For any non-zero real numbers x and y, the Data Sufficiency target question 'Is \frac{x}{y… — GMAT

For any non-zero real numbers $x$ and $y$ , the Data Sufficiency target question 'Is $\frac{x}{y} > 0$ ?' is algebraically equivalent to the rephrased target question 'Do $x$ and $y$ have the same sign?'

Answer: Answer

Answer

True. The target question simplifies directly to asking whether

x

and

y

share the same sign.

The target question asks if the ratio

\frac{x}{y}

is positive. In arithmetic, the quotient of two real numbers is positive if and only if both numbers have the same sign (both positive or both negative). Thus, rephrasing the target to 'Do

x

and

y

have the same sign?' is a completely equivalent simplification.

Step-by-Step Solution

Analyze the condition for a fraction to be positive

For

\frac{x}{y} > 0

, either (

x > 0

and

y > 0

) or (

x < 0

and

y < 0

Dividing two numbers with identical signs yields a positive quotient, while dividing numbers with opposite signs yields a negative quotient.

Compare the condition to the proposed rephrased question

The condition 'both positive or both negative' is the definition of

x

and

y

having the same sign.

Rephrasing a Data Sufficiency stem requires finding a target condition that is true under the exact same conditions as the original question.

Key Concept

Question Stem Rephrasing for Quotient Inequalities

Question

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

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