What are the values of 3 integers \(a\), \(b\), and \(c\)?
I. \(ab = 8\)
II. \(bc = 9\)
I. \(ab = 8\)
II. \(bc = 9\)
Show Hint
- Statement I alone is sufficient
- Statement II alone is sufficient
- Both statements I and II together are sufficient, but neither alone is sufficient
- The question cannot be answered even with the help of both statements
The Correct Option is C
Solution and Explanation
ab = 8 has many solutions for (a, b), and c is not fixed, so I alone is not sufficient.
Step 2: Statement II alone.
bc = 9 does not fix a, so II alone is not sufficient.
Step 3: Both together.
Taking a, b and c as positive integers, b divides both 8 and 9, so b = 1. Then a = 8 and c = 9, a unique triple. So the two statements together are sufficient, but neither alone is.
Note: if negative integers were also allowed, (-8, -1, -9) would be a second solution. The published key assumes positive integers.
Final Answer:
The correct option is (3): Both statements I and II together are sufficient, but neither alone is sufficient
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