15 November 2025 · Shift 3

Calendar and odd days An ordinary year has 365 days = 52 weeks $+1$ day, so it gives 1 odd day; a stretch of 366 days gives 2 odd days. Move forward year by year from 29 February 2032, using 28 February as the marker for the three ordinary years. From 28 February 2035 to 29 February 2036 there are 366 days, i.e. 2 odd days. Total odd days = 1 + 1 + 1 + 2 = 5. Counting 5 days on from Sunday: Monday, Tuesday, Wednesday, Thursday, Friday. Hence 29 February 2036 is a Friday, option (b).

Composite and prime numbers A composite number has more than two factors. The even numbers are $2,4,6,8,\dots$; here 2 is prime, so the smallest even composite number is 4 (factors 1, 2, 4). The prime numbers are $2,3,5,7,\dots$; the first of them, 2, is even, so the smallest odd prime number is 3. Required product $=4\times 3=12$. Hence the correct option is (b).

BODMAS with decimals By the BODMAS rule the multiplication is carried out before the addition and the subtraction. $3.6\times 5.4=19.44$ (since $36\times 54=1944$ and two decimal places are needed). 19.44 + 17.6 = 37.04. 37.04 - 8.3 = 28.74. Hence the correct option is (c).

Consecutive odd numbers Let the five consecutive odd numbers be $x-4,x-2,x,x+2,x+4$, taking the middle one as x. Their sum = 5x, so 5x = 85 and x = 17. The numbers are therefore 13, 15, 17, 19, 21. The largest number = x + 4 = 17 + 4 = 21. Hence the correct option is (a).

Average of a group Total = average $\times$ number of items, so the total weight of the 4 boys $=55\times 4=220$ kg. After the new boy joins, total weight = 220 + 75 = 295 kg and the number of boys becomes 5. New average $=\frac{295}{5}=59$ kg. Short cut: the new boy is 75 - 55 = 20 kg above the old average, and this excess is shared by 5 boys, so the average rises by $\frac{20}{5}=4$ kg, giving 55 + 4 = 59 kg. Hence the correct option is (d).

Statement and inference An inference is what reasonably follows from the fact stated — not an accusation and not an extreme claim. I: making the online mode the only mode is workable only if the internet is within the reach of most citizens; the government's step therefore rests on that belief, so I follows. II: when every application passes through a single online channel, each step leaves a record and the counter clerk can no longer be approached, so a gain in transparency is a fair inference — II follows. III: the statement nowhere says the offline system was corrupt; a system may be replaced simply because it is slow or costly, so this charge is too strong — III does not follow. Hence both I and II follow, option (b).

Statement and inference Judge each inference against what the corporation has actually done — launched a scheme to reduce the water crisis. I: a body launches such a scheme only when it treats the shortage as a real and continuing problem, so I follows. II: 'there will never be a water shortage now' is an extreme claim; harvesting reduces the crisis, it cannot guarantee that shortage will never occur again — II does not follow. III: rainwater harvesting stores a natural resource instead of letting it run off, which is precisely environmental protection and sustainable development, so III follows. Hence both I and III follow, option (b).

Number analogy Compare the two numbers of the first pair: $256=16\times 16={16}^2$ and 16 = 15 + 1. So the rule is: second number $={\left(\mathrm{first}\mathrm{number}+1\right)}^2$. Applying the same rule to 20: ${\left(20+1\right)}^2={21}^2=441$. Note that $400={20}^2$ and $484={22}^2$, which are the tempting but wrong squares. Hence the correct option is (a).

Geometric series Check the ratio of consecutive terms: $125÷25=5$ and $625÷125=5$, so each term is 5 times the one before it. 4th term $=625\times 5=3125$. 5th term $=3125\times 5=15625$. In powers of 5: the terms are $5^2,5^3,5^4,5^5,5^6$, so the 5th term $=5^6=15625$. Hence the correct option is (b).

Number pair series Treat the two members of every pair as two separate series. First members: 1, 4, 9, 16, ?, 36 are the squares $1^2,2^2,3^2,4^2,5^2,6^2$, so the missing first member is $5^2=25$. Second members: 2, 4, 6, 8, ?, 12 are the even numbers $2\times 1,2\times 2,\dots$, so the missing second member is $2\times 5=10$. So the nth pair is $\left(n^2,2n\right)$ and the 5th pair is (25, 10). Hence the correct option is (b).

Number pair series Split each pair and read the two positions as separate series. First members: 4, 9, 16, 25, ?, 49 are $2^2,3^2,4^2,5^2,6^2,7^2$, so the missing first member is $6^2=36$. Second members: 3, 5, 7, 9, ?, 13 are consecutive odd numbers rising by 2, so the missing second member is 9 + 2 = 11. So the nth pair is $\left({\left(n+1\right)}^2,2n+1\right)$ and the missing pair is (36, 11). Option (d) has the same two numbers but in the reversed order, which breaks the pattern. Hence the correct option is (b).

Divisibility rules A number divisible by both 7 and 13 must be a multiple of their LCM, and since 7 and 13 are co-prime, LCM $=7\times 13=91$. $1001÷91=11$, i.e. $1001=7\times 11\times 13$, so it is divisible by both. The other options: $299=13\times 23$, $715=5\times 11\times 13$ and $286=2\times 11\times 13$ — each is a multiple of 13 but none is a multiple of 7. Hence the correct option is (b).

