Question

if x mod 3=1 and x mod 7=4 then which of these is the value of x:
a). 25.
b). 35.
c). 28
d). 67
solve with explanation..
more than one option can be correct. ​

Answer 1

$\sf \huge \red{Answer}$

71 - x = 8n

71 - x is the multiple of 8

if x = 1, 71 - x = 70 is not the multiple of 8,

The number which is nearest to 71 is 64 (multiple of 8).In order to make this 71 as 64, we have to subtract 7.

So, the value of x is 7.

Hence 7 is the least number.

(ii) 78 + x ≡ 3 (mod 5)

Answer 2

Given: xmod3=1, xmod7=4

To find: Value of x

Solution:  Option a.) 25 and d.)67 are two appropriate values of x

To solve this problem taking up a trial and error approach is the best way, as we can simply replace the values given to us in the options as x to realize whether it is the right value or not.

Therefore replacing option a.) 25 as the correct value of x we get,

25mod3= 3*8 + 1  

25mod7= 7*3 + 4

Since 25 satisfies both the given conditions, therefore it is an eligible value for x

Replacing Option b.) 35 as x

35mod3= 3*11 + 2

Since 35 fails to satisfy given conditions, it is not a suitable value for x.

Replacing Option c.) 28 as x

28mod3= 3*9 + 1

28mod7= 7*4 + 0

Since 28 fails to satisfy given conditions it is not a suitable value for x.

Replacing Option d.) 67 as x

67mod3= 3*22 + 1

67mod7= 7*9 + 4

Since 67 satisfies both the given conditions, it is a suitable value for x.

Hence we conclude that amongst the given options,

Option a.) 25 and Option b.) 67 are the suitable values to replace x.

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