gmat_guy666 wrote:The number of touchscreen personal organizers currently in stock is p times what it was at the beginning of the year. If the number of touchscreen organizers currently in stock is t and the number in stock at the beginning of the year is x (where t, x and p do not equal zero), are there more touchscreen personal organizers in stock now than there were at the beginning of the year?

1)p > x
2)tp > t

Target question: Are there more touchscreen personal organizers in stock now than there were at the beginning of the year?

Given:
t = number of touchscreen organizers CURRENTLY in stock
x = the number in stock at the BEGINNING of the year
t = px [from the fact that the number of touchscreen personal organizers currently in stock is p times what it was at the beginning of the year]

REPHRASED target question: Is px > x?

Since x > 0, we can divide both sides of the inequality by x to get: "Is p > 1?"
RE-REPHRASED target question: Is p > 1?

ASIDE: this RE-REPHRASED target question should make sense. We're told that the number of touchscreen personal organizers currently in stock is p times what it was at the beginning of the year. So, if p < 1, then the CURRENT number of organizers will be LESS THAN the number at the beginning of the year. Conversely, if p > 1, then the CURRENT number of organizers will be GREATER THAN the number at the beginning of the year.

Okay, onto the statements....

Statement 1: p > x
We know that x ≠ 0 and we know that x must be an INTEGER. So, the smallest possible value of x is 1.
If p > x, then we can be certain that p > 1
Since we can answer the RE-REPHRASED target question with certainty, statement 1 is SUFFICIENT

Statement 2: tp > t
Since t > 0, we can divide both sides of the inequality by t to get: p > 1
PERFECT - this is exactly what our RE-REPHRASED target question is asking.
Since we can answer the RE-REPHRASED target question with certainty, statement 2 is SUFFICIENT

Answer = D

Cheers,
Brent