Please explain how to workout the below question, much appreciated
The four digits of the PIN number of my debit card are such that their numerical value is the same as their numerical product. The first letter of each digit, when written in order as words, can be used to form the word FOOT. What is the total number of letters required to spell the first, second and the last digits?
A 9
B 10
C 11
D 12
To find the answer to this question, we need to analyze the given information carefully.
First, let’s understand what is meant by the numerical value and numerical product of a digit.
The numerical value of a digit refers to the actual value of the digit itself (e.g., 1, 2, 3, etc.).
The numerical product of a digit refers to the result of multiplying all the digits together. For example, if the PIN number were 1234, the numerical product would be 1 * 2 * 3 * 4 = 24.
Now, let’s break down the given information step by step:
1. The numerical value of each digit is the same as the numerical product of the digits. This means that each digit must be either 1 or 2, as these are the only two digits whose numerical value is equal to their numerical product.
2. The first letters of the digits, when written in order as words, can be used to form the word FOOT. This means that the possible digits for the first, second, and last positions are limited to either 1 or 2.
3. We need to determine the total number of letters required to spell the first, second, and last digits.
Based on the information above, we can conclude that the possible digits for the PIN number are 1, 1, 2, and 2. This is because the numerical value of each digit must be equal to its numerical product, and using 1 and 2 as the digits provides the desired result.
Now, let’s spell out the first, second, and last digits:
- The first digit is 1, which is spelled "O-N-E." Therefore, it requires 3 letters.
- The second digit is also 1, spelled "O-N-E." Therefore, it requires 3 letters.
- The last digit is 2, spelled "T-W-O." Therefore, it requires 3 letters.
Finally, let’s add up the total number of letters required to spell the first, second, and last digits:
3 (letters for the first digit) + 3 (letters for the second digit) + 3 (letters for the last digit) = 9
Therefore, the answer to the question is A) 9.