6 February 2025 · Shift 3

Dice - opposite faces Both the pictures show E on the top face. With E on top, the four side faces seen are B and C in view I, and A and F in view II. Five of the six letters are now placed - E on top and B, C, A, F around it. The letter left over, D, must be on the hidden bottom face, so D lies opposite E. Hence the face opposite D carries E, and option (d) is correct.

Figure series - shading The hexagon is cut into six parts - two triangles on top, two rectangles at the sides and two triangles below. At each step the shaded part moves one place clockwise: top-right triangle, right rectangle, bottom-right triangle, bottom-left triangle. One more step clockwise carries the shading to the left rectangle. Only option (a) has the left rectangle shaded, so option (a) is correct.

Circular seating P is an immediate neighbour of both Q and E, so the block Q - P - E is fixed. Q is an immediate neighbour of D as well, so D takes the free side of Q: D - Q - P - E. Only L is left, and the one empty seat is the one between E and D. This fits the last clue: facing the centre, the seat immediately left of E is the next seat clockwise, and L sits there. D now has Q on one side and L on the other, so option (c) is correct.

Letter-number analogy In MC 5 to PF 10: M + 3 = P and C + 3 = F, while the number rises by 5. The second pair obeys the same rule: H + 3 = K, Q + 3 = T and 20 + 5 = 25. Apply it to JW 30: J + 3 = M, W + 3 = Z and 30 + 5 = 35. So JW 30 is related to MZ 35, and option (b) is correct.

Venn diagram - classes Every room is a part of some house, so the class Room lies completely inside the class House. A shirt is a garment - it is neither a room nor a house, so Shirt stands completely apart from both. The picture needed is therefore a small circle (Room) drawn inside a large circle (House), with a separate circle for Shirt. Option (b) is drawn exactly like this, so option (b) is correct.

Letter series - blanks The line holds twenty letters, so split it into four groups of five. Group 1 is V _ _ Y Z, which needs W and X. Group 2 is V W X _ _, which needs Y and Z. Group 3 is _ _ X Y Z, which needs V and W. Group 4 is V _ X _ Z, which needs W and Y. Reading the blanks from left to right gives W X Y Z V W W Y, so option (a) is correct.

Embedded figure Figure (X) is one vertical line with two arms on its right - a long arm at the very top that ends free, and a shorter arm lower down that ends in a solid dot, the vertical line running on below that arm. Option (d) carries exactly that: the top arm runs right and ends free, the lower arm ends in a solid dot, and the vertical line continues below it. In option (b) the upper arm ends in a dot and is shorter than the lower arm, so the pair of arms is not the same. In options (a) and (c) no vertical line carries such a pair of arms at all. Hence option (d) is correct.

Syllogism - conclusions All colours are reds, all colours are blacks and all colours are paints, so the class of colours lies inside all three classes. Conclusion (I) All reds are paints - the reds may spread well outside the paints, so it does not follow. Conclusion (II) Some paints are blacks - every colour is a paint and also a black, so the two classes certainly share members; it follows. Only conclusion (II) follows, so option (a) is correct.

Letter-cluster analogy Compare MQTR with SWZX letter by letter: M + 6 = S, Q + 6 = W, T + 6 = Z, R + 6 = X. The second pair obeys the same rule, counting on past Z: Q + 6 = W, U + 6 = A, X + 6 = D, V + 6 = B. For TXAY: T + 6 = Z, X + 6 = D, A + 6 = G, Y + 6 = E. So TXAY is related to ZDGE, and option (d) is correct.

Letter-cluster series Take the first letters: D, H, L, P - each is 4 places after the one before, so the next is T. The second letters G, K, O, S also move +4 and give W; the third letters C, G, K, O give S. The missing cluster is TWS, so option (b) is correct.

Rearranging letters ELECTRIC is made of the letters E, L, E, C, T, R, I, C. Reverse alphabetical order means the largest letter first: T, R, L, I, E, E, C, C. Comparing the two rows place by place, only the 8th letter C is the same in both. So exactly one letter keeps its position, and option (d) is correct.

Symbol substitution Put the signs in place of the letters: P = ×, Q = ÷, R = - and S = +. The expression becomes $\left(35\times 2\right)÷5+\left(86÷2\right)-\left(3\times 15\right)+90$ Clear the brackets first: $=70÷5+43-45+90$ Then divide: =14+43-45+90 Finally add and subtract: =102 Hence option (a) is correct.

Number series Find the gap between one term and the next. 27-22=5, 37-27=10, 52-37=15 and 72-52=20. The gaps themselves rise by 5 each time, so the next gap must be 25. Therefore ?=72+25=97, and option (d) is correct.

Letter-digit coding 'GELS' and 'SELF' share the letters E, L and S; their codes 9872 and 8276 share the digits 8, 2 and 7. So E, L and S stand for 8, 2 and 7 in some order. The letter left over in 'GELS' is G and the digit left over is 9, so G = 9. The letter left over in 'SELF' is F and the digit left over is 6, so F = 6. Hence option (d) is correct.

Linear seating Number the seats 1 to 7 from the left. Nobody sits to the right of E, so E is at seat 7. Exactly two people sit between E and L, so L is at seat 4; L is immediately left of K, so K is at seat 5. Three people sit between G and K, so G is at seat 1 (seat 9 does not exist). Seats 2, 3 and 6 are left for F, H and N; N is immediately right of H, so H is at 2 and N at 3, leaving F at 6. Between F (seat 6) and N (seat 3) sit L and K - two people, so option (c) is correct.

Letter-digit coding 'HALF' and 'LATH' share the letters H, A and L; the codes 1059 and 9750 share the digits 0, 5 and 9. So H, A and L stand for 0, 5 and 9 in some order. The letter left over in 'HALF' is F and the digit left over is 1, so F = 1. The letter left over in 'LATH' is T and the digit left over is 7, so T = 7. Hence option (b) is correct.

Odd one out - letters Count the gaps between the letters of each cluster. JNP is J +4 N +2 P, TXZ is T +4 X +2 Z and HLN is H +4 L +2 N - all three use the pattern +4, +2. NRV is N +4 R +4 V, which uses +4, +4 instead. NRV does not belong to the group, so option (a) is correct.

Alternate number series The terms do not fall steadily, so read the alternate terms as two separate series. The 1st, 3rd, 5th and 7th terms are 789, 780, 772, 765, falling by 9, then 8, then 7. The 2nd, 4th and 6th terms are 790, 782, 775, falling by 8 and then 7, so the next fall is 6. Therefore ?=775-6=769, and option (c) is correct.

Paper folding and cutting The lower half is folded up first and then the right half is folded to the left, so the packet is the top-left quarter of the sheet. Two cuts are made on it - a notch on its left edge and a leaf at the corner where the two creases meet. Opening the side fold mirrors both cuts about the vertical crease, and opening the top fold mirrors them again about the horizontal crease. So the notch appears twice on the left edge and twice on the right edge, and the leaf becomes four leaves meeting at the centre. Option (a) shows exactly this, so option (a) is correct.

Coded blood relations Break the string 'S<H:A!M/E' into its pieces and read each sign with the meaning given. S < H says S is the son of H, and H : A says H is the wife of A, so A is the father of S. A ! M says A is the brother of M, and M / E says M is the father of E. So E's father is M, M's brother is A, and A's son is S. S is therefore E's father's brother's son, and option (d) is correct.