What number goes in the box so that $10 \times 20 \times 30 \times 40 \times 50=100 \times 2 \times 300 \times 4 \times \square$ ?
(A) 0.5
(B) 5
(C) 50
(D) 500
(E) 5000
Solution 1

We first evaluate the product on the left side of the equation.

$10 \times 20 \times 30 \times 40 \times 50=200 \times 30 \times 40 \times 50=6000 \times 40 \times 50=240000 \times 50=12000000$.

Similarly, we evaluate the product on the right side of the equation.

$100 \times 2 \times 300 \times 4 \times \square=200 \times 300 \times 4 \times \square=60000 \times 4 \times \square=240000 \times \square$.

The left side of the equation is equal to the right side of the equation, so then

$12000000=240000 \times \square$.

Therefore, the number that goes in the box is $12000000 \div 240000=50$.

## Solution 2

The product of the first two numbers on the left side of the equation is equal to the product of the first two numbers on the right side of the equation.

That is, $10 \times 20=200=100 \times 2$.

Similarly, the product of the next two numbers (the third and fourth numbers) on the left
side of the equation is equal to the product of the next two numbers on the right side of the equation.

That is, $30 \times 40=1200=300 \times 4$.

Since the products of the first four numbers on each side of the equation are equal, then the final (fifth) number on each side of the equation must be equal.

Therefore, the number that goes in the box is equal to the fifth number on the left side of the equation or 50 .

ANSWER: $(\mathrm{C})$