Value vs. Yes/No Data Sufficiency Decision Logic

In a GMAT Data Sufficiency 'Value' question asking for the numerical value of $x + y$, a statement that establishes that $x + y$ can equal either $5$ or $-5$ is considered sufficient.

Is the integer $n$ odd?

(1) $n$ is a multiple of 4.
(2) $n > 5$

A statement determining that a real variable $x$ satisfies the quadratic equation $x^2 - 5x + 6 = 0$ is sufficient to answer the Data Sufficiency question 'Is $x$ an integer?', but is insufficient to answer the Data Sufficiency question 'What is the value of $x$?'

If $x$ is a positive integer, is $x$ an even number?

(1) $x$ is a prime number greater than 2.
(2) $x + 1$ is an odd number.

In a GMAT Data Sufficiency 'Value' question asking for the specific numerical value of a variable $x$, a statement that narrows $x$ down to exactly two distinct numerical solutions provides sufficient information.

In a GMAT Data Sufficiency 'Value' question asking for the numerical value of the expression $xy$, a statement that permits $x$ to be either $2$ or $-2$ while establishing that $y = \frac{8}{x}$ is insufficient to answer the question because $x$ itself is not uniquely determined.

If $r$ and $s$ are integers, is $r + s$ an even integer?

(1) $r^2 - s^2$ is an odd integer.
(2) $r$ is an odd integer.

If $a$ and $b$ are real numbers, is $a^2 + b^2 < 4$?

(1) $(a - 2)^2 + (b - 2)^2 = 18$
(2) $a^2 - 6a + b^2 - 8b = -24$

In a GMAT Data Sufficiency 'Yes/No' question asking whether $a^2 > b^2$, a statement establishing that $a + b = 0$ (where $a \neq 0$) is sufficient to answer the question.

In a GMAT Data Sufficiency 'Yes/No' question regarding whether a real variable $x$ is positive, a statement establishing that $x^2 - 4x + 3 = 0$ is sufficient, whereas in a 'Value' question asking for the exact numerical value of $x$, the exact same statement is insufficient.

In a GMAT Data Sufficiency 'Yes/No' question asking whether a real variable $x > 0$, a statement that establishes definitively that $x < 0$ is considered INSUFFICIENT because it yields a negative answer to the question stem.

If $p$ and $q$ are real numbers such that $p \neq 0$, is $p^2 q < 0$?

(1) $|q - 5| = q - 5$ and $q \neq 5$
(2) $p + q = 2$

In GMAT Data Sufficiency logic, if a statement determines a single unique numerical value for a variable $x$, that statement is sufficient to answer a 'Value' question asking for the exact value of $x$, but is insufficient to answer a 'Yes/No' question asking whether $x > 5$.

If $a$ and $b$ are non-zero real numbers, is $a^3 b + a b^3 > 0$?

(1) $a^2 - 5ab + 6b^2 = 0$
(2) $|a + b| < |a - b|$

Which of the following choices correctly describes the sufficiency of the statements?

If $a$ and $b$ are real numbers, is $a^2 - b^2 > 0$?

(1) $|a| < b$
(2) $a + b > 0$

In a GMAT Data Sufficiency 'Yes/No' question, if a statement permits multiple numerical values for a variable, but every permitted value yields a conclusive 'No' to the question stem, the statement is sufficient to answer the question.

If $x$ and $y$ are real numbers, is $x > y$?

(1) $y - x = |x + 3| + 1$
(2) $x + y = 10$

If $x$ is a real number, is $x > 0$?

(1) $x^3 - x = 0$ and $x \neq 0$
(2) $|x + 2| = -x - 2$

Which of the following choices correctly identifies the sufficiency of the statements?

In a GMAT Data Sufficiency question framed as a 'Yes/No' question (such as 'Is $x > 0$?'), a statement that conclusively proves that the condition is always false (e.g., $x < 0$) is classified as insufficient because it results in a negative response.

If $x$ and $y$ are non-zero real numbers, is $\frac{x}{y} + \frac{y}{x} < 2$?

(1) $(x + y)^2 > x^2 + y^2$
(2) $x^3 y^2 < 0$