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Overlapping Sets

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Overlapping Sets

by swerve » Sun Feb 16, 2020 1:32 pm
A certain hospital has 400 patients, who are classified in one of two categories: intensive care (IC) and regular care (RC). What percent of the hospital's patients are in IC?

1) 60% of the patients are male, and the rest are female.
2) 25% of the male patients are in IC, and 80% of the female patients are in the RC.

The OA is C

Source: Magoosh
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Source: — Data Sufficiency |
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Re: Overlapping Sets

by deloitte247 » Sat Feb 22, 2020 7:21 pm
Given that the total patient = 400 patients
Target questions : what percent of the hospital's patient are in IC?
Statement 1
60% of the patients are male and the rest are females
$$=\frac{60}{100}\cdot400=240male\ patients$$
Female patient = 400-240 160 female patients, there is no information about no of patient in IC or RC. Hence statement 1 is INSUFFICIENT.

Statement 2
25% of male patients are in IC and 80%of the female in the RC
Total number of male and female patient is unknown, only a percentage of exact number is given hence statement 2 is INSUFFICIENT.

Combining both statements together.
60% of total patient = no of male patient , 25% of male patients are in IC the remaining 75% of the male will in RC.
80% of female are in RC the remaining 20 % will be in IC.
Total number of patient in IC = 20% will be in IC
Total no of patients in IC = 25%of male + 20% of females


$$\frac{60}{100}\cdot400=240male\ patient\ s$$
$$Female\ \ patients=400-240=160$$
$$25\%of\ male=\frac{25}{100}\cdot240=60$$
$$20\%of\ females=\frac{20}{100}\cdot160=32$$
no of patients in IC= 60+32=92
$$\%of\ patients\ in\ IC=\frac{92}{400}\cdot100=23\%$$

Both statements together are SUFFICIENT.

$$Answer\ is\ Option\ C$$
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