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

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

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[Math Revolution GMAT math practice question]

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

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

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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
Target question: Is x > y?
This is a good candidate for rephrasing the target question.
Since y is POSITIVE, we can safely take the inequality x > y and divide both sides by y to get: x/y > 1
REPHRASED target question: Is x/y > 1?

Aside: Here’s a video with tips on rephrasing the target question: http://www.gmatprepnow.com/module/gmat-data-sufficiency?id=1100

Statement 1: 2x > 3y
Since y is POSITIVE, we can safely divide both sides by y to get: 2x/y > 3
Now divide both sides by 2 to get: x/y > 3/2
If x/y is greater than 3/2, then we can be certain that x/y is greater than 1
So, the answer to the REPHRASED target question is YES, it is true that x/y > 1
Since we can answer the REPHRASED target question with certainty, statement 1 is SUFFICIENT

Statement 2: -5x < -7y
Since y is POSITIVE, we can safely divide both sides by y to get: -5x/y < -7
Now divide both sides by -5 to get: x/y > 7/5 [since we divided by a NEGATIVE value, we REVERSED the inequality symbol]
If x/y is greater than 7/5, then we can be certain that x/y is greater than 1
So, the answer to the REPHRASED target question is YES, it is true that x/y > 1
Since we can answer the REPHRASED target question with certainty, statement 2 is SUFFICIENT

Answer: D

Cheers,
Brent

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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.

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The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
Only $99 for 3 month Online Course
Free Resources-30 day online access & Diagnostic Test
Unlimited Access to over 120 free video lessons-try it yourself
Email to : info@mathrevolution.com

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