5 February 2025 · Shift 3

Positional letter shift Compare each given pair letter by letter; the shift depends on the position in the word, not on the letter itself. AMBUSH → FPIWTH: A+5=F, M+3=P, B+7=I, U+2=W, S+1=T, H+0=H. LYPASE → QBWCTE: L+5=Q, Y+3=B (counting round the alphabet, 25+3=28=2), P+7=W, A+2=C, S+1=T, E+0=E. So the fixed pattern of shifts is +5, +3, +7, +2, +1, 0. Apply it to OCTANE: O+5=T, C+3=F, T+7=A (since 20+7=27=1), A+2=C, N+1=O, E+0=E. Hence OCTANE is related to TFACOE, i.e. option (d).

Reverse-alphabet number coding The plain sum of the alphabet positions of USJI is 21+19+10+9=59, not 49, so the code is not the direct sum. Rule: replace each letter by its reverse-alphabet value, 27- (its position), and add the four values. USJI: 27-21=6, 27-19=8, 27-10=17, 27-9=18, and 6+8+17+18=49. DPTQ: 27-4=23, 27-16=11, 27-20=7, 27-17=10, and 23+11+7+10=51. FAUL: 27-6=21, 27-1=26, 27-21=6, 27-12=15. Adding, 21+26+6+15=68. So 'FAUL' is coded as 68, i.e. option (c).

Number series - square differences The series is 19, 19, 20, 24, 33, ? Take the differences of consecutive terms: 19-19=0, 20-19=1, 24-20=4, 33-24=9. These are the perfect squares $0^2$, $1^2$, $2^2$, $3^2$, so the next difference must be $4^2=16$. Therefore the missing term is 33+16=49. So the answer is 49, option (d).

Dice - opposite faces Rule: faces that are seen together in one view touch each other, so they can never be opposite. The first view shows C, F and D together, so D is adjacent to C and to F. The second view shows C, F and E together, so E is adjacent to C and to F as well. C and F are the two faces common to both views; the two uncommon faces are D and E. D and E never appear together, so they lie on opposite faces. Hence the face opposite E carries D - option (b).

Coded blood relations Read the expression 'E % L # R + B' one link at a time, from left to right. 'E % L' means E is the brother of L, so E is male and E and L are siblings. 'L # R' means L is the sister of R, so L is female and L and R are siblings. 'R + B' means R is the daughter of B, so R is female and B is the parent. E, L and R are children of the same parent B, and R is female. So R is the sister of E - option (a).

Mirror image MN is a vertical mirror, so the image is the figure turned left to right; top stays top and bottom stays bottom. In the given figure the small circle sits at the top right, so in the image it must move to the top left. The line therefore runs downwards to the right, and the hollow arrowhead on it and the small arrow at its far end both point down to the right. Options (a) and (b) still keep the circle at the top right, so they are copies of the figure, not its mirror image. Option (c) is turned the right way but its arrowhead is half shaded, which the given figure is not. Only option (d) matches, so the answer is option (d).

Number series - growing difference The series is 419, 424, 430, 437, 445, ? Take the differences: 424-419=5, 430-424=6, 437-430=7, 445-437=8. The difference grows by 1 every step, so the next difference is 9. Therefore the missing term is 445+9=454 - option (b).

Venn diagram of classes Every horse is an animal, so the class of horses lies wholly inside the class of animals. A tree is neither a horse nor an animal, so the class of trees stays wholly outside both. The diagram needed is therefore a small circle inside a larger circle, with a third circle standing apart. Option (a) makes all three classes overlap and option (c) puts two overlapping classes inside animals, neither of which is true. Option (b) makes horses overlap animals only partly, which is also wrong. Option (d) shows exactly the required picture, so the answer is option (d).

Letter series - repeating block The series has eleven places, of which five are blank: _ O _ K R _ _ J K _ E. The printed letters are O at place 2, K at place 4, R at place 5, J at place 8, K at place 9 and E at place 11. Places 4 and 9 both carry K and they are five apart, which suggests a block of five letters repeating. Take the block EOJKR: places 1 to 5 read E, O, J, K, R and places 6 to 10 read E, O, J, K, R again, with E at place 11. This agrees with every printed letter, so the block is correct. The blanks at places 1, 3, 6, 7 and 10 are therefore E, J, E, O and R - option (b).

Odd letter-cluster Write the alphabet position of each letter and look at the two gaps inside every cluster. LOU: L(12)+3=O(15) and O(15)+6=U(21), so the gaps are +3 and +6. BEK: B(2)+3=E(5) and E(5)+6=K(11) - the same +3, +6. HKQ: H(8)+3=K(11) and K(11)+6=Q(17) - again +3, +6. OIG: O(15)-6=I(9) and I(9)-2=G(7), so its gaps are -6 and -2. OIG is the only cluster that does not move forward by 3 and then by 6, so it is the odd one - option (d).

