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# At a bakery, cakes are sold every day for a certain number of days. If

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Math Expert
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At a bakery, cakes are sold every day for a certain number of days. If  [#permalink]

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14 May 2017, 10:51
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95% (hard)

Question Stats:

40% (01:52) correct 60% (02:24) wrong based on 161 sessions

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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.

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At a bakery, cakes are sold every day for a certain number of days. If  [#permalink]

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09 Jul 2017, 11:35
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TheMastermind wrote:
I am still not able to successfully dissect statement (2). Can someone help me out?

Hi TheMastermind ,

I am happy to help.

Let me decode this question for you.

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?

Let total number of days = 100x.

=> 6 or more were sold for 20x.

=> 1 to 5 were sold for 80x.

We need to find out the median number of cakes. That means if I arrange my cakes in ascending order, the number of cakes sold on the average of (50x)th and (51x)th days will be the median.

(2) On 50% of the days that 4 or more cakes were sold, the number of cakes sold each day was 6 or more.

It says on 50% of the days when 4 or more were sold were 20x.

=> other 50% will have 4 or 5. This is also equal to 20x.

=>For 40x days, we have 4 or more.

=> For the initial 60x days, we have less than 4.

=> (50x)th and (51x)th day will have less than 4 cakes.

Hence, statement 2 is sufficient.

I hope that makes sense.
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Re: At a bakery, cakes are sold every day for a certain number of days. If  [#permalink]

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14 May 2017, 10:53
Bunuel wrote:
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.

Similar question on mean: https://gmatclub.com/forum/at-a-bakery- ... 40180.html
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Re: At a bakery, cakes are sold every day for a certain number of days. If  [#permalink]

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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)
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Re: At a bakery, cakes are sold every day for a certain number of days. If  [#permalink]

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17 Jun 2017, 03:33
Bunuel wrote:
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.

Bunuel:

Let the total number of days=10
# Days on which 6 or more cakes are sold=2

A: 0.75*0.8=0.6 => 6days on which less than 4 cakes are sold. Therefore, SUFFICIENT

B: Number of days on which 6 or more cakes are sold = 2 as given by question; I am getting confused with the 50%. How do I evaluate this information?

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Re: At a bakery, cakes are sold every day for a certain number of days. If  [#permalink]

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17 Jun 2017, 03:42
gmatexam439 wrote:
Bunuel wrote:
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.

Bunuel:

Let the total number of days=10
# Days on which 6 or more cakes are sold=2

A: 0.75*0.8=0.6 => 6days on which less than 4 cakes are sold. Therefore, SUFFICIENT

B: Number of days on which 6 or more cakes are sold = 2 as given by question; I am getting confused with the 50%. How do I evaluate this information?

I got how option B is correct. no of days on which 4 or more are sold = 4 therefore no of days on which less than 4 sold = 6. thus median must be less than 4. hence D
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Re: At a bakery, cakes are sold every day for a certain number of days. If  [#permalink]

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05 Jul 2017, 13:41
I am still not able to successfully dissect statement (2). Can someone help me out?
Re: At a bakery, cakes are sold every day for a certain number of days. If   [#permalink] 05 Jul 2017, 13:41
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