Three of the following numbers are alike in a certain way and one is different. Pick the odd one out. (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)18 – 11 – 63
- (b)12 – 8 – 36
- (c)21 – 14 – 72
- (d)15 – 3 – 108
Answer
Why
Correct — C. Keep the numbers whole, as the note instructs, and look for one operation that ties all three together.
Rule: (first − second) × 9 = third.
18 − 11 = 7, and 7 × 9 = 63, which is printed.
12 − 8 = 4, and 4 × 9 = 36, which is printed.
15 − 3 = 12, and 12 × 9 = 108, which is printed.
21 − 14 = 7, so the rule demands 63 — but the triple prints 72. That makes 21 – 14 – 72 the odd one → option (c).
Why the others are wrong
- (a)18 – 11 – 63 — 18 – 11 – 63 obeys the rule exactly: the gap is 7 and 7 × 9 = 63, the number printed.
- (b)12 – 8 – 36 — 12 – 8 – 36 obeys it too. The gap is 4 and 4 × 9 = 36.
- (d)15 – 3 – 108 — 15 – 3 – 108 carries the largest third number, but the gap of 12 gives 12 × 9 = 108 all the same. A big result never makes a triple the odd one.
Concept
Odd-one-out on number triples asks you to find the rule three of them share, not to spot the number that looks unusual.
Work the arithmetic on every option before deciding. Here 18 − 11 and 21 − 14 both give 7, which is exactly the coincidence the setter is using: the two look like a pair until you carry the multiplication through.
The long note on whole numbers is doing real work. It forbids splitting 18 into 1 and 8, which closes off the digit tricks that would otherwise give several competing answers.
Key facts
- Three of the four triples satisfy (first − second) × 9 = third.
- 21 − 14 = 7 would give 63 under that rule, but the triple prints 72.
- The note bars digit-splitting, so 18 must be handled as eighteen throughout.
Study next
Common traps
- Splitting 18 into 1 and 8, which the printed note forbids.
- Seeing that 21 − 14 matches 18 − 11 at 7 and pairing them off.
- Stopping at the first option that fits some rule instead of finding the rule three share.
The same odd-one-out with the whole-numbers rider is set at 13 Sep 2024, 09:00, Reasoning Q.16 (31 – 5 – 160, 13 – 8 – 109, 21 – 4 – 89, 27 – 9 – 243), where the link is a product plus a constant instead.
Related PYQs
No directly related past PYQ was found.