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 largest of three consecutive even numbers?
I. The sum of the three numbers is 78.
II. The smallest of the three numbers is 4 less than the largest.
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 even numbers can be written as \(a\), \(a+2\) and \(a+4\).
Statement I alone:
\(a+(a+2)+(a+4)=78\)
\(3a+6=78\), so \(3a=72\) and \(a=24\)
The largest number is 28 (the numbers are 24, 26, 28): sufficient
Statement II alone:
The smallest is always 4 less than the largest for any three consecutive even numbers (2, 4, 6 or 24, 26, 28), so it gives no new information: not sufficient