Question:
What is the value of \(x\)?
I) \(2x + 3y = 12\)
II) \(x - 2y + z = 15\)
What is the value of \(x\)?
I) \(2x + 3y = 12\)
II) \(x - 2y + z = 15\)
I) \(2x + 3y = 12\)
II) \(x - 2y + z = 15\)
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If the number of independent equations is less than the number of variables, a unique solution cannot be determined.
Updated On: Apr 21, 2026
- Statement I alone is sufficient to answer the question
- Statement II alone is sufficient to answer the question.
- Statement I and II together are sufficient to answer the question but neither statement alone is sufficient.
- Statement I and II together are not sufficient to answer the question and additional data is required.
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The Correct Option is D
Solution and Explanation
Concept:
To find a unique value of a variable, the number of independent equations must be sufficient compared to the number of variables involved.
Step 1: Analyze Statement I alone.
\[ 2x + 3y = 12 \] Two variables and one equation → infinite solutions.
Statement I alone is NOT sufficient.
Step 2: Analyze Statement II alone.
\[ x - 2y + z = 15 \] Three variables and one equation → infinite solutions.
Statement II alone is NOT sufficient.
Step 3: Combine both statements.
We now have: \[ 2x + 3y = 12 \] \[ x - 2y + z = 15 \] Still 3 variables with only 2 equations → cannot determine a unique value of \(x\).
Hence, even both statements together are NOT sufficient.
Step 1: Analyze Statement I alone.
\[ 2x + 3y = 12 \] Two variables and one equation → infinite solutions.
Statement I alone is NOT sufficient.
Step 2: Analyze Statement II alone.
\[ x - 2y + z = 15 \] Three variables and one equation → infinite solutions.
Statement II alone is NOT sufficient.
Step 3: Combine both statements.
We now have: \[ 2x + 3y = 12 \] \[ x - 2y + z = 15 \] Still 3 variables with only 2 equations → cannot determine a unique value of \(x\).
Hence, even both statements together are NOT sufficient.
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