A statement determining that a real variable x satisfies the quadratic equation x^2 - 5x +… — GMAT

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 $x$ ?'

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The statement is True because both solutions

x = 2

and

x = 3

produce a definitive 'Yes' to the integer question, satisfying Yes/No sufficiency, whereas the existence of two distinct numerical values fails to satisfy Value sufficiency.

Solving the equation

x^2 - 5x + 6 = 0

gives

x = 2

and

x = 3

. Because both values are integers, the answer to 'Is

x

an integer?' is a definitive 'Yes' regardless of which root is chosen, making the statement sufficient for the Yes/No structure. However, because

x

can equal either

2

3

, a single unique value cannot be pinpointed, rendering the statement insufficient for the Value structure.

Adım Adım Çözüm

Solve the quadratic equation in the statement for all possible real values of

x

x^2 - 5x + 6 = 0 \Rightarrow (x - 2)(x - 3) = 0

, so

x = 2

x = 3

Identify the complete solution set permitted by the statement.

Evaluate the solution set against the Yes/No question 'Is

x

an integer?'.

x = 2

x

is an integer (Yes). If

x = 3

x

is an integer (Yes). The answer is conclusively 'Yes' in all cases.

In Yes/No Data Sufficiency, a statement is sufficient if it guarantees a single definitive outcome (always Yes or always No).

Evaluate the solution set against the Value question 'What is the value of

x

?'.

x

can be either

2

3

. Since two distinct values are possible, the value of

x

is not uniquely determined.

In Value Data Sufficiency, a statement is sufficient if and only if it leads to exactly one unique numerical value.

Compare the analytical results with the assertions made in the True/False statement.

The statement accurately classifies the equation as sufficient for the Yes/No question and insufficient for the Value question. Therefore, the statement is True.

Confirm alignment between analytical findings and the prompt statement.

Anahtar Kavram

Value vs. Yes/No Data Sufficiency Decision Logic

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