Question

Is \(x>9\)?
1. \(x^2+3x=28\)
2. \(9x-5x=28\)

• A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked
• B. Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed
• C. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked
• D. EACH statement ALONE is sufficient to answer the question asked
• E. Both statements (1) and (2) TOGETHER are sufficient to answer the question asked; but NEITHER statement ALONE is sufficient

Hint:

Remember that for a "Yes/No" data sufficiency question, a statement is sufficient if it gives a definite "Yes" or a definite "No". It is not sufficient only if it can lead to both a "Yes" and a "No" answer depending on the possibilities it allows.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
This is a "Yes/No" data sufficiency question. We need to determine if each statement provides enough information to give a definitive "Yes" or a definitive "No" answer to the question "Is \(x>9\)?". A statement is sufficient if it leads to a single, unambiguous answer.

Step 2: Key Formula or Approach:
We will solve the equation in each statement to find the possible value(s) for x. Then, for each possible value, we will check if it is greater than 9.

Step 3: Detailed Explanation:
Analyzing Statement (1): \(x^2+3x=28\).
This is a quadratic equation. To solve it, we first set it to zero.
\[ x^2 + 3x - 28 = 0 \] Now, we can factor the quadratic expression. We are looking for two numbers that multiply to -28 and add to +3. These numbers are +7 and -4.
\[ (x+7)(x-4) = 0 \] This gives two possible values for x: \(x = -7\) or \(x = 4\).
Now we check these values against the question "Is \(x>9\)?".
For \(x = -7\): Is \(-7 > 9\)? The answer is "No".
For \(x = 4\): Is \(4 > 9\)? The answer is "No".
In both possible cases, the answer to the question is a definite "No". Since we get a single, consistent answer, statement (1) is sufficient.
Analyzing Statement (2): \(9x-5x=28\).
This is a linear equation. We can solve for x directly.
\[ 9x - 5x = 28 \] \[ 4x = 28 \] \[ x = \frac{28}{4} \] \[ x = 7 \] Now we check this value against the question "Is \(x>9\)?".
Is \(7 > 9\)? The answer is a definite "No".
Since we get a single, consistent answer, statement (2) is sufficient.

Step 4: Final Answer:
Since each statement alone is sufficient to answer the question, the correct choice is (D).