The question below is followed by two statements numbered I and II. Decide whether the data given in the statements are sufficient to answer the question.
What is the smallest of three consecutive odd numbers?
I. The sum of the three numbers is 63.
II. The largest of the three numbers is 4 more than the smallest.
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → Statement I alone is sufficient, but statement II alone is not sufficient.
Three consecutive odd numbers can be written as \(a\), \(a+2\) and \(a+4\).
Statement I alone:
\(a+(a+2)+(a+4)=63\)
\(3a+6=63\), so \(3a=57\) and \(a=19\)
The smallest number is 19 (the numbers are 19, 21, 23): sufficient
Statement II alone:
The largest is always 4 more than the smallest for any three consecutive odd numbers (1, 3, 5 or 19, 21, 23), so it gives no new information: not sufficient