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If x, y, p, and q are positive. . . .

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Source: — Data Sufficiency |

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by Jay@ManhattanReview » Mon Oct 16, 2017 10:42 pm
VJesus12 wrote:$$If\ x,\ y,\ p,\ and\ q\ are\ positive,\ is\ x\ge y?$$
$$(1)\ \frac{px}{qy}=\frac{p}{q}$$
$$(2)\ \ xy=p$$

The OA is A.

Experts, can you explain to me this DS question? I didn't know how to solve it.
Statement 1: $$\ \frac{px}{qy}=\frac{p}{q}$$
Canceling p and q from both the sides, we get $$\frac{x}{y} = 1 => x = y$$. Sufficient.

Statement 2: $$ xy=p$$
We do not know the value of p, thus, we cannot compare x and y. Insufficient.

The correct answer: A

Hope this helps!

-Jay

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by [email protected] » Tue Oct 17, 2017 10:58 am
Hi VJesus12,

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: A

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Rich
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