Select the set in which the numbers are NOT related in the same way as are the…
2023
Select the set in which the numbers are NOT related in the same way as are the numbers of the following set.
(NOTE : Operations should be performed on the whole numbers, without breaking down the numbers into their constituent digits. E.g. 13 – Operations on 13 such as adding / subtracting / multiplying etc. to 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is not allowed.)
(5, 13, 16)
(4, 11, 14)
Answer: D. (9, 21, 26) — Concept: in a set analogy of the form (a, b, c), one fixed arithmetic rule ties the three whole numbers together, and every set that belongs to the family…
- A.
(8, 13, 10)
- B.
(12, 21, 18)
- C.
(7, 17, 20)
- D.
(9, 21, 26)
Attempted by 1 students.
Show answer & explanation
Correct answer: D
Concept: in a set analogy of the form (a, b, c), one fixed arithmetic rule ties the three whole numbers together, and every set that belongs to the family must obey that same rule. A reliable way to expose such a rule is to measure the gap b − a between the first two numbers and then ask what single operation on that gap reproduces the third number c. Because the note forbids splitting a number into its digits, the rule may use each number only as a whole.
Applying that method to the two given sets:
In (5, 13, 16) the gap between the first two numbers is 13 − 5 = 8.
Doubling that gap gives 2 × 8 = 16, which is exactly the third number of the set.
In (4, 11, 14) the gap between the first two numbers is 11 − 4 = 7.
Doubling that gap gives 2 × 7 = 14, which is again exactly the third number of the set.
So the family rule is c = 2 × (b − a): the third number is twice the gap between the first two.
Testing every candidate set against the rule c = 2 × (b − a):
Set | b − a | 2 × (b − a) | Third number listed |
|---|---|---|---|
(8, 13, 10) | 5 | 10 | 10 |
(12, 21, 18) | 9 | 18 | 18 |
(7, 17, 20) | 10 | 20 | 20 |
(9, 21, 26) | 12 | 24 | 26 |
Cross-check: the tempting alternative reading — adding the first two numbers — already breaks on the given sets themselves, because 5 + 13 = 18 and not 16, so doubling the gap is genuinely the rule this family follows. Three of the candidate sets reproduce their third number as twice their gap; the set (9, 21, 26) would need 24 to do so and lists 26 instead. Since the question asks for the set that is NOT related in the same way, the required set is (9, 21, 26).