17 February 2025 · Shift 1

Coded blood relations Break the string $B+C\times D-E÷F$ at each symbol and read the symbols one at a time. B+C: B is the mother of C. $C\times D$: C is the wife of D, so D is C's husband. D-E: D is the brother of E. $E÷F$: E is the father of F. D is the brother of E, and E is the father of F, so D is the brother of F's father. Hence D is F's father's brother - option (c).

Figure series rotation In every figure the same four symbols D, △, Ω and @ appear; only their places change. In figures 1 and 3 they sit at the mid-points of the four sides, and in figures 2 and 4 at the four corners, so the two layouts alternate. From figure 1 to figure 2, D goes from the left mid-point to the top-left corner, △ from the top to the top-right corner, @ from the right to the bottom-right corner and Ω from the bottom to the bottom-left corner - every symbol moves one step of 45° clockwise. The same 45° clockwise step carries figure 2 to figure 3 and figure 3 to figure 4. Figure 4 has Ω top-left, D top-right, △ bottom-right and @ bottom-left, so one more step puts Ω at the top, D at the right, △ at the bottom and @ at the left. Options (b) and (c) place the symbols at the corners, which is the wrong layout for the fifth figure. Option (d) has the right layout but D at the left and @ at the right, the exact opposite of what the clockwise turn gives; only option (a) keeps D on the right and @ on the left. Hence the answer is option (a).

Odd letter-cluster out Write the alphabet position of each letter and take the gap between consecutive letters. JKP gives 10, 11, 16 - gaps +1 and +5. FGL gives 6, 7, 12 and RSX gives 18, 19, 24 - again gaps +1 and +5. MRZ gives 13, 18, 26 - gaps +5 and +8, so both gaps are wrong. Hence MRZ does not belong to the group - option (d).

Embedded figure First fix what figure (X) is made of: a trapezium whose shorter side is on top, and three stems hanging from its lower edge - one at each end and one at the middle - each ending in a solid dot, the middle stem being the longest. Since rotation is not allowed, the answer must show that trapezium the same way up, with all three stems below it. Option (b) contains exactly this: the same trapezium, the same three stems and the same three solid dots below it, and the only extra strokes are two stems rising from its top corners. Option (a) is built round a circle and option (c) round a triangle, so neither has a trapezium at all. Option (d) is only a zigzag of straight lines joining dots, with no closed four-sided figure in it. Hence the answer is option (b).

Venn diagram of classes Take the three classes two at a time. Shoes are footwear, not clothes, so Clothes and Shoes have nothing in common and their circles must stay completely apart. Some clothes are black and some are not, so Clothes and Black overlap only partly. In the same way some shoes are black and some are not, so Shoes and Black also overlap only partly. The required picture is therefore a middle circle cutting two outer circles that do not touch each other. Option (a) is a single circle and option (b) puts two separate circles inside one big circle, which would make clothes and shoes both black. Option (c) makes the two big classes overlap, which would make some shoes clothes. Hence the answer is option (d).

Linear seating arrangement Everyone faces north, so left and right in the question are the reader's left and right; number the seats 1 to 7 from the left. Only two people sit to the left of I, so I is at seat 3. Only three people sit between I and K, so K is at seat 3+4=7 (seat 3-4 does not exist). L sits second to the right of I, so L is at seat 5. Only two people sit between L and G, so G is at seat 5-3=2 (seat 8 does not exist). Seats 1, 4 and 6 are left for H, M and J, and H must be left of M and M left of J, so H =1, M =4 and J =6. Seats 5, 6 and 7 lie to the right of M, so three people sit to his right - option (c).

Letter-to-number coding Replace each letter by its position in the English alphabet and add. HXCT: 8+24+3+20=55, which is the given code. LAMU: 12+1+13+21=47, again the given code, so the rule is confirmed. ZFGD: 26+6+7+4=43. Hence the code for ZFGD is 43 - option (d).

Interchange of signs Make the swaps first: every + becomes $÷$, every $÷$ becomes +, every - becomes $\times$ and every $\times$ becomes -. So $112+8\times 2-13÷21$ turns into $112÷8-2\times 13+21$. Now apply BODMAS. Division first: $112÷8=14$. Then multiplication: $2\times 13=26$. Left with 14-26+21=9. Hence the answer is option (b).

Number series Take the difference between each term and the one before it. 800-789=11, 789-767=22, 767-734=33. 734-690=44 and 690-635=55. The numbers subtracted are 11, 22, 33, 44, 55, i.e. multiples of 11, so the next one is 66. 635-66=569. Hence the answer is option (a).

Alternating letter series The series is made of two chains sitting one inside the other, so separate the odd places from the even places. Odd places give Y, X, W, V, ? - each letter is one step back in the alphabet. Even places give N, L, J, H, F - each letter is two steps back, which confirms the split. The ? is at the ninth place, an odd place, so it follows V. V =22, so the next letter is 22-1=21, which is U. Hence the answer is option (c).

