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 13.
II. The number is 45 less than the number formed by reversing its digits.
III. Its tens 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 \(9(u-t)\).
Each statement alone:
I: \(t+u=13\) fits 49, 58, 67, 76, 85, 94
II: \(9(u-t)=45\), so \(u-t=5\); it fits 16, 27, 38 and 49
III: \(t=4\) fits 40, 41, …, 49
No statement alone is sufficient
Each pair:
I and II: \(t+u=13\) and \(u-t=5\) give \(t=4\), \(u=9\): 49
I and III: \(t=4\), so \(u=13-4=9\): 49
II and III: \(t=4\), so \(u=4+5=9\): 49
Every pair gives 49, so any two of the statements are sufficient; no option naming only one pair is correct.