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

Question

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 average 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.

GMATGuruNY · Accepted Answer

Since 20% = 1/5 and 75% = 3/4, let the total number of days = the LCM of the two denominators = 20.
For the average number of cakes per day to be less than 4, the total number of cakes sold must be less than the following value:
20*4 = 80
Question stem, rephrased:
 Were fewer than 80 cakes sold ?

Since 6 cakes or more are sold on 20% of the 20 days -- implying that on each of these 4 days an INFINITE number of cakes can be sold -- it is clearly possible that 80 or more cakes are sold.
In this case, the answer to the blue question will be NO.

Statement 1:
The following distribution is implied:
20% of all 20 days = 4 days --> average of 6 or more per day
75% of the remaining 16 days = 12 days --> average of fewer than 4 per day
Remaining 4 days --> average of 4 or 5 per day

Minimum possible total for all 20 days = (4*6) + (12*0) + (4*4) = 40
In this case, the answer to the blue question will be YES.
Since the answer can be NO (as shown above) or YES (as shown here), Statement 1 is INSUFFICIENT.

Statement 2:
Examine the green values implied by Statement 1:
 4 days --> average of 6 or more per day
4 days --> average of 4 or 5 per day 
12 days --> average of less than 4 per day
Of the 8 days on which 4 or more cakes are sold, 50% have sales of 6 or more per day.
Implication:
Statement 2 implies the same distribution as Statement 1.

Thus, even when the statements are combined, the answer to the blue question can be NO or YES.
INSUFFICIENT.

E

Bunuel · Answer

Similar question on median : https://gmatclub.com/forum/at-a-bakery- ... 40179.html

AliciaSierra · Answer

Hello  Bunuel ,

How to interpret second statement "(2) On 50% of the days that 4 or more cakes were sold, the number of cakes sold each day was 6 or more."

catinabox · Answer

Statement 2 tells you the exact same thing that statement 1 does.

Since it's given in the question stem that on 20% of the days, 6 or more cakes were sold, statement 2 tells us that on 50% of the days, between 4 (inclusive) and 6 cakes were sold, and 50% >=6 cakes were sold. That means, 20% of the days, 4 - 6 cakes were sold and on 60% of the days, less than 4 cakes were sold.

AdiBir · Answer

ammuseeru

It's given in the stem that on  20 % of days, 6 or more cakes were sold.
Now  2)  says that on 50% of the days that 4 or more cakes were sold, the number of cakes sold each day was 6 or more.

Let total number of days be  x .
So acc. to stem, on  \frac{x}{5}  days, 6 or more cakes were sold.
Now let  y  be number of days on which 4 or more cakes are sold.

So acc. to  2)   \frac{y}{2} = \frac{x}{5} . So  y = \frac{2*x}{5}  or y=40% of x.

I hope this clears your doubt.

Hit Kudos if you like the explanation.

bumpbot · Answer

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

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