29 November 2025 · Shift 2

Number series First look at the gaps: 9-5=4, 17-9=8, 33-17=16, 65-33=32 — every gap doubles. The same rule written as one operation is $\times 2-1$, since $5\times 2-1=9$, $9\times 2-1=17$, $17\times 2-1=33$ and $33\times 2-1=65$. So the missing term $=65\times 2-1=130-1=129$. Check the last term: $129\times 2-1=258-1=257$, exactly as given. Hence option (b) is correct.

Coded operation Look for one rule that turns the two given numbers into the stated result. For the first pair, 25-30=-5 and $-5\times 5=-25$, which is the given value. For the second pair, 8-24=-16 and $-16\times 5=-80$, again the given value. So the rule is (first number - second number) $\times 5$. Applying it, the required value $=\left(4-16\right)\times 5=\left(-12\right)\times 5=-60$. Hence option (a) is correct.

Coded operation Multiply the two given numbers first and compare the product with the stated result. First pair: $15\times 7=105$ and $105\times 4=420$. Second pair: $30\times 18=540$ and $540\times 4=2160$. So the rule is (first number $\times$ second number) $\times 4$. Therefore the required value $=50\times 20\times 4=1000\times 4=4000$. Hence option (c) is correct.

Number series The gaps are 19-8=11, 41-19=22 and 85-41=44, so each gap is double the one before. Written as a single operation the rule is $\times 2+3$: $8\times 2+3=19$, $19\times 2+3=41$, $41\times 2+3=85$. So the next term $=85\times 2+3=170+3=173$. The same answer follows from the gaps: next gap $=44\times 2=88$ and 85+88=173. Hence option (b) is correct.

Number series Each term is roughly four times the previous one, since $\frac{84}{20}\approx 4$, so test $\times 4$ with a small correction. $20\times 4+4=84$, $84\times 4+4=340$, $340\times 4+4=1364$ — the rule holds at every step. Therefore the next term $=1364\times 4+4=5456+4=5460$. Hence option (b) is correct.

Letter series Replace each letter by its place in the alphabet: A = 1, B = 2, D = 4, H = 8. Every place value is double the one before it, so the next place value $=8\times 2=16$. The 16th letter of the alphabet is P. Hence option (b) is correct.

Order and ranking Arrange the five from tallest to shortest. 'C is taller than only two people' means exactly two people stand below C, so C is 3rd from the top. E is the tallest, so E takes the 1st place; the 2nd place must be filled by one of A, B or D. B>D and B<E are consistent with either A or B occupying that 2nd place, so the order is not fully fixed. But only one place lies between E and C, so exactly one person is taller than C and yet shorter than the tallest. Hence option (a) is correct.

Circular seating All five face the centre, so each person's left hand points in the clockwise direction of the table. Fix T at the top seat. 'Q is second to the left of T' puts Q two seats clockwise from T, leaving three seats for P, R and S. 'P is second to the left of R' means P sits two seats clockwise from R. Try R in the seat next to T: then P falls two seats clockwise from R and S takes the last seat, and R's neighbours are only T and Q, which satisfies 'R is not next to S or P'. The clockwise order is therefore T, R, Q, P, S. With only five seats, going four seats to the left is the same as going one seat to the right, and one seat to Q's right is R. Hence option (c) is correct.

Row arrangement Draw two rows of three facing each other and number the columns 1, 2 and 3. R has a north-facing flat, and U's flat is next to R's, so U is in the same row, i.e. the north row as well. Q and T face the same direction; they cannot both be in the north row, which already holds R and U, so Q and T are both in the south row. S is diagonally opposite U, so S is in the south row too; the south row is therefore Q, T, S and the north row is R, U, P. Fixing the columns: S at one end of the south row, U diagonally across from it, R beside U, and P in the remaining north flat; Q is not next to S, so T takes the middle south flat and Q the far end. The people with north-facing flats are R, U and P, so the pair offered is U and P. Hence option (c) is correct.

Number analogy Use the two complete pairs to find the rule, working on the whole numbers. First pair: 3461-2511=950. Third pair: 8624-7674=950 — the same constant difference. So the rule is (first number +950) = second number. For the middle pair, the missing number =4874-950=3924. Hence option (c) is correct.

Number analogy The second number is about one-sixth of the first, since $\frac{3480}{6}=580$, which is close to 577. Test 'divide by 6, then subtract 3': $3480÷6=580$ and 580-3=577. Check on the second pair: $4206÷6=701$ and 701-3=698. So the rule is (number $÷6$) -3. Therefore $2160÷6=360$ and 360-3=357. Hence option (a) is correct.

Sign interchange Swap the signs - and $÷$ wherever they occur, then simplify each side by the BODMAS order. Equation I becomes $50+10÷5-15\times 2$, i.e. 50+2-30=22, which is exactly the value stated, so I is correct. Equation II becomes $20+40-38÷19\times 3$; here $38÷19=2$ and $2\times 3=6$. So the left side of II is 20+40-6=54, while the equation claims 63. Only equation II fails to balance after the interchange. Hence option (b) is correct.

Signs in equation Put each option's signs into the four $*$ places of $250*5*3*50*20$ and simplify by BODMAS. Taking $÷,\times ,+,-$ in order gives $250÷5\times 3+50-20$. Division and multiplication come first, from left to right: $250÷5=50$ and $50\times 3=150$. Then the addition and subtraction: 150+50-20=200-20=180. This equals the required value 180, while no other arrangement of the given signs produces 180. Hence option (c) is correct.

