Select the set in which the numbers are related in the same way as are the numbers of the following set. (66, 57, 48) (94, 85, 76) (NOTE: Operations should be performed on the whole numbers, without breaking down the numbers into its constituent digits. E.g. 13 – Operations on 13 such as adding/deleting/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.)
- (a)(85, 77, 64)
- (b)(79, 70, 59)
- (c)(81, 72, 63)
- (d)(98, 90, 83)
Answer
Why
Correct — C.
Rule: inside each set the numbers fall by 9, then 9 again.
66 minus 9 is 57, and 57 minus 9 is 48
94 minus 9 is 85, and 85 minus 9 is 76
Test option (c): 81 minus 9 is 72, and 72 minus 9 is 63. Both steps match, so that is the set.
The note printed with the question bars working on the digits, so the operation has to be on the whole numbers, exactly as here.
Why the others are wrong
- (a)(85, 77, 64) — 85 minus 77 is 8 and 77 minus 64 is 13. Neither gap is 9, and the two gaps are not even equal to one another.
- (b)(79, 70, 59) — The first gap is 9, but the second is 11, since 70 minus 59 is 11. Both steps have to be the same subtraction.
- (d)(98, 90, 83) — The gaps are 8 and then 7, a shrinking difference rather than the constant 9 the sample sets show.
Concept
Number-set analogies turn on the rule inside each set, never on a resemblance between one set and another. Compute the differences before anything else.
Both sample sets give the same pair of gaps, minus 9 and minus 9, so the target is a three-term run with common difference 9.
The printed note matters too: it forbids treating 66 as a 6 and a 6, so the rule must be an ordinary operation applied to the number as a whole.
Only one option keeps its gap constant at all, which is worth checking before hunting for a subtler rule.
Key facts
- In both sample sets the numbers fall by 9 at each step: 66, 57, 48 and 94, 85, 76.
- A three-term set with a constant difference is fixed by its first term and that difference.
- The note printed with the question bars breaking a number into its digits before operating.
Study next
Common traps
- Comparing across sets, for instance hunting for a link between 66 and 94
- Checking only the first gap and settling on 79, 70, 59
- Breaking the numbers into digits, which the printed note forbids
Two sample sets are given rather than one, which lets you confirm the operation before testing any option. The same three-number format is set at Reasoning Q.3 of the 11 Sep 2024, 12:30 shift.
Related PYQs
No directly related past PYQ was found.