Data Sufficiency

[Math Revolution GMAT math practice question]

Is x/y < 0?

1) x^4y^5 < 0
2) x^5y^3 < 0

Is x/y < 0?

1) x^4*y^5 < 0
As x^4 is always positive, it implies y < 0
if x > 0
then x/y < 0

if x < 0, then x/y > 0
Insufficient

2) x^5*y^3 < 0
As X,Y are both having the odd power, they retain their sign, and
Since the product is positive , both the variables have same sign

Positive * positive = positive
negative*negative = positive

So, x/y will be greater than zero as sign cancels out
Sufficient

Option B is correct

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

Is x/y < 0?

1) x^4y^5 < 0
2) x^5y^3 < 0

$$\frac{x}{y}\,\,\mathop < \limits^? \,\,0$$
$$\left( 1 \right)\,\,{x^4}{y^5} < 0\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,x \ne 0\,\,\,{\rm{and}}\,\,\,y < 0\,\,\,\,\,\,\left\{ \matrix{
\,{\rm{Take}}\,\,\left( {x,y} \right) = \left( {1, - 1} \right)\,\,\,\,\, \Rightarrow \,\,\,\,\,\left\langle {{\rm{YES}}} \right\rangle \,\, \hfill \cr
\,{\rm{Take}}\,\,\left( {x,y} \right) = \left( { - 1, - 1} \right)\,\,\,\,\, \Rightarrow \,\,\,\,\,\left\langle {{\rm{NO}}} \right\rangle \,\, \hfill \cr} \right.$$
$$\left( 2 \right)\,\,{x^5}{y^3} < 0\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\left\{ \matrix{
\,x > 0\,\,\,{\rm{and}}\,\,\,y < 0\,\,\,\,\, \Rightarrow \,\,\,\,\,\left\langle {{\rm{YES}}} \right\rangle \hfill \cr
\,{\rm{or}} \hfill \cr
\,x < 0\,\,\,{\rm{and}}\,\,\,y > 0\,\,\,\,\, \Rightarrow \,\,\,\,\,\left\langle {{\rm{YES}}} \right\rangle \hfill \cr} \right.\,\,\,\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,\left\langle {{\rm{YES}}} \right\rangle $$

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 question is equivalent to asking if xy < 0. This can be seen by multiplying both sides of the inequality by y^2.

Since we can ignore even exponents in inequalities like x^4y^5 < 0, condition 1) is equivalent to the statement y < 0 and condition 2) is equivalent to the statement xy < 0.

Therefore, the answer is B.
Answer: B