Question : The remainder when $75 \times 73 \times 78 \times 76$ is divided by 34 is:
Option 1: 15
Option 2: 18
Option 3: 22
Option 4: 12
Correct Answer: 12
Solution :
$\frac{ (75 × 73 × 78 × 76)}{34}$
Divide each number individually by 34 and break it into a small number.
$\frac{75}{34} \times \frac{73}{34} \times \frac{78}{34} \times \frac{76}{34}$
Remainders = $7 × 5 × 10 × 8$
Again, $\frac{35 \times 80}{34}$ ⇒ $\frac{35}{34} \times \frac{80}{34}$
Remainders = 1 × 12 = 12, which is smaller than 34.
Hence, the correct answer is 12.
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