Number & Letter Series MCQs for UPSC Prelims

Correct answer: A - 5

In each column the bottom number equals the top number multiplied by one less than itself, i.e. n x (n - 1). Check: 3x2 = 6, 8x7 = 56, 10x9 = 90, 2x1 = 2, 1x0 = 0. For the missing entry the bottom value is 20, so n x (n - 1) = 20, which gives n = 5 (since 5x4 = 20). The missing number is 5.

Correct answer: C - Two

INCOMPREHENSIBILITIES has 21 letters with counts: I x 5, E x 3, N x 2, S x 2, and one each of C, O, M, P, R, H, B, L, T. In reverse alphabetical order the word becomes T S S R P O N N M L I I I I I H E E E C B, so the block of five I's occupies positions 11 to 15. In the original word, I's sit at positions 1, 13, 15, 17 and 19; comparing position by position, only positions 13 and 15 hold an I in both arrangements, and no other letter lands on its original position. So exactly two positions are unchanged - option (c). 'None' (a) misses the overlapping I block, 'One' (b) catches only one of the two coincidences, and 'Three' (d) overcounts.

Correct answer: B - 15

The k-th pass moves the ring k places clockwise, so after k passes the ring sits at position 1 + (1 + 2 + ... + k) = 1 + k(k+1)/2, taken modulo 40. The ring returns to child-1 when k(k+1)/2 is a multiple of 40, i.e. k(k+1) is a multiple of 80. Testing: k = 14 gives 210 (no), k = 15 gives 240 = 3 x 80 (yes). So after 15 changes the ring is back with child-1 - option (b), as per the official key. Option (c) 16 is the trap of counting the 16 holders (including child-1 at the start) instead of the 15 passes; options (a) and (d) fail the divisibility test.

Correct answer: B - T

Reversing each block of 4 letters and swapping Y and Z gives the new order: DCBA HGFE LKJI PONM TSRQ XWVU ZY. Counting along this arrangement, the 13th letter is P (the blocks contribute 4 letters each, so positions 13-16 are P, O, N, M). The fourth letter to the right of position 13 is the letter at position 17, which is T - option (b). Option (a) N is at position 15, option (c) H is at position 5, and option (d) I is at position 12, so none of them fits.

Correct answer: C - 9.375

The rule in Sequence-I uses multipliers that grow by 1 at each step: 8 x 0.5 = 4, 4 x 1.5 = 6, 6 x 2.5 = 15, 15 x 3.5 = 52.5, 52.5 x 4.5 = 236.25. Since Sequence-II is built by the identical rule starting from 5: A = 5 x 0.5 = 2.5, B = 2.5 x 1.5 = 3.75, C = 3.75 x 2.5 = 9.375. So option (c) is correct. Option (a) 2.5 is the value of A, not C. Option (b) 5 is just the first term of Sequence-II. Option (d) 32.8125 is the value of D (9.375 x 3.5), one step too far.

Correct answer: B - 64

Split the sequence into two interleaved sub-sequences. The terms in odd positions are 4, 16, 36, 64 = 2^2, 4^2, 6^2, 8^2 (squares of even numbers). The terms in even positions are 196, 144, 100, X = 14^2, 12^2, 10^2, X. The pattern is decreasing even squares: 14, 12, 10, then 8, so X = 8^2 = 64. Answer (b) 64.

Correct answer: B - July, April

Number the months (Jan=1 ... Dec=12) and subtract an increasing offset from a fixed reference. Reading the positions, each term is obtained by going back 0, 1, 2, 3, 4, 5, 6, 7, 8 months from January (treated cyclically): position 1 = Jan (Jan - 0), position 2 = Jan (Jan - 0 again as the base), position 3 = December (back 1 from Jan), position 4 = October (back further), and so on, with the step between successive terms growing. Following this decreasing-month pattern, the 5th term X = July and the 8th term Y = April. Hence X = July, Y = April. Official UPSC 2025 key: B.

Correct answer: C - 13

The gaps between successive terms increase by 2 each time: starting from 7 the differences run +6, +8, +10, +12. So 7 + 6 = 13 (= X), 13 + 8 = 21, 21 + 10 = 31, 31 + 12 = 43, which fits the rest of the series. Hence X = 13.