NIMCET 2024 — Reasoning PYQ

Step 1: Understand the Concept of Odd Days

In calendar problems, we calculate the number of days between two given dates and convert them into odd days.

• An odd day is the remainder left after dividing the total number of days by $7$ (since a week consists of 7 days).

  $$\text{Odd Days}=\text{Total Days}(\mathrm{mod}7)$$

Step 2: Identify if the year is a Leap Year

We need to cross through February 1992. Let's check if $1992$ is a leap year by dividing it by $4$:

$$1992÷4=498\text{ (with 0 remainder)}$$

Since $1992$ is perfectly divisible by 4, it is a leap year. Therefore, February 1992 has $29$ days.

Step 3: Count the total number of days from Oct 1991 to Mar 14, 1992

We count the remaining days starting from October 1st, 1991 up to March 14th, 1992:

• October 1991: $31$ days

• November 1991: $30$ days

• December 1991: $31$ days

• January 1992: $31$ days

• February 1992 (Leap Year): $29$ days

• March 1992: $14$ days (up to the target date)

$$\text{Total Days}=31+30+31+31+29+14=166\text{ days}$$

Step 4: Find the total number of Odd Days

Divide the total number of days by $7$ to extract the number of odd days:

$$\text{Odd Days}=166÷7$$

$$166=(23\times 7)+5$$

The remainder is $5$. So, there are $5$ odd days.

Step 5: Determine the final day

Add the $5$ odd days to the reference starting day (Wednesday):

$$\text{Wednesday}+1=\text{Thursday}$$

$$\text{Wednesday}+2=\text{Friday}$$

$$\text{Wednesday}+3=\text{Saturday}$$

$$\text{Wednesday}+4=\text{Sunday}$$

$$\text{Wednesday}+5=\text{Monday}$$

Conclusion

The day on 14th March 1992 was a Monday.

Therefore, the correct option is B.