Paper folding and cutting The first fold brings the bottom half up onto the top half and the second fold brings the right half onto the left half, so the piece that is finally cut is the top-left quarter and it is four sheets thick. Both cuts are triangles lying wholly inside that quarter - neither of them touches a fold line - so each cut goes through all four layers and opens out into four separate triangles, one in each quarter. Two cuts through four layers therefore give $2\times 4=8$ triangles, and they must be placed symmetrically about both fold lines. One cut lies near the top of the quarter and the other near its left side, so the eight triangles form four pairs - two near the top edge, two near the bottom edge, two near the left edge and two near the right edge - with the corners and the centre left uncut. Options (c) and (d) show only four triangles, and option (b) only four placed with no symmetry at all, so none of them can come from two cuts through four layers. Hence the answer is option (a).

Number series Take the difference between each term and the one before it. 650-645=5, 656-650=6, 663-656=7 and 671-663=8. The numbers added are 5, 6, 7, 8, each one more than the last, so the next one added is 9. 671+9=680. Hence the answer is option (c).

Letter-cluster analogy Compare MISC with OFUZ letter by letter: M$\to$O is +2, I$\to$F is -3, S$\to$U is +2 and C$\to$Z is -3 (counting back from C runs round to Z). Check the rule on the second pair: Z$\to$B is +2, D$\to$A is -3, E$\to$G is +2 and N$\to$K is -3. So the rule is +2, -3, +2, -3 on the four letters. Apply it to PVAT: P =16, 16+2=18= R. V =22, 22-3=19= S; A =1, 1+2=3= C; T =20, 20-3=17= Q. So PVAT is related to RSCQ - option (b).

Circular seating arrangement Everyone faces the centre, so each person's right hand points anticlockwise and the left hand points clockwise. Number the seats 1 to 7 clockwise and put E at seat 1. N is immediately to the right of E, so N takes the seat one step anticlockwise from E, that is seat 7. Counting from the left of N means counting clockwise from seat 7; three people (seats 1, 2, 3) sit in between, so H is at seat 4. Three people also sit between E and K: going clockwise from E the in-between seats are 2, 3, 4, so K is at seat 5 (going the other way would leave only two seats). F is immediately to the right of G, so F is one step anticlockwise from G; the free seats are 2, 3 and 6, and only F =2 with G =3 fits, leaving L at seat 6. Counting from the right of G means going anticlockwise from seat 3: seat 2 holds F and seat 1 holds E. So exactly one person, F, sits between them - option (c).

Letter series with blanks There are five blanks and every option gives five letters, so the series must break into blocks of four letters starting at the first blank. The blocks are (blank)QMR, N(blank)OT, PU(blank)V, RWS(blank) and TYU(blank). Compare block 2 with block 1 place by place: N is 2 after L, S is 2 after Q, O is 2 after M and T is 2 after R - each block is the one before it with every letter moved 2 places on. Working forward with that rule the blocks are LQMR, NSOT, PUQV, RWSX and TYUZ. The letters that were missing are L, then S, then Q, then X, then Z. Hence the answer is option (a).

Word coding Write the two statements with their codes one below the other and look for what they share. 'trees' is the only word that appears in both statements. 'gk' is the only code that appears in both code groups. A word common to two statements must carry the code common to their codes, so 'trees' is coded as 'gk'. Hence the answer is option (d).

Dice opposite faces U shows in both positions and in both of them it is on the same (left) face, so the cube has only been turned about the axis through U. Every other letter that shows is therefore on a face touching U. The first view gives A and T next to U, and the second view gives H and S next to U - four different faces. A cube has six faces, so the four faces around U are A, T, H and S, and the only letter left, J, must be on the face hidden opposite U. So J and U are on opposite faces, and the face opposite J is U - option (c).

Rearranging letters of a word Reverse alphabetical order means Z first and A last, so sort the eight letters F, U, N, F, A, I, R, S from the largest downwards. That gives U, S, R, N, I, F, F, A. Now compare the two words place by place: F/U, U/S, N/R, F/N, A/I, I/F, R/F, S/A. No place holds the same letter in both words, so not a single letter keeps its position. Hence the answer is zero - option (a).

Opposite-letter coding Take the first pair place by place: G =7 and T =20, and 7+20=27. The other places agree: T$\left(20\right)\to$G(7), S$\left(19\right)\to$H(8) and U$\left(21\right)\to$F(6) - every pair adds up to 27. The second pair obeys the same rule: K$\left(11\right)\to$P(16), J$\left(10\right)\to$Q(17), I$\left(9\right)\to$R(18) and E$\left(5\right)\to$V(22). So each letter is replaced by its opposite letter, whose position is 27 minus its own. For ALMO: A$\left(1\right)\to$Z(26), L$\left(12\right)\to$O(15), M$\left(13\right)\to$N(14) and O$\left(15\right)\to$L(12). So ALMO is written as ZONL - option (c).

Syllogism 'All vacuums are machines' puts the whole of Vacuums inside Machines. 'All games are toys' puts the whole of Games inside Toys, and 'no vacuum is a game' keeps Vacuums and Games apart. Conclusion (I) says no toy is a machine, but nothing in the statements forbids a toy from being a machine, and the diagram shows Toys and Machines overlapping, so (I) does not follow. Conclusion (II) says some toys are vacuums; the statements only keep vacuums out of games, so every vacuum may lie outside Toys altogether, and (II) does not follow either. Since a conclusion must be true in every possible diagram, neither follows - option (d).