Select the option in which the numbers are related in the same way as the numbers of the following set.
(8, 48, 120)
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → (15, 35, 63)
Each number of the given set is one less than a perfect square, so look for the set in which all three numbers are one less than a square.
Given set: \(8=3^2-1\), \(48=7^2-1\), \(120=11^2-1\)
(24, 50, 99): \(24=5^2-1\) and \(99=10^2-1\), but \(50+1=51\) is not a square
(3, 16, 81): \(3=2^2-1\), but 16 and 81 are themselves squares (\(4^2\), \(9^2\)), not one less than a square
(15, 35, 63): \(15=4^2-1\), \(35=6^2-1\), \(63=8^2-1\), all three fit
(8, 25, 143): \(8=3^2-1\) and \(143=12^2-1\), but 25 is itself a square (\(5^2\)) and \(25+1=26\) is not
So the set related in the same way is (15, 35, 63).