Number series Take the differences of consecutive terms: 58.5 - 22 = 36.5, 122 - 58.5 = 63.5, 214.5 - 122 = 92.5, 338 - 214.5 = 123.5. Now take the differences of these differences: 63.5 - 36.5 = 27, 92.5 - 63.5 = 29, 123.5 - 92.5 = 31 — consecutive odd numbers. So the next second difference is 33, giving the next difference = 123.5 + 33 = 156.5. Required term = 338 + 156.5 = 494.5. Hence the correct option is (d).

Number series The differences that can be seen are 13.5 - 8.5 = 5 and 40.5 - 29.5 = 11. Between them two differences are missing, and 5 and 11 fit the pattern of consecutive odd numbers +5, +7, +9, +11. Missing term = 13.5 + 7 = 20.5. Check: 20.5 + 9 = 29.5 and 29.5 + 11 = 40.5, which match the given terms. Hence the correct option is (b).

Number series The decimals suggest a common divisor, so multiply every term by 5: $0,1,?,27,64$. These are the perfect cubes $0^3,1^3,2^3,3^3,4^3$, so the nth term of the given series is $\frac{n^3}{5}$ with n = 0, 1, 2, 3, 4. Missing term $=\frac{2^3}{5}=\frac{8}{5}=1.6$. Check: $\frac{3^3}{5}=\frac{27}{5}=5.4$ and $\frac{4^3}{5}=\frac{64}{5}=12.8$, which match the given terms. Hence the correct option is (c).

Letter series completion The string has 24 places and 8 blanks, so break it into four blocks of six letters each. Wherever the letters are visible they read P, C, T, P, R, S, so the block P C T P R S simply repeats four times. Block 1 needs C and R, block 2 needs P and P, block 3 needs T and S, and block 4 needs C and P. Reading the missing letters in order gives CRPPTSCP. Hence option (d) is the answer.

Alphanumeric series Each term is a letter followed by a number, so treat the two parts separately. The letters P, Q, R, S, T, U are consecutive, so the next letter is V. The numbers are perfect squares: $0^2=0$, $1^2=1$, $2^2=4$, $3^2=9$, $4^2=16$, $5^2=25$. The next number is therefore $6^2=36$. So the missing term is V36 and option (d) is the answer.

Alphanumeric series The letters G, H, I, J, K, L are consecutive, so the next letter must be M. The numbers use two operations turn by turn: a multiplication, then +0.5. $1\times 1=1$, then 1+0.5=1.5, then $1.5\times 2=3$, then 3+0.5=3.5, then $3.5\times 3=10.5$. The next step is an addition, so the number is 10.5+0.5=11. The required term is M11, so option (c) is the answer.

Symbol substitution First replace every sign of the expression by the sign it is changed into. So $96÷\left(12+4\right)\times \left(6-2\right)+10$ becomes $96÷\left(12-4\right)+\left(6\times 2\right)-10$. Now apply BODMAS. Brackets first: $96÷8+12-10$. Division next: 12+12-10. Finally 24-10=14. Hence option (c) is the answer.

Symbol substitution Change each sign exactly as the question directs, and only then work the sum out. So $\left(\left(6+3\right)\times \left(18-6\right)\right)÷\left(20-5\right)$ becomes $\left(\left(6\times 3\right)+\left(18+6\right)\right)-\left(20+5\right)$. Inner brackets: [18+24]-25. Square bracket: 42-25. So the value is 17, and option (c) is the answer.

Letter pairs in a word Number the letters of DAUGHTER: D-1, A-2, U-3, G-4, H-5, T-6, E-7, R-8. A pair counts when the number of letters standing between the two in the word equals the number standing between them in the alphabet, counting either forward or backward. D–G, D–H and G–H match in the forward direction, while T–R matches in the backward direction. That gives four such pairs, so option (a), Four, is the answer.

Word formation The letters available in PARALLELOGRAM are P, A, R, A, L, L, E, L, O, G, R, A, M. ROLE needs R, O, L, E and LARGE needs L, A, R, G, E — every one of those letters is present. LEAP needs L, E, A, P, which are present as well. ALERT needs the letter T, and there is no T anywhere in PARALLELOGRAM. So ALERT cannot be formed, and option (d) is the answer.

Letter pairs in a word Number the letters of CLUSTERS: C-1, L-2, U-3, S-4, T-5, E-6, R-7, S-8. A pair counts when the letters standing between the two in the word are as many as those standing between them in the alphabet, in either direction. S–T and R–S are neighbours in the word and neighbours in the alphabet as well, so both qualify. In T…R only E stands between them in the word, and only S stands between R and T in the alphabet, so this backward pair qualifies too. There are three such pairs, so option (d) is the answer.

Number series The terms grow quickly, so divide each term by the one before it. $14÷7=2$, $42÷14=3$, $168÷42=4$ — the multiplier rises by one every time. The next multiplier is therefore 5. So the next term is $168\times 5=840$, and option (a) is the answer.

Prime number series The differences 3, 6, 6, 6, 8, 10 form no pattern, so look at the nature of the terms instead. Every term is a prime number: 2, 5, 11, 17, 23, 31, 41. Write the primes in order — 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47 — and the rule appears: take one prime, skip the next. After 41 the prime 43 is skipped, so the next term is 47. Hence option (b) is the answer.