Molly assigns every letter of the alphabet a different whole number value. She finds the value of a word by multiplying the values of its letters together. For example, if $\mathrm{D}$ has a value of 10 , and $\mathrm{I}$ has a value of 8 , then the word DID has a value of $10 \times 8 \times 10=800$. The table shows the value of some words. What is the value of the word MATH?

| Word | Value |
| :---: | :---: |
| TOTE | 18 |
| TEAM | 168 |
| MOM | 49 |
| HOME | 70 |
| MATH | $?$ |

(A) 19
(B) 840
(C) 420
(D) 190
(E) 84
Since $\mathrm{M} \times \mathrm{O} \times \mathrm{M}=49$, either $\mathrm{M}=7$ and $\mathrm{O}=1$ or $\mathrm{M}=1$ and $\mathrm{O}=49$.

However, since the value of the word TOTE is 18, O cannot have a value of 49 because 18 is not divisible by 49 .

Thus, $\mathrm{M}=7$ and $\mathrm{O}=1$.

Since $\mathrm{T} \times \mathrm{O} \times \mathrm{T} \times \mathrm{E}=18$ and $\mathrm{O}=1$, we have $\mathrm{T} \times \mathrm{T} \times \mathrm{E}=18$.

Therefore, either $\mathrm{T}=3$ and $\mathrm{E}=2$ or $\mathrm{T}=1$ and $\mathrm{E}=18$.

However, $\mathrm{O}=1$, and since every letter has a different value, $\mathrm{T}$ cannot be equal to 1 .

Thus, $\mathrm{T}=3$ and $\mathrm{E}=2$.

The value of the word TEAM is 168 , so $\mathrm{T} \times \mathrm{E} \times \mathrm{A} \times \mathrm{M}=168$, or $3 \times 2 \times \mathrm{A} \times 7=168$.

Thus, $42 \times \mathrm{A}=168$ or $\mathrm{A}=168 \div 42=4$.

The value of the word HOME is 70 , so $\mathrm{H} \times \mathrm{O} \times \mathrm{M} \times \mathrm{E}=70$, or $\mathrm{H} \times 1 \times 7 \times 2=70$.

Thus, $14 \times \mathrm{H}=70$ or $\mathrm{H}=70 \div 14=5$.

Finally, the value of the word MATH is $\mathrm{M} \times \mathrm{A} \times \mathrm{T} \times \mathrm{H}=7 \times 4 \times 3 \times 5=420$.

ANSWER: (C)