Three of the following four options are alike in a certain way and thus form a group. Which is the one that does NOT belong to that group? (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/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.)
- (a)540 – 188 – 128
- (b)81– 101– 92
- (c)90 – 22– 12
- (d)72 – 284 – 266
Answer
Why
Correct — D. Rule: first number = (second − third) × 9.
(a) 188 − 128 = 60, and 60 × 9 = 540 ✓
(b) 101 − 92 = 9, and 9 × 9 = 81 ✓
(c) 22 − 12 = 10, and 10 × 9 = 90 ✓
(d) 284 − 266 = 18, and 18 × 9 = 162, not the 72 that is printed.
Three rows obey the rule and one does not, so 72 – 284 – 266 is outside the group → option (d).
Why the others are wrong
- (a)540 – 188 – 128 — 540 = (188 − 128) × 9. The gap between the last two numbers is 60, and nine sixties is 540, so this row belongs to the group.
- (b)81– 101– 92 — 81 = (101 − 92) × 9. Here the second number is larger than the first, but the rule is about the gap between the last two, and that gap is 9.
- (c)90 – 22– 12 — 90 = (22 − 12) × 9. The gap is 10 and nine tens is 90, so the smallest triple in the set fits the rule exactly.
Concept
An odd-one-out on number triples is settled by finding one relation that three of the four rows satisfy exactly. Do not look for a story; look for an arithmetic link between the three numbers of a row.
The link here runs backwards along the row. Take the last two numbers, subtract, and multiply by 9 to reach the first.
Once a candidate rule fits two rows, test it on all four before answering. A rule that fits three and fails one is the answer; a rule that fits two is a coincidence.
The stem's NOTE forbids breaking a number into its digits, so 128 may not be read as 1, 2 and 8. That removes digit-sum and digit-reversal leads before you start.
Key facts
- In rows (a), (b) and (c) the first number is nine times the gap between the second and the third.
- For row (d) that product is 162, while the row prints 72.
- The NOTE rules out digit-level operations, so every link must act on the whole number.
Study next
Common traps
- Testing only the first-to-second gaps and giving up when they look random.
- Splitting the numbers into digits, which the NOTE rules out.
- Stopping at the first row that fits instead of confirming that exactly three fit.
Reasoning Q.5 of this shift carries the same whole-numbers NOTE, in slightly different words, and also asks for one arithmetic link that a whole row obeys, so the reading habit transfers directly.
Related PYQs
No directly related past PYQ was found.