A number when divided by 95 leaves a remainder 43. If the same number is divided by 19, then the remainder will be:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 5
Let the number be N.
Given:
$N \equiv 43 \pmod{95}$
Since
$95 = 19 \times 5$
Now divide the congruence by 19:
$N \equiv 43 \pmod{19}$
Reduce 43 modulo 19:
$43 = 19 \times 2 + 5$
So,
$N \equiv 5 \pmod{19}$