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If 7+y=4(mod8). Find the least value if 10≤y≤30

A. 11

B. 13

C. 19

D. 21

**Comments**

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7 + y = 4 (mod 8)

subtract 7 from both sides

y = 4 - 7 (mod 8)

y = -3 (mod 8)

In linear congrugence negative or decimal values are not accepted, so, we add 8 (because its in mod 8)

y = - 3 + 8 (mod 8)

y = 5

But 5 dosen't fall within he range, so we add 8 again

y = 5 + 8

y = 13

since 13 fall within the range, thus the minimum value of y is 13 within the range 10 ≤ y ≤ 30

**Ans B**

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7 + y = 4(mod 8)

Test from the range given

7 + 10 = 1(mod 8)

7 + 11 = 2(mod 8)

7+12 = 3(mod 8)

7 + 13 = 4(mod 8)

The least value of y is 13

**Ans B**

This method is unacceptable

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