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At a bakery, cakes are sold every day for a certain number

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At a bakery, cakes are sold every day for a certain number

by swerve » Sun Dec 01, 2019 11:21 am
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.

The OA is E

Source: Veritas Prep
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Source: — Data Sufficiency |
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by deloitte247 » Sat Dec 07, 2019 7:46 pm
Let the total number of days = x
Given that, at least 6 cakes were sold for 20% of x days.
$$i.e\ 0.2\cdot x=\frac{1}{5}\cdot x=\frac{x}{5}days$$
Question => Is the average number of cake less than 4?
$$Average\ cake=\frac{Total\ number\ of\ cakes}{Total\ number\ of\ days}$$
Statement 1: On 75% of the days that less than 6 cakes were sold, the number of cakes sold each day was less than 4.
i.e 75% of x < 6 cakes were sold.
25% of x > 6 cakes may be sold
Total number of cakes for each day of 75% of x is < 4.
If cakes sold for 25% of x is > then 4, then the average is > 4; but if cakes sold for 25% of x is < 4, then the average is < 4. Hence, statement 1 is NOT SUFFICIENT.

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.
This statement does not provide data for 100% of x days statement 1. So, the average might be greater or less than 4. Hence, statement 2 is NOT SUFFICIENT.

Combining both statements together:
No of the statement gives information on 100% of x and cakes produced for each day of 100% of x, so the average cannot be evaluated. Therefore, both statements combined together are NOT SUFFICIENT. Hence, the correct answer is option E.

Thanks
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