The question below is followed by three statements numbered I, II and III. Decide which of the statements are sufficient to answer the question.
What is the two-digit number?
I. The sum of its digits is 11.
II. The number is 27 more than the number formed by reversing its digits.
III. Its units digit is 4.
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → Any two of the three statements together are sufficient.
Let the number be \(10t+u\). Reversing gives \(10u+t\), and the difference is \(9(t-u)\).
Each statement alone:
I: \(t+u=11\) fits 29, 38, 47, 56, 65, 74, 83, 92
II: \(9(t-u)=27\), so \(t-u=3\); it fits 41, 52, 63, 74, 85 and 96, among others
III: \(u=4\) fits 14, 24, …, 94
No statement alone is sufficient
Each pair:
I and II: \(t+u=11\) and \(t-u=3\) give \(t=7\), \(u=4\): 74
I and III: \(u=4\), so \(t=11-4=7\): 74
II and III: \(u=4\), so \(t=4+3=7\): 74
Every pair gives 74, so any two of the statements are sufficient; no option naming only one pair is correct.