Select the set in which the numbers are related in the same way as are the…
2025
Select the set in which the numbers are related in the same way as are the numbers of
the following sets.
(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 to 13 can be performed. Breaking down 13 into 1 and 3
and then performing mathematical operations on 1 and 3 is not allowed.)
(35, 116, 3)
(49, 164, 5)
- A.
(39, 182, 21)
- B.
(23,99, 11)
- C.
(32, 168, 25)
- D.
(11,42,4)
Show answer & explanation
Correct answer: A
Concept: In a number-triplet analogy, every given set (a, b, c) obeys the SAME fixed whole-number rule linking all three values. The task is to derive that single rule from the given sets, then test which answer option’s own triplet satisfies the identical rule.
Application:
Write the two given sets as (a, b, c): (35, 116, 3) and (49, 164, 5).
Try a rule of the form b = k × (a + c) + m, combining the first and third whole numbers without splitting digits.
For (35, 116, 3): a + c = 38, so k × 38 + m = 116.
For (49, 164, 5): a + c = 54, so k × 54 + m = 164.
Subtracting the two equations: k × (54 − 38) = 164 − 116, i.e. 16k = 48, so k = 3.
Substituting k = 3 into k × 38 + m = 116 gives 114 + m = 116, so m = 2.
The derived rule is b = 3 × (a + c) + 2.
Cross-check against the given sets:
(35, 116, 3): 3 × (35 + 3) + 2 = 3 × 38 + 2 = 116, matching the given middle value.
(49, 164, 5): 3 × (49 + 5) + 2 = 3 × 54 + 2 = 164, matching the given middle value.
Applying b = 3 × (a + c) + 2 to each option’s own (a, c):
(39, 182, 21): 3 × (39 + 21) + 2 = 3 × 60 + 2 = 182.
(23, 99, 11): 3 × (23 + 11) + 2 = 3 × 34 + 2 = 104.
(32, 168, 25): 3 × (32 + 25) + 2 = 3 × 57 + 2 = 173.
(11, 42, 4): 3 × (11 + 4) + 2 = 3 × 15 + 2 = 47.
Only the set (39, 182, 21) reproduces its own given middle value exactly under the same rule derived from the two example sets.