Question 16/20: Set 4 - Try Out - General Reasoning (SNBT)

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Dito is guessing a passcode consisting of a 4-digit combination of distinct numbers and letters with the following clues:

The numbers chosen are natural numbers less than 7.
The first digit is a factor of 7.
The second digit is a number.
The third digit chosen is $3$ or $4$ .
The last digit is a consonant letter forming the name Dito.

The maximum number of passcodes Dito has to try is...

Explanation

We can solve this problem using the filling slots method for the 4-digit passcode.

The available numbers are natural numbers less than 7, which are:

S = \{1, 2, 3, 4, 5, 6\}

Here is the analysis of possibilities for each digit position:

Position	Condition	Choices	Count
Digit 1	Factor of 7	Only number 1 (since 7 is not in $S$ )	1
Digit 3	Number 3 or 4	$\{3, 4\}$	2
Digit 4	Consonant in "Dito"	$\{\text{D}, \text{T}\}$	2
Digit 2	Remaining numbers	From 6 numbers, 2 are already used (in Digit 1 and 3)	4

Additional Explanation for Digit 2

Since the passcode must consist of distinct numbers, we must subtract the numbers already used in other positions from the total available numbers.

Total available numbers: 6
Used in Digit 1: 1 number
Used in Digit 3: 1 number
Remaining choices: $6 - 1 - 1 = 4$ numbers.

Total Calculation

The maximum number of passcodes is the product of the possibilities for each position:

\begin{aligned} \text{Total} &= (\text{Digit 1}) \times (\text{Digit 2}) \times (\text{Digit 3}) \times (\text{Digit 4}) \\ &= 1 \times 4 \times 2 \times 2 \\ &= 16 \end{aligned}

Thus, Dito has to try a maximum of 16 passcodes.

Command Palette

Number 16

Explanation

Additional Explanation for Digit 2

Total Calculation