If x, y, p, and q are positive, is x>=y?

Question: is \(x\) more than or equal to \(y\) (is \(x\geq{y}\))?

(1) \(\frac{px}{qy}=\frac{p}{q}\) --> reduce by \(\frac{p}{q}\) --> \(\frac{x}{y}=1\) --> \(x=y\), so we can answer yes to the question: \(x\) is equal to \(y\). Sufficient.

(2) \(xy=p\) --> Clearly not sufficient (if \(x\), \(y\) and \(p\) equal to 1, 2, and 2 respectively then the answer is NO but if they equal to 2, 1 and 2 then the answer is YES).

Answer: A.

Hope it's clear.
_________________

from A we get x=y only , but what abut x > y ?
Answer should be E

The answer is A, not E.

The question asks: is x greater than or equal to y. (1) says that x IS equal to y, so we have an YES answer to the question.
_________________

However in the first statement it is not greater than y as in the condition x> y is not fulfilled. How can we still go ahead and mark A as the correct answer.

Kinda confusing.

Can we use this logic for any similar question we encounter in the exam?

The question asks whether \(x\geq{y}\). (1) says that x = y, so the answer to the question is YES.
_________________

Hi All,

We're told that X, Y, P and Q are POSITIVE. We're asked if X is >= to Y. This is a YES/NO question. We can solve it with a mix of arithmetic and TESTing VALUES.

1) (P)(X)/(Q)(Y) = P/Q

If we cross-multiply this fraction, we get...
(P)(X)(Q) = (P)(Q)(Y)

Since we know that all of the variables are POSITIVE, we can 'cancel out' the P and Q, which leaves us...
X = Y
Thus, the answer to the question is ALWAYS YES.
Fact 1 is SUFFICIENT

2) (X)(Y) = P

With this Fact, we have no idea how X and Y relate to one another. For example:
IF... X=1, Y=2, P=2 then the answer to the question is NO.
IF... X=1, Y=1, P=1 then the answer to the question is YES.
Fact 2 is INSUFFICIENT

Final Answer:

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