Question

if x mod 3 is 1 and x mod 7 is 4 then which of the following are the possible values of x​

Answer 1

Given :  x mod 3=1 and x mod 7=4

To Find :  which of these is the value of x:

https://brainly.in/question/25460642 refer this for options

a). 25.

b). 35.

c). 28

d). 67

Solution:

x mod 3=1 and x mod 7=4

a mod b = c  => when a divided by b  the remainder is c

Hence a = bq  + c

x mod 3=1

=> x  = 3m + 1

x mod 7=4

=> x  = 7n  + 4

3m + 1  = 7n  + 4

=> 3m - 3 = 7n

=> 3(m - 1) = 7n

Hence least possible value of n = 3

least possible value of  m  = 8

x  = 3m + 1  = 3*8 + 1 =  25

x  = 7n  + 4  = 7*3 + 4 = 25

Hence  25 can be the value of x

or all options can be checked

25 = 8 * 3 + 1  ,   25 = 7* 3 + 4

35 = 11* 3 + 2  Hence remainder is not 1

28 = 7 * 4   Hence  remainder is not 4

67 = 9 * 7  + 2   Hence remainder is not 4

So only correct option is option a )  25

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Answer 2

Step-by-step explanation:

x mod 3= 1 and x mod 7= 4

a mod b=c= when a divided by b the remainder is c.

Hence a = bq + c

x mod 3=1

= x = 3m +1

x mod 7=4

= x = 7n +4

3m + 1 = 7n +4

= 3m - 3 = 7n

= 3(m - 1) = 7n

Hence the possible value of n = 3

Possible value for m = 8 x = 3m + 1 = 3*8 + 1 = 25.

x = 7n +4 = 7*3+ 4 = 25.

Hence 25 can be the value of x.