In the following number-pairs, the second number is obtained by applying certain mathematical operations to the first number. 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.) (96, 29) (112, 33)
- (a)(188, 52)
- (b)(176, 45)
- (c)(108, 30)
- (d)(204, 55)
Answer
Why
Correct — A. Find one chain of operations that turns both given first numbers into their partners.
96 ÷ 4 = 24, and 24 + 5 = 29
112 ÷ 4 = 28, and 28 + 5 = 33
Rule: second = first ÷ 4, then + 5.
Test the options. 188 ÷ 4 = 47.
47 + 5 = 52, which is exactly the partner printed in option (a).
Why the others are wrong
- (b)(176, 45) — 176 ÷ 4 = 44 and 44 + 5 = 49, not 45. Reaching 45 would need the added constant to be 1, which neither worked pair supports.
- (c)(108, 30) — 108 ÷ 4 = 27 and 27 + 5 = 32, not 30. The pair fails by two, which is close enough to survive an eyeball and not close enough to survive the arithmetic.
- (d)(204, 55) — 204 ÷ 4 = 51 and 51 + 5 = 56, not 55. It misses by one, so the chain has to be finished rather than judged by how nearly right it looks.
Concept
These items hand you two worked pairs and ask which option obeys the same chain. Two pairs are enough to pin a two-step rule, and testing both is what makes the answer safe.
The productive first move is to divide the larger number by a small factor and see what is left over.
96 and 112 are both multiples of 4, giving 24 and 28, and each partner exceeds those by exactly 5.
The bracketed note forbids digit-splitting, so 96 may not be read as 9 and 6. Every operation acts on the whole number.
The rule can be written the other way round as first = 4 × second − 20. Checking that 4 × 52 − 20 = 188 is a fast independent confirmation of the chosen option.
Key facts
- 96 ÷ 4 + 5 = 29 and 112 ÷ 4 + 5 = 33, so the chain is divide by 4 then add 5.
- 188 ÷ 4 + 5 = 52.
- The same rule reversed reads first = 4 × second − 20.
Study next
Common traps
- Fixing the rule from one given pair, when two are supplied for a reason.
- Dividing correctly and then forgetting the constant.
- Picking the option nearest the target instead of the one that satisfies the chain.
This stem carries a bracketed note about whole numbers.
24 Sep 2024, 16:00, Reasoning Q.11 asks it with the option set (22, 88), (15, 70), (18, 74) and (25, 105), and 9 Sep 2024, 09:00, Reasoning Q.4 runs the odd-one-out variant on 335 - 119, 358 - 152, 317 - 101 and 308 - 92.
Related PYQs
No directly related past PYQ was found.