x}{5}\) = \(\frac{3x}{5}\) days
This is 60% of the total days, on which the bakery sells less than 4 cakes.
So, the median will definitely be lesser than 4. Sufficient
(2) On 50% of the days that 4 or more cakes were sold, the number of cakes sold each day was 6 or more.[/quote]
From this statement, on 50% (of days 4+ were sold), the number of cakes sold are 6+.
Since from the question stem, we know that 6+ cakes were definitely sold on 20% of days,
4+ cakes will definitely be sold on 40%, making the sale of cakes on 60% of the total days more than 4.
The median will definitely be greater than 4. Sufficient(Option D)
Given that 6+ cakes are sold on x/5 days
(1) On 75% of the days that less than 6 cakes were sold, the number of cakes sold each day was less than 4.
From this statement, on 75%(of remaining days) * \(\frac{4x}{5}\) = \(\frac{3x}{5}\) days
This is 60% of the total days, on which the bakery sells less than 4 cakes.
So, the median will definitely be lesser than 4. Sufficient
(2) On 50% of the days that 4 or more cakes were sold, the number of cakes sold each day was 6 or more.[/quote]
From this statement, on 50% (of days 4+ were sold), the number of cakes sold are 6+.
Since from the question stem, we know that 6+ cakes were definitely sold on 20% of days,
4+ cakes will definitely be sold on 40%, making the sale of cakes on 60% of the total days more than 4.
The median will definitely be greater than 4. Sufficient(Option D)
