In a GMAT Data Sufficiency Value question asking for the unique numerical value of a varia… — GMAT

In a GMAT Data Sufficiency Value question asking for the unique numerical value of a variable $x$ , if Statement (1) alone restricts $x$ to a set of two distinct real numbers and Statement (2) alone also restricts $x$ to a set of two distinct real numbers, then combining Statement (1) and Statement (2) is guaranteed to determine a unique value for $x$ .

Answer: Answer

Answer

The statement is false because the intersection of the solution sets of two statements can contain multiple values, failing to yield a unique numerical answer.

The statement is false. Combining two Data Sufficiency statements requires finding the values common to both solution sets. If both statements individually narrow the variable to the exact same pair of values, combining them does not eliminate either value. Consequently, the combined statements still leave multiple possibilities and remain insufficient.

Step-by-Step Solution

Formulate the mathematical condition for combining Data Sufficiency statements

Evaluating Statement (1) and Statement (2) together requires finding the set of values that satisfy both statements simultaneously, which is the set intersection

S_1 \cap S_2

of their individual solution sets

S_1

and

S_2

Both statements are taken to be true at the same time when analyzing their combined sufficiency.

Analyze whether the intersection of two 2-element sets necessarily contains exactly one element

S_1 = \{2, 3\}

and

S_2 = \{2, 3\}

, then

S_1 \cap S_2 = \{2, 3\}

, which contains two elements rather than one.

Two independent DS statements can be algebraically redundant or share identical candidate roots without contradicting one another.

Determine the sufficiency outcome of the combined statements

Since

x

can still equal either

2

3

, the combined statements do not yield a single, unique value for

x

A Value-type Data Sufficiency question requires a single, unambiguous value for a condition to be deemed sufficient.

Key Concept

Statement Combination and Solution Set Intersection

Question

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Topics

More questions from this topic