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Solved odd one pair numbers MCQs — 10 questions on finding the pair that does not follow the rule, by primes, digit sums, squares, cubes and products, with verified answers and explanations. Free online practice for FPSC, PPSC, NTS and all one-paper exams. Covers odd one pair numbers.
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About this paper
This is the General Ability: Odd One Pair Numbers solved MCQ bank from Advanced FPSC & Other Federal Model Papers (Edition 32): 10 published questions (book pp. 785-786, all 10 printed) on finding the pair that does not follow the rule shared by the other three, covering primality, doubling, squares, cubes, digit sums and consecutive products. Every answer was re-solved from scratch against the printed Answer Key, and every question carries a worked explanation.
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10 solved MCQs shown directly below
Correct Answer: 51, 63
In the first, second and fourth pairs both numbers are prime (11 and 23; 31 and 43; 71 and 83), while in 51, 63 both numbers are composite (51 = 3 x 17 and 63 = 7 x 9), so 51, 63 is the odd pair out. All four pairs share the same difference, 12, so difference alone cannot separate them.
Correct Answer: 10, 25
Three pairs follow second = 2 x first + 2 (2 x 5 + 2 = 12; 2 x 8 + 2 = 18; 2 x 12 + 2 = 26), while 2 x 10 + 2 = 22, not 25, so 10, 25 is the odd pair out.
Correct Answer: 6, 108
Three pairs follow second = 2 x first squared (2 x 16 = 32; 2 x 64 = 128; 2 x 100 = 200), while 2 x 36 = 72, not 108, so 6, 108 is the odd pair out.
Correct Answer: 81, 9
56 / 7 = 8, 48 / 6 = 8 and 32 / 4 = 8, while 81 / 9 = 9, so 81, 9 is the odd pair out.
Correct Answer: 441, 12
The second number is the digit sum of the first for 256 (2 + 5 + 6 = 13), 484 (4 + 8 + 4 = 16) and 289 (2 + 8 + 9 = 19), while the digit sum of 441 is 9, not 12, so 441, 12 is the odd pair out.
Correct Answer: 225, 5
The first numbers are squares with roots 11, 12, 13 and 15, and the second numbers run 2, 3, 4, 5: the roots should run 11, 12, 13, 14, so 225 (15 squared) breaks the run. Equivalently, second = root - 9 gives 2, 3, 4 for the first three but 6, not 5, for 225, so 225, 5 is the odd pair out.
Correct Answer: 5, 122
Three pairs follow second = first cubed + 3 (1 + 3 = 4; 8 + 3 = 11; 64 + 3 = 67), while 5 cubed + 3 = 128, not 122, so 5, 122 is the odd pair out.
Correct Answer: 49, 216
The first numbers are squares (2 squared, 3 squared, 5 squared, 7 squared) and the second numbers are the cubes of their roots (2 cubed = 8; 3 cubed = 27; 5 cubed = 125), while the square root of 49 is 7 and 7 cubed = 343, not 216, so 49, 216 is the odd pair out.
Correct Answer: 42, 216
With first = n(n + 1) for n = 2, 3, 4, 6, three pairs follow second = n cubed + n (8 + 2 = 10; 27 + 3 = 30; 64 + 4 = 68), while 6 cubed + 6 = 222, not 216, so 42, 216 is the odd pair out. Note 216 is exactly 6 cubed: the +6 is what is missing.
Correct Answer: 20, 130
The keyed odd pair is 20, 130: under the three-consecutive-product rule that fits 30, 210 (5 x 6 x 7) and 6, 24 (2 x 3 x 4), 20 should pair with 4 x 5 x 6 = 120, not 130. Retained note: printed option (42, 332) is itself 4 short of the rule's 6 x 7 x 8 = 336, an apparent book misprint; the published answer follows the printed Answer Key, which marks (c).
Source & verification
Built by GK360 from verified bank questions — every answer rechecked before publishing.
Questions
10 questions, all 10 printed in the book. No item was dropped: every keyed answer was verified by re-solving.
Finding the pair that breaks the rule shared by the other three: by primality (both numbers prime vs both composite), by doubling rules, by squares and cubes, by digit sums, and by products of consecutive integers.
Yes. Every published answer was re-solved from scratch and checked against the book's printed Answer Key at the top left of p. 786. Nine published answers agree with the key; one is a verified override: in Q54 the printed key marks (c) (25, 125), but (25, 125) follows the same-base square/cube rule as (a) (4, 8) and (b) (9, 27) (5 squared to 5 cubed), while (d) (49, 216) breaks it — 49 is 7 squared but 216 is 6 cubed, not 7 cubed = 343 — and 216 is the only second number not a multiple of its first, so the published answer is (49, 216) with the book key preserved as a flag. One further item carries a retained note rather than an override: in Q56 the keyed odd pair is (20, 130), since the three-consecutive-product rule that fits (30, 210) = 5 x 6 x 7 and (6, 24) = 2 x 3 x 4 would give 4 x 5 x 6 = 120 for 20, not 130 — while printed option (42, 332) is itself 4 short of the rule's 6 x 7 x 8 = 336, an apparent book misprint. The published answer follows the printed Answer Key.
Odd-one-pair questions of this form appear in FPSC, PPSC, NTS, OTS and other one-paper exams, as well as CSS MPT-style quantitative sections, so the bank is tagged for all of them.
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