The possible value (s) of \( x \) such that \( 28\equiv x(mod\ 6) \) are :-
(A) -2
(B) 4
(C) 6
(D) 10
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → (A), (B) and (D) only
\( 28\equiv x\pmod 6 \) means that \( 28-x \) is divisible by 6. Since 28 = 6 × 4 + 4, 28 leaves remainder 4 on division by 6.
So x must be of the form 6k + 4: …, −8, −2, 4, 10, 16, …
Checking the statements
(A) −2 — Correct. \( 28-(-2)=30=6\times 5 \).
(B) 4 — Correct. \( 28-4=24=6\times 4 \).
(C) 6 — Incorrect. \( 28-6=22 \), which is not divisible by 6.
(D) 10 — Correct. \( 28-10=18=6\times 3 \).