Max@Math Revolution wrote:[Math Revolution GMAT math practice question]

If x and y are positive, is x > y?

1) 2x > 3y
2) -5x < -7y

$$x,y\,\, > 0\,$$
$$x\,\mathop > \limits^? \,\,y$$

$$\left( 1 \right)\,\,2x > 3y\,\,\,\,\,\,\mathop \Rightarrow \limits^{:\,\,2} \,\,\,\,\,\,x\,\, > \,\,{3 \over 2}y\,\,\,\mathop > \limits^{\left( * \right)} \,\,\,y\,\,\,\,\, \Rightarrow \,\,\,\,\,\left\langle {{\rm{YES}}} \right\rangle $$
$$\left( * \right)\,\,\,{3 \over 2} > 1\,\,\,\,\,\mathop \Rightarrow \limits^{y\,\, > \,\,0} \,\,\,\,\,{3 \over 2}y > y$$

$$\left( 2 \right)\,\, - 5x < - 7y\,\,\,\,\,\,\mathop \Rightarrow \limits^{ \cdot \,\,\left( { - {1 \over 5}} \right)} \,\,\,\,\,\,x\,\, > \,\,\,{7 \over 5}y\,\,\,\mathop > \limits^{{\rm{idem!}}} \,\,\,y\,\,\,\,\, \Rightarrow \,\,\,\,\,\left\langle {{\rm{YES}}} \right\rangle $$


This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.

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Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question.

Since x and y are positive, condition 1) tells us that 3x > 2x > 3y or x > y.
Thus, condition 1) is sufficient.

Condition 2)
-5x < -7y
=> 5x > 7y
This implies that 7x > 5x > 7y or x > y, since x and y are positive.
Condition 2) is sufficient.

Therefore, D is the answer.
Answer: D

FYI, Tip 1) of the VA method states that D is most likely to be the answer if conditions 1) and 2) provide the same information.