Question

J and K are positive numbers. Is J/K>1?
(1) JK<1
(2) J-K>0

• A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
• B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
• C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
• D. EACH statement ALONE is sufficient.
• E. Statements (1) and (2) TOGETHER are NOT sufficient

Hint:

Always try to simplify or rephrase the question in Data Sufficiency before analyzing the statements. Changing "Is J/K>1?" to "Is J>K?" (given K>0) makes evaluating the statements much more direct.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
This is a Yes/No Data Sufficiency question involving inequalities with positive numbers. The core question can be simplified.
Step 2: Key Formula or Approach:
The question asks: Is \(J/K>1\)?
Since we are given that \(K\) is a positive number (\(K>0\)), we can multiply both sides of the inequality by \(K\) without changing the direction of the inequality sign.
So, the question is equivalent to asking: Is \(J>K\)?
Step 3: Detailed Explanation:
Analyzing Statement (1):
"JK<1"
This means the product of two positive numbers is less than 1. Let's test cases to see if we can get both "Yes" and "No" answers to the question "Is \(J>K\)?".
- Case 1 (No): Let \(J=0.2\) and \(K=4\). Both are positive. \(JK = 0.2 \times 4 = 0.8\), which is less than 1. In this case, \(J\) is not greater than \(K\). The answer is "No".
- Case 2 (Yes): Let \(J=4\) and \(K=0.2\). Both are positive. \(JK = 4 \times 0.2 = 0.8\), which is less than 1. In this case, \(J\) is greater than \(K\). The answer is "Yes".
Since we can get both a "Yes" and a "No", statement (1) is not sufficient.
Analyzing Statement (2):
"J - K>0"
This inequality can be rearranged by adding \(K\) to both sides:
\[ J>K \] This directly answers our rephrased question ("Is \(J>K\)?") with a definitive "Yes".
Therefore, statement (2) is sufficient.
Step 4: Final Answer:
Statement (2) alone is sufficient to answer the question, but statement (1) alone is not.