Odd letter-number cluster In each cluster add the alphabetical place values of the four letters and compare the total with the number attached. SDTR: 19+4+20+18=61, which matches 61. QTVS: 17+20+22+19=78, which matches 78; GTRD: 7+20+18+4=49, which matches 49. TFRE: 20+6+18+5=49, but this cluster carries 50, so the rule breaks here. Hence option (d) is correct.

Odd letter-number pair In every pair check two things: how far each letter moves, and how much the number changes. WE to BK: W+5=B and E+6=K, counting round the alphabet, while 610-240=370. MQ to RW: M+5=R and Q+6=W, while 680-310=370. CI to HO: C+5=H and I+6=O, while 740-370=370. TL to YR also has the shifts +5 and +6, but 770-420=350, not 370, so this pair breaks the rule. Hence option (c) is correct.

Odd number pair (cubes) Compare the two numbers of each pair: the number on the left should be the cube of the number on the right. ${15}^3=3375$, ${17}^3=4913$ and ${16}^3=4096$, so those three pairs obey one and the same rule. ${18}^3=5832$, but the fourth pair shows 5833, which is one more than the cube. So 5833-18 is the pair that does not fit. Hence option (d) is correct.

Odd number pair (squares) Here the left number is small and the right one is large, so try adding a fixed number and then squaring. ${\left(12+2\right)}^2={14}^2=196$, ${\left(15+2\right)}^2={17}^2=289$ and ${\left(18+2\right)}^2={20}^2=400$, so the rule is: add 2, then square. ${\left(21+2\right)}^2={23}^2=529$, but the fourth pair shows 530, which is one more than the square. So 21-530 breaks the rule. Hence option (d) is correct.

Word coding by letter sum Add the positional values of the letters of the word and compare the total with the code. For STAR: 19+20+1+18=58, and the code is 59, i.e. the sum plus 1. For MOON: 13+15+15+14=57, and the code is 58, again the sum plus 1. For PLANT: 16+12+1+14+20=63, so the code is 63+1=64. Hence option (d) is correct.

Word formation from letters EDUCATION is made of the letters E, D, U, C, A, T, I, O, N, each of them once. A word can be formed only if every letter it needs is present in this list. DANGER needs G and R, ACTIONS needs S, and UNITY needs Y - none of these letters occurs in EDUCATION. CAUTION needs C, A, U, T, I, O, N, and all seven are available, so it can be formed. Hence option (c) is correct.

Word formation from letters GARDEN uses the six letters G, A, R, D, E, N, so the correct option must contain all six of them. RANGE has no D, ENDAR has no G, and GRAND has no E, so none of these three can give GARDEN. DANGER contains exactly D, A, N, G, E, R, which is the same set of six letters. Rearranging the letters of DANGER therefore gives GARDEN. Hence option (a) is correct.

Letter-number cluster analogy Read the two complete analogies first, because they fix the rule. In KP910 : LQ1100 each letter moves one step forward ($K\to L$, $P\to Q$) and the number rises by 1100-910=190. In CD340 : DE530 the letters again move one step forward ($C\to D$, $D\to E$) and the number again rises by 530-340=190. The missing cluster must give LN720 under this same rule, so work backwards. Its letters are one step behind L and N, that is K and M, and its number is 720-190=530. So the missing cluster is KM530. Hence option (b) is correct.

Letter-number cluster analogy In MT180 : PW270 both letters move three steps forward ($M\to P$, $T\to W$) and $180\times 1.5=270$. In CZ240 : FC360 the letters again move three steps forward ($C\to F$, and $Z\to C$ counting past Z) and $240\times 1.5=360$. So the rule is: each letter +3, and the number multiplied by $\frac{3}{2}$. Apply it to FK120: F+3=I and K+3=N. The number becomes $120\times 1.5=180$. So the required cluster is IN180. Hence option (b) is correct.

Letter-number cluster analogy In AB14 : BC26 each letter moves one step forward ($A\to B$, $B\to C$) and the number rises by 26-14=12. The second analogy confirms it: in PQ35 : QR47, $P\to Q$, $Q\to R$ and 47-35=12. Apply the rule to LM22: L+1=M and M+1=N. The number becomes 22+12=34. So the required cluster is MN34. Hence option (a) is correct.

Mixed letter-number series Break each term into its first letter, its second letter and its number, and treat the three parts separately. First letters: B, E, H, K move forward by 3 each time, so the next is K+3=N. Second letters: F, K, P, U move forward by 5 each time, so the next is U+5=Z. Numbers: $12\times 2+1=25$, $25\times 2+1=51$ and $51\times 2+1=103$, so the rule is $\times 2+1$. The next number is $103\times 2+1=207$. So the missing term is NZ207. Hence option (a) is correct.

Wrong term in a series Check the letters first: B, J, R, Z, H move forward by 8 each time (after Z the count starts again from A), so the first letters are correct. The second letters D, H, L, P, T move forward by 4 each time, so they are correct too; the error must be in a number. Numbers: $24\times 3+3=75$, $75\times 3+3=228$ and $228\times 3+3=687$, so the rule is $\times 3+3$. The fifth number should be $687\times 3+3=2064$, but the series shows 2060. So the wrong term is HT2060. Hence option (d) is correct.