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?'

Cevap: Cevap

Cevap

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.

Adım Adım Çözüm

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.

Anahtar Kavram

Question Stem Rephrasing for Quotient Inequalities

Soru

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

Konular

Bu konudan daha fazla soru