Paper folding and cutting The sheet is folded upwards twice, so the final strip is one quarter of the sheet and four layers thick. Each cut passes through all four layers, so every cut reappears once in each of the four quarters of the opened sheet. So the answer must show four rows of shapes, which rules out option (a) with three rows and option (d) with two. A diamond is symmetrical about a horizontal line, so it looks the same in all four rows. The half-circle is not: at every crease it is turned upside down. In the cut strip the half-circle has its flat edge on top, so reading downwards the four rows are flat-side-up, flat-side-down, flat-side-up, flat-side-down. Option (c) has the first two alike and the last two alike, so it breaks this alternation. Only option (b) alternates correctly, so the answer is option (b).

Linear seating arrangement Number the seats 1 to 7 from the left end of the row. Only G sits to the left of J, so G takes seat 1 and J takes seat 2. Only four people sit between G and H, so H takes seat 6. Only K sits between L and I, so L, K, I occupy three seats in a row with K in the middle; the only free block of three consecutive seats is 3, 4, 5. L is not an immediate neighbour of H, so L cannot take seat 5; hence L is at 3, K at 4 and I at 5, and M gets the last free seat 7. Between M at seat 7 and J at seat 2 sit H, I, K and L. That is four people - option (a).

Letter-sum coding Rule: the code is the sum of the alphabet positions of the four letters. LTRH: 12+20+18+8=58, which is the given code. NBZW: 14+2+26+23=65, again the given code. GSCE: G=7, S=19, C=3, E=5. Adding, 7+19+3+5=34. So 'GSCE' is coded as 34 - option (a).

Interchange of signs Make the two swaps in the given expression: every + becomes $\times$, every $\times$ becomes +, every - becomes $÷$ and every $÷$ becomes -. So $28-4\times 12÷5+3$ turns into $28÷4+12-5\times 3$. By BODMAS, do the division and the multiplication first: $28÷4=7$ and $5\times 3=15$. The expression is now 7+12-15. Finally 7+12=19 and 19-15=4. So the value is 4 - option (a).

Letter-cluster series Treat the three letters of each term separately. First letters: M, O, Q, ?, U each move forward by 2, so the missing first letter is Q+2=S. Middle letters: every term has A in the middle, so the missing middle letter is A. Third letters: N, P, R, ?, V also move forward by 2, so the missing third letter is R+2=T. The missing term is therefore SAT - option (c).

Circular seating arrangement All seven face the centre, so for each person the left hand points clockwise and the right hand points anticlockwise. Three people between H and N counted from the left of H means N is the fourth seat clockwise from H. Three people between L and E counted from the right of E means L is the fourth seat anticlockwise from E, which on a circle of seven is the third seat clockwise from E. K is immediately to the right of L, so K sits one seat anticlockwise from L. F must touch both E and N, so F sits between them; putting these facts together, the clockwise order is H, K, L, G, N, F, E. Check: from H, the seats K, L, G lie between H and N clockwise; from E, the seats F, N, G lie between E and L anticlockwise; K is one seat anticlockwise from L; F touches N and E. Second to the right of G means two seats anticlockwise from G: the first is L and the second is K. So K sits second to the right of G - option (d).

Rearranging letters of a word REVERSAL has eight letters: R, E, V, E, R, S, A, L. Reverse alphabetical order means the letter nearest to Z comes first. Sorting them that way gives V, S, R, R, L, E, E, A. Now compare the two rows place by place: R with V, E with S, V with R, E with R, R with L, S with E, A with E, L with A. No place holds the same letter in both rows. So the number of unchanged positions is zero - option (a).

Syllogism - statements and conclusions Draw the three statements as circles: salads inside appetizers, salads inside food, and food inside rice. Conclusion (I): every salad is food and every food is rice, so every salad is rice - it follows. Conclusion (II): every salad is food and every salad is also an appetizer, so the salads are a part of food that is made up of appetizers. Hence at least some food are appetizers - it follows as well. Both conclusions follow, so the answer is option (a).

Figure series - number of parts The four given figures are different shapes, so the rule must lie in the way each one is divided. The hexagon has one line across the middle from top to bottom, one across from side to side, and one extra line in the lower-left quarter, which cuts it into 4+1=5 parts. The trapezium has both diagonals and a line from their crossing straight down to the base, again 5 parts. The circle has two diameters and one extra radius in the lower-left quarter, again 5 parts. The square has its two middle lines and one diagonal in the lower-left quarter, again 5 parts. So the missing figure must also be cut into 5 parts by a line down the middle, a line across the middle and one extra line in the lower-left quarter. The triangle in option (b) has exactly that, while (a) and (d) are cut into more parts and (c) is cut into many. Hence the answer is option (b).

Letter-number analogy Handle the letters and the number separately. Letters: G+1=H and D+1=E; also C+1=D and J+1=K, so each letter moves one step forward. Number: 34-10=24 and 12-10=2, so the number falls by 10. Apply both rules to XV 56: X+1=Y, V+1=W and 56-10=46. So XV 56 is related to YW 46 - option (b).