CAT 1995 | Question: 151

Question

The following table gives data of some students. However, some data has been spoilt and cannot be read on the computer floppy

It is also known that:

1. Half the students were either excellent or good.

2. 40% of the students were females

3. One-third of the male students were average. Based on the above answer the following questions.

How many students are both female and excellent?

• A. $0$
• B. $8$
• C. $16$
• D. $32$

Answer 1

Let's start with fill the gaps in table:

		Performance		Total
	Average	Good	Excellent
Male			10
Female				32
Total		30

We know that Total female students = 32

$40\%$ of the total students were females.

$∴ \text{Total students} = \dfrac{32 \times 100}{40} = 80$

		Performance		Total
	Average	Good	Excellent
Male			10
Female				32
Total		30		$\color{blue}{80}$

 

$∴\text{Total Male students = (80-32) = 48}$

		Performance		Total
	Average	Good	Excellent
Male			10	$\color{blue}{48}$
Female				32
Total		30		$\color{blue}{80}$

$\dfrac{1}{3}^{rd} \text{of the male students =} \{(\dfrac{1}{3}\times 48) = 16\}\text{ were average}$

		Performance		Total
	Average	Good	Excellent
Male	$\color{blue}{16}$		10	$\color{blue}{48}$
Female				32
Total		30		$\color{blue}{80}$

$∴\text{ Good male students = 48 - (16+10)= 22}$

$∴\text{ Good female students = 30 - 22 = 8}$

		Performance		Total
	Average	Good	Excellent
Male	$\color{blue}{16}$	$\color{blue}{22}$	10	$\color{blue}{48}$
Female		$\color{blue}{8}$		32
Total		30		$\color{blue}{80}$

Now, we know that half of the students i.e. $\dfrac{80}{2} = 40$ students were either excellent or good.

∴ Rest $(80-40)=40$ students were average

		Performance		Total
	Average	Good	Excellent
Male	$\color{blue}{16}$	$\color{blue}{22}$	10	$\color{blue}{48}$
Female	$\color{blue}{(40-16) = 24}$	$\color{blue}{8}$		32
Total	$\color{blue}{40}$	30		$\color{blue}{80}$

∴ $\color{green}{\text{There are}}$ $\color{red}{no}$ $\color{green}{\text{female students who are excellent.}}$

		Performance		Total
	Average	Good	Excellent
Male	$\color{blue}{16}$	$\color{blue}{22}$	10	$\color{blue}{48}$
Female	$\color{blue}{(40-16) = 24}$	$\color{blue}{8}$	--	32
Total	$\color{blue}{40}$	30	$\color{blue}{10}$	$\color{blue}{80}$