## Tuesday, October 11, 2011

### this week's Math Beast Challenge problem

Here it is-- "Slash and Burn": _

#### 1 comment:

Kevin Kim said...

No one likes a fraction made out of fractions, so we've got to do something to make the fraction in Quantity B look a little more civilized. The denominators in that fraction are n, 3x, and x, so the least common denominator is 3nx.

When I multiply the fraction by (3nx/3nx), I get a simpler-looking fraction:

12x/(n + 15n) = (3/4)(x/n)

At this point, it's just a matter of plugging in numbers. We know that x and n have to be nonzero quantities, but we're not told whether they might be positive or negative. So let's try some combinations of x and n that cover the major possibilities:

x = 1, n = 1 (+/+)
x = -1, n = -1 (-/-)
x = -1, n = 1 (-/+)
x = 1, n = -1 (+/-)

For the first pair:

A = 1
B = 3/4

A is greater than B.

For the second pair:

A = 1
B = 3/4

A is greater than B.

For the third pair:

A = -1
B = -3/4

B is greater than A.

For the fourth pair:

A = -1
B = -3/4

B is greater than A.

By plugging in simple numbers like 1 and -1, we quickly see that there are times when A is greater, and times when B is greater.

The answer is D: The relationship cannot be determined from the information given.

Or so I say, anyway.