Question

4. An integer is divided by 4 and gives a remainder of 2. The resulting quotient is divided by 4 and gives a
remainder of 2. The resulting quotient is then divided by 7 giving a quotient of 1 and a remainder of 2. Find
the number?​

Answer 1

Answer:

Step-by-step explanation:

• Let the number is equal to x
• it is divided by 4 and gives a remainder 2
• x = 4 * q(x) + 2
• => q(x) = (x-2)/4  ------------------------- (i)
• then q(x) is divided by 4 and gives remainder 2
• q(x) = 4 * Q(x) + 2
• => Q(x) = ( q(x) - 2 ) /4 -------------------------(ii)
• then the Q(x) is divided by 7 giving quotient of 1 and  remainder of 2
• Q(x) = 7 * 1 + 2
• Q(x) = 9

By putting the value of Q(x) in equation ii

   we get,

• 9 = ( q (x) -2 )/4
• => q(x) -2 = 36
• => q(x) = 38

By putting the value of q(x) in equation i

     we get,

• 38 = ( x-2 )/4
• x - 2 = 152
• x = 146 (Ans.)

Therefore the integer is 154 .

                                             hope it helps

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