Algebra Play | IT

Question 4

Context: In the date trick, the final answer is given by 100M+165+D100M + 165 + D, where MM is the month and DD is the day.

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

(i) 1269 (ii) 394 (iii) 296

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Solution

We will use the given formula to find the month and day.

Step 1 — Understand the formula

The problem gives us a formula for a date trick. Let MM be the month number. January is 1, February is 2, and so on. Let DD be the day of the month. The formula connects these to a final answer.

100M+165+D=Final Answer100M + 165 + D = \text{Final Answer}

We need to find MM and DD for given final answers. First, we will rearrange the formula. We want to isolate the 100M+D100M + D part.

100M+D=Final Answer−165100M + D = \text{Final Answer} - 165

When 100M+D=X100M + D = X, we find MM and DD. MM is the number of hundreds in XX. DD is the remaining part. Remember, DD must be a day, from 1 to 31.

Step 2 — Solve for the first date (1269)

We are given the final answer is 1269. Let us substitute this into our rearranged formula.

100M+D=1269−165100M + D = 1269 - 165

100M+D=1104100M + D = 1104

Now we need to find MM and DD. MM is the number of hundreds in 1104. DD is the remaining part.

M=11M = 11 D=4D = 4

So, the month is the 11th month. The 11th month is November. The day is the 4th.

Date: 4th of November\boxed{\text{Date: 4th of November}}

Step 3 — Solve for the second date (394)

We are given the final answer is 394. Let us substitute this into our rearranged formula.

100M+D=394−165100M + D = 394 - 165

100M+D=229100M + D = 229

Now we need to find MM and DD. MM is the number of hundreds in 229. DD is the remaining part.

M=2M = 2 D=29D = 29

So, the month is the 2nd month. The 2nd month is February. The day is the 29th.

Date: 29th of February\boxed{\text{Date: 29th of February}}

Step 4 — Solve for the third date (296)

We are given the final answer is 296. Let us substitute this into our rearranged formula.

100M+D=296−165100M + D = 296 - 165

100M+D=131100M + D = 131

Now we need to find MM and DD. MM is the number of hundreds in 131. DD is the remaining part.

M=1M = 1 D=31D = 31

So, the month is the 1st month. The 1st month is January. The day is the 31st.

Date: 31st of January\boxed{\text{Date: 31st of January}}

Answer

(i) 4th of November (ii) 29th of February (iii) 31st of January

More questions in IT

Q1

Context: Think of a number trick:

  1. Think of a number.
  2. Double it.
  3. Add four.
  4. Divide by two.
  5. Subtract the original number you thought of.

Q. I predict you get 2. Am I right? Try it out with different starting numbers. Do you always end up with the same value, 2? Why?

Q2

Context: Consider the following number trick:

  1. Think of a number.
  2. Double it.
  3. Add four.
  4. Divide by two.
  5. Subtract the original number you thought of. (This trick always results in 2).

Q. How would you change this game to make the final answer 3? What about 5?

Q3

Context: Consider the following number trick:

  1. Think of a number.
  2. Double it.
  3. Add four.
  4. Divide by two.
  5. Subtract the original number you thought of. (This trick always results in 2).

Q. Can you come up with more complicated steps that always lead to the same final value?

Q4

Context: In the date trick, the final answer is given by 100M+165+D100M + 165 + D, where MM is the month and DD is the day.

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

(i) 1269 (ii) 394 (iii) 296

Q5

Context: In the date trick, the final answer is given by 100M+165+D100M + 165 + D, where MM is the month and DD is the day.

Q. Can you change the steps in this trick and still find the original date? Instead of subtracting 165 from the final answer, you might have to subtract some other number.

Q6

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Q8

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Q9

What is the relationship between the numbers in the bottom row and the number at the top?

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Q10

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Q11

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Q12

Context: 6.5 The Largest Product

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Q13

Context: Mukta's trick: Choose a 2-digit number of different digits, reverse the digits to get another number, find their difference, and divide the result by 9.

Q. If we choose other 2-digit numbers, and follow the steps, will there always be no remainder?

Q14

Context: Suppose a two-digit number is abab. When it is reversed, the new number is baba. If b>ab > a, the difference is ba−ab=9(b−a)ba - ab = 9(b - a), which is divisible by 9.

Q. Can you work out what happens if a>ba > b?

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