Problem of the Day


The difference between integers a and b is 7, and a>b. What is a?

(1) a^b=1
(2) ab \geq 0

Reveal Answer

Answer

E. Statements (1) and (2) together are not sufficient.

See the Solution

Solution

[latexpage]

From the given information, we can say that $a-b=7$. There is nothing else to deduce or simplify, so let’s look at the statements.

Statement 1: INSUFFICIENT. This statement gives us three possibilities: $a=7, b=0$ or $a=1, b=-6$ or $a=-1, b=-8$.

Statement 2: INSUFFICIENT. There are infinitely many possibilities here. This will always be true as long as $a>7$ or $a<0$.

Statements 1 and 2 together: INSUFFICIENT. Taking both statements together only eliminates one of the three possibilities that arise from taking Statement 1 by itself. $a=7, b=0$ and $a=-1, b=-8$ are both still possible.


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