What number should be placed in the box to make $10^{4} \times 100^{\square}=1000^{6}$ ?
(A) 7
(B) 5
(C) 2
(D) $\frac{3}{2}$
(E) 10

## Part C: Each correct answer is worth 8.
What number should be placed in the box to make $10^{4} \times 100^{\square}=1000^{6}$ ?
(A) 7
(B) 5
(C) 2
(D) $\frac{3}{2}$
(E) 10

## Solution

Since 1000 has 3 zeros, $1000^{6}$ has 18 zeros, so the left side should have 18 zeros too. The number $10^{4}$ has 4 zeros, so that leaves 14 zeros for the number $100^{\square}$. Since 100 has 2 zeros, the number in the box should be 7 .

ANSwER: (A)

## Part C