Question

The largest two digit number that satisfies is \[{\text{5x = 6(MOD4)}}\]
A. \[96\]
B. \[97\]
C. \[98\]
D. \[99\]

Answer 1

Hint: Consider the largest two-digit number in the sequence of \[99,98,97...\]. , firstly multiply it with 5 and then Subtract \[6\]from the obtained number and look that it should be perfectly divisible by \[4\]. So, we need to select the first largest number and check whether it satisfies the condition, if not then we go for the next number and check, and so on.

Complete step by step answer:

Given The largest two - digit number that satisfy \[{\text{5x = 6(MOD4)}}\] is
Let take the first number as \[99\]
Multiplying it by \[5\]and subtracting \[6\] from it,
\[
   \Rightarrow 5 \times 99 = 495 \\
   \Rightarrow 495 - 6 = 489 \\
 \]
Divide it by \[4\], if it is divisible it will be our answer otherwise it will be rejected and we will move to the next number.
\[ \Rightarrow \dfrac{{489}}{4} = 122.5\]
So , \[99\]will be rejected. Now , move for \[98\]
Multiplying it by \[5\]and subtracting \[6\]from it ,
\[
   \Rightarrow 5 \times 98 = 490 \\
   \Rightarrow 490 - 6 = 484 \\
 \]
Divide it by \[4\], if it is divisible it will be our answer otherwise it will be rejected and we will move to the next number.
\[ \Rightarrow \dfrac{{484}}{4} = 121\]
Hence, \[98\] will be accepted.
So, option (c) is our required correct answer.

Note: Another option to approach the above question is by trail and approach method.
Trial and error is a problem-solving method in which multiple attempts are made to reach a solution. Trial and error is trying a method, observing if it works and if it doesn't try another new method. This process is repeated until success or a solution is reached.
We need to find the digits as per satisfying the given condition one by one and the one which satisfies it at the earliest will be our answer.