OG #216

bml1105 wrote:If 1/x - 1/x+1 = 1/x+4, then x could be:

(A) 0
(B) -1
(C) -2
(D) -3
(E) -4

Here's how I'd solve the problem.

First recognize that 1/0 is undefined. So, the correct response CANNOT be A, B or E.
Here's why:
A) If x = 0, we get 1/0 - 1/1 = 1/4, but 1/0 is UNDEFINED, so there's way that this equation can ever work out.
B) If x = -1, we get 1/-1 - 1/0 = 1/3, but 1/0 is UNDEFINED, so there's way that this equation can ever work out.
E) If x = -4, we get 1/-4 - 1/-3 = 1/0, but 1/0 is UNDEFINED, so there's way that this equation can ever work out.

This leaves us with answer choices C and D.

Test answer choice C:
If x = -2, we get: 1/-2 - 1/-1 = 1/2 PERFECT!
The answer must be C

ASIDE: If it had been the case that answer choice C did not work out, we would have AUTOMATICALLY selected D as the correct answer (WITHOUT doing any extra work)

Cheers,
Brent

Hi bml1105,

I'm a big fan of Brent's approach to this question (TESTing the ANSWERS); on certain Quant questions on the GMAT, strategically plugging in the answers to find the one that matches will get the correct answer faster than the traditional "math approach."

There is one additional Number Property in this question that meshes with what Brent already showed you: one involving Common Denominators….

Here, we're subtracting one fraction from another to get a third fraction.

Notice that the first two fractions are over "X" and over "X+1"…

If X = odd, then X+1 = even
If X = even, then X+1 = odd

With one even and one odd, we'll end up with a common denominator that is EVEN…

So, X+4 = EVEN

Thus, X MUST be EVEN

Combining this deduction with Brent's eliminations, the correct answer would have to be B

GMAT assassins aren't born, they're made,
Rich

bml1105 wrote:Thanks everyone! I think sometimes I get so wrapped up trying to understand a method to solve, that I don't think to test answers.

That's totally understandable. After years and years of math tests, we have been conditioned to answer questions a certain way (e.g.,always show our work), so we're not accustomed to using the answer choices to our advantage.

If you're interested, I recently wrote an article about this: https://www.beatthegmat.com/mba/2013/12/ ... ath-part-i

Cheers,
Brent