Context: In the date trick, the final answer is given by , where is the month and is the day. Q. Find the dates if the final answers are the following: (i) 1269 (ii) 394 (iii) 296

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Question 4

Context: In the date trick, the final answer is given by $100M + 165 + D$ , where $M$ is the month and $D$ is the day.

Q. Find the dates if the final answers are the following:

(i) 1269

(ii) 394

(iii) 296

Solution

Understand the Question

The date trick formula is given by: $\text{Final Answer} = 100M + 165 + D$ where $M$ represents the month number ( $1$ for January, $2$ for February, etc.) and $D$ represents the day of the month ( $1$ to $31$ ).
Subtracting $165$ from the final answer isolates the date components: $100M + D = \text{Final Answer} - 165$
In the resulting number, the hundreds place gives the month $M$ , and the remaining two digits (units and tens) give the day $D$ .

(i) Find the date if the final answer is $1269$ .

Step 1 · Calculate Month and Day for 1269

Substitute the final answer into the formula:

\begin{aligned} 100M + D &= 1269 - 165 \\[0.6em] &= 1104 \end{aligned}

Separating the hundreds and the day:

\begin{aligned} M &= 11 \implies \text{November} \\[0.6em] D &= 4 \implies 4^{\text{th}} \end{aligned}

Answer

(i) 4th of November

(ii) Find the date if the final answer is $394$ .

Step 1 · Calculate Month and Day for 394

Substitute the final answer into the formula:

\begin{aligned} 100M + D &= 394 - 165 \\[0.6em] &= 229 \end{aligned}

Separating the hundreds and the day:

\begin{aligned} M &= 2 \implies \text{February} \\[0.6em] D &= 29 \implies 29^{\text{th}} \end{aligned}

Answer

(ii) 29th of February

(iii) Find the date if the final answer is $296$ .

Step 1 · Calculate Month and Day for 296

Substitute the final answer into the formula:

\begin{aligned} 100M + D &= 296 - 165 \\[0.6em] &= 131 \end{aligned}

Separating the hundreds and the day:

\begin{aligned} M &= 1 \implies \text{January} \\[0.6em] D &= 31 \implies 31^{\text{st}} \end{aligned}

Answer

(iii) 31st of January

Common Mistakes

Subtraction Error: Forgetting to subtract $165$ first before splitting the number into month and day.
Misinterpreting Digits: For a single-digit day such as in $1104$ , incorrectly reading $D = 40$ instead of $D = 4$ .
Swapping Month and Day: Mixing up $M$ (hundreds digits) and $D$ (last two digits), leading to invalid dates.