80 is related to 99 following certain logic. Following the same logic, 0 is related to 3. To which of the following numbers is 35 related, following the same logic? (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)42
- (b)48
- (c)44
- (d)46
Answer
Why
Correct — B. Rule: each number is one less than a perfect square, and the answer is one less than the next square up.
80 = 9² − 1
next square: 10² − 1 = 99, the number given
0 = 1² − 1
next square: 2² − 1 = 3, the number given
35 = 6² − 1
next square: 7² − 1 = 49 − 1 = 48 → option (b)
Why the others are wrong
- (a)42 — 42 breaks the shape of the rule, because 42 + 1 = 43 is not a perfect square. Every number in the chain — 80, 99, 0, 3, 35 — is one less than a square.
- (c)44 — 44 + 1 = 45, which is not a perfect square either. It is 35 + 9, a jump to 6² + 9 rather than to the next square, 49.
- (d)46 — 46 + 1 = 47, again not a square. The step from 35 is 6 + 7 = 13, the gap between consecutive squares, which lands on 48 and not on 46.
Concept
When two given pairs share no obvious difference and no obvious ratio, test the neighbours of squares and cubes. 80 sits beside 81 and 99 beside 100, and that is the clue the item is built on.
Written out, n² − 1 becomes (n + 1)² − 1. The amount added is therefore n + (n + 1), which is 19 when n = 9, 3 when n = 1 and 13 when n = 6.
The second pair, 0 to 3, is the confirmation. A rule that carries 80 to 99 and also carries 0 to 3 is very unlikely to be a coincidence.
0 = 1² − 1 is the pair candidates skip, because 0 looks like a special case rather than a worked example. It is the cheapest check available in the question.
Key facts
- 80 = 9² − 1 and 99 = 10² − 1.
- 0 = 1² − 1 and 3 = 2² − 1.
- 35 = 6² − 1, so the answer is 7² − 1 = 48.
- Among the four options, 48 is the one that is one less than a perfect square.
Study next
Common traps
- Hunting for a constant difference, when 99 − 80 = 19 and 3 − 0 = 3 do not agree
- Reading 80 as 8 and 0 after the question has barred digit-splitting
- Taking the next square as 49 and forgetting to subtract the 1
SSC gives one pair, confirms it with a second and prints the whole-number rider, which rules out any route that splits the digits.
Perfect-square framings sit alongside plain arithmetic ones such as 09 Sep 2024, 09:00, Reasoning Q.24, where 19 becomes 209 by multiplying by 11.
Related PYQs
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