2009

The question asks for the number of persons who are either good speakers or post graduates or doctors. This corresponds to the union of the three sets (S $\cup$ P $\cup$ D).
The number of elements in the union of sets is the sum of the numbers in all the distinct regions covered by the circles.
These regions are:
– Only Good Speakers (S only): 3
– Only Post Graduates (P only): 5
– Only Doctors (D only): 4
– Good Speakers and Post Graduates only (S $\cap$ P only): 2
– Good Speakers and Doctors only (S $\cap$ D only): 1
– Post Graduates and Doctors only (P $\cap$ D only): 3
– Good Speakers, Post Graduates, and Doctors (S $\cap$ P $\cap$ D): 4

Total number of persons in the union = Sum of numbers in all these regions
Total = 3 + 5 + 4 + 2 + 1 + 3 + 4 = 22.

Comparing the volumes: $V_A = 2$, $V_B = 5$, $V_C = 6$.
Block C has the largest volume (6 cubic units) and is therefore the heaviest.

Let’s look for a relationship between the columns within each row.
Observe $R_1$: $1, 7, 9$. $1^2 + 7 + 1 = 1 + 7 + 1 = 9$. So $C_1^2 + C_2 + C_1 = C_3$.
Observe $R_3$: $3, 105, 117$. Let’s test the same relationship: $3^2 + 105 + 3 = 9 + 105 + 3 = 117$. This relationship holds for R3 as well.
Let’s apply this relationship to $R_2$: $C_1=2, C_2=14$.
The missing number ($C_3$) should be $C_1^2 + C_2 + C_1 = 2^2 + 14 + 2 = 4 + 14 + 2 = 20$.

From “SERVANT is coded as 6789450”:
S -> 6
E -> 7
R -> 8
V -> 9
A -> 4 (Matches the code from WOMAN)
N -> 5 (Matches the code from WOMAN)
T -> 0

We need to find the code for “VOTERS”. We use the established codes for each letter:
V -> 9
O -> 2
T -> 0
E -> 7
R -> 8
S -> 6
Combining these, VOTERS is coded as 920786.

The final position is (3, 4) and the starting position is (0, 0).
The distance from the starting point is the straight-line distance between (0, 0) and (3, 4).
Using the distance formula: Distance = $\sqrt{(x_2 – x_1)^2 + (y_2 – y_1)^2}$
Distance = $\sqrt{(3 – 0)^2 + (4 – 0)^2} = \sqrt{3^2 + 4^2} = \sqrt{9 + 16} = \sqrt{25} = 5$ km.

We need to find the day of the week for 1st December of the previous year.
Let the current year be Y. We are finding the day of 1st December, Y-1.
The period is from 1st December, Y-1 to 6th January, Y.
Number of days in December Y-1 = 31 days.
Number of days in January Y up to 6th = 6 days.
Total number of days = 31 + 6 = 37 days.

To find the day of the week 37 days before Tuesday, we find the number of odd days in 37.
Number of odd days = $37 \pmod 7$.
$37 = 5 \times 7 + 2$. The remainder is 2.
So, 37 days is equal to 5 weeks and 2 days.
The day of 1st December, Y-1 is 2 days before Tuesday.
Tuesday – 1 day = Monday.
Monday – 1 day = Sunday.