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 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.) (5, 80, 16) (18, 108, 6)
- (a)(15, 185, 14)
- (b)(17, 8, 135)
- (c)(13, 91, 7)
- (d)(9, 81, 8)
Answer
Why
Correct — C. Look for one operation that links all three numbers in both model sets.
Rule: first number × third number = middle number.
5 × 16 = 80
18 × 6 = 108
Both models fit, so test the options the same way.
13 × 7 = 91, and 91 is exactly what sits in the middle.
The set built on the same rule is (13, 91, 7) — option (c).
Why the others are wrong
- (a)(15, 185, 14) — 15 × 14 = 210, not 185. No smaller adjustment rescues it either, since 185 is neither 15 + 14 nor a near multiple of them.
- (b)(17, 8, 135) — In (17, 8, 135) the large number sits third, not in the middle, so the shape is wrong before the arithmetic is. And 17 × 8 = 136, which is not 135 in any case.
- (d)(9, 81, 8) — 9 × 8 = 72, not 81. The set baits anyone who reads 81 as 9², but a 9 × 9 reading would need a 9 in third place, and the third number is 8.
Concept
A number-set analogy is decided by one operation that holds across every given set, not by a separate story for each. With two models to work from, test the cheapest relations first — sum, difference, product, ratio — between the two outer numbers and the middle one.
Here 5 and 16 make 80 and 18 and 6 make 108, so the outer pair multiplies to the middle. Once the rule is fixed, each option is one multiplication, and there is nothing left to judge.
The bracketed NOTE is part of the question, not decoration: it forbids the digit-splitting route that would otherwise let a candidate build an argument for almost any set. The same rider is printed on the odd-one-out item at Reasoning Q.22 of this shift.
Key facts
- Both model sets satisfy first × third = middle: 5 × 16 = 80 and 18 × 6 = 108.
- The question's rider forbids breaking a number into its digits, so 91 may not be read as 9 and 1.
- 13 × 7 = 91 is the one option whose middle number is the product of the other two.
Study next
Common traps
- Fitting a different relation to each model set instead of one rule that covers both.
- Splitting a number into its digits, which the question's rider expressly forbids.
- Accepting (9, 81, 8) because 81 reads as a perfect square.
SSC gives two model sets so a single rule can be pinned down, then offers near misses that satisfy part of it. The identical rider and a product-based rule return at Reasoning Q.22 of this shift.
Related PYQs
No directly related past PYQ was found.