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Question
If 9≡3(mod 6) and 14≡2(mod 6), then −5≡y(mod 6). Find y.
If 9≡3(mod 6) and 14≡2(mod 6), then −5≡y(mod 6). Find y.
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Solution
The correct option is D 1
Given:−5≡y(mod 6)
By the theorem on modulo operations, if a, b, c and d are integers and m is a positive integer such that if a≡b(mod m) and c≡d(mod m) , then
(i) (a−c)≡(b−d)(mod m)
Given, 9≡3(mod 6) and 14≡2(mod 6)
Hence, from the (i) theorem,
(9−14)≡(3−2)(mod 6)
⇒ −5≡1(mod 6)
By comparing the above expression with the given one, we get y = 1.
Given:−5≡y(mod 6)
By the theorem on modulo operations, if a, b, c and d are integers and m is a positive integer such that if a≡b(mod m) and c≡d(mod m) , then
(i) (a−c)≡(b−d)(mod m)
Given, 9≡3(mod 6) and 14≡2(mod 6)
Hence, from the (i) theorem,
(9−14)≡(3−2)(mod 6)
⇒ −5≡1(mod 6)
By comparing the above expression with the given one, we get y = 1.
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