ILLUSTRATION 2

Directions for Questions 1 to 4: Refer to the data below and answer the questions that follow:

In an examination 43% passed in Math, 52% passed in Physics and 52% passed in Chemistry.

Let Set P, Set C and Set M denotes the students who passed in Physics, Chemistry and Math respectively. Then

1. How many students passed in Math only?

(à) 16 (b) 32

(ñ) 48 (d) 80

2. Find the ratio of students passing in Math only to the students passing in

Chemistry only?

(a) 16:37 (b) 29:32

(c) 16:19 (d) 31:49

3. What is the ratio of the number of students passing in Physics only to the students

passing in either Physics or Chemistry or both?

(a) 34/46 (b) 26/84

(c) 49/32 (d) None of these

4. A student is declared pass in the exam only if he/she clears at least two subjects.

The number of students who were declared passed in this exam is?

(a) 33 (b) 66

(c) 39 (d) 78

Sol. Let P denote Physics, C denote Chemistry and M denote Maths.

% of students who passed in P and C only is given by

% of students who passed in P and C - % of students who passed all three =

20% - 8% - 12%

% of students who passed in P and M only is given by

% of students who passed in P and M - % of students who passed all three =

14% - 8% - 6%

% of students who passed in M and C only is:

% of students who passed in C and M - % of students who passed all three =

21%-8% = 13%

So, % of students who passed in P only is given by:

Total no. passing in P - No. Passing in P & C only - No. Passing P & M only -

No. Passing in all three√^zE

52% - 12% - 6% - 8%- - 26%

% of students who passed in M only is:

Total no. passing in M - No. Passing in M & C only - No. Passing P & M only -

No. Passing in all three√^zE

43% - 13% - 6% - 8%- - 16%

% of students who passed in Chemistry only is

Total no. passing in C - No. Passing in P & C only - No. Passing C & M only - No. Passing in all three √^zE

52% - 12% - 13% - 8%- - 19%

The answers are:

1. Only Math = 16% = 32 people. Option (b) is correct.

2. Ratio of Only Math to Only Chemistry = 16:19. Option (c) is correct.

3. 26:84 is the required ratio. Option (b) is correct.

4. 39 % or 78 people. Option (d) is correct.