# Problem of the Day

If , , and represent real numbers, is ?

(1)

(2)

### Solution

[latexpage]

**Statement (1)**: INSUFFICIENT. This tells us that $a$ is positive which means that $a^7$ is positive. Â However, we don’t have any information about $b$ or $c$. Â If $b$ and $c$ are both positive, then$a^7b^3c^4$ is positive. Â If $b$ is negative and $c$ is positive,Â $a^7b^3c^4$ is negative.

**Statement (2)**: INSUFFICIENT. This is insufficient for the same reason statement 1 is insufficient. Â If $a$ and $c$ are both positive, thenÂ $a^7b^3c^4$ is positive. Â If $a$ is negative and $c$ is positive,Â $a^7b^3c^4$ is negative.

**Statements (1) and (2)**: INSUFFICIENT. Â Both statements taken together is almost enough to be sure thatÂ $a^7b^3c^4$ is positive, but we can’t rule out the possibility that $c=0$, which would makeÂ $a^7b^3c^4=0$ and hence not positive.

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