10 February 2025 · Shift 3

Letter-cluster analogy Compare ERHT with BLEN letter by letter: E $\to$ B is -3, R $\to$ L is -6, H $\to$ E is -3, T $\to$ N is -6. The same pattern works on the second pair: X -3= U, S -6= M, N -3= K, R -6= L, which is UMKL. Apply it to DIOQ: D (4)-3=1= A, I (9)-6=3= C, O (15)-3=12= L, Q (17)-6=11= K. So DIOQ is related to ACLK, i.e. option (d).

Alphabetical rearrangement Put the letters of KNIFERS in alphabetical order: E, F, I, K, N, R, S. The second letter from the left end is F and the third letter from the right end is N. F is the 6th letter of the alphabet and N is the 14th. Letters lying strictly between them =14-6-1=7 (G, H, I, J, K, L, M). Hence the correct option is (a).

Symbol interchange First swap the signs everywhere they occur: + becomes $÷$, $÷$ becomes +, - becomes $\times$ and $\times$ becomes -. So $9-4\times 58+2÷22$ is read as $9\times 4-58÷2+22$. By BODMAS, divide first: $58÷2=29$. Then multiply: $9\times 4=36$. Finally 36-29+22=7+22=29. Hence the correct option is (a).

Letter-cluster series Read the three positions of the clusters as three separate series. First letters R, T, V, X move +2 each time, so the next is X+2= Z. Second letters F, H, J, L move +2 each time, so the next is L+2= N. Third letters G, I, K, M move +2 each time, so the next is M+2= O. The missing cluster is therefore ZNO, option (d).

Coded blood relations Break $P+Q-R\times S÷T$ into single links and read them from the right. $S÷T$: S is the father of T. $R\times S$: R is the wife of S, so R is the mother of T. Q-R: Q is the brother of R, so Q is T's mother's brother. P+Q: P is the daughter of Q. So P is the daughter of T's mother's brother, option (b).

Odd one out, letter gaps Measure the gap between the 1st and 2nd letter and between the 2nd and 3rd letter of each cluster. CEF: C $\to$ E is +2 and E $\to$ F is +1. RTU and GIJ give the same $+2,+1$ pattern. UWY: U $\to$ W is +2 but W $\to$ Y is +2, not +1. So UWY does not belong to the group, option (b).

Venn diagram of classes Take the three classes two at a time. A sister can never be a brother, so Sister and Brother have nothing in common - those two circles must stay apart. A friend may be someone's sister and another friend may be someone's brother, so Friend partly overlaps Sister and also partly overlaps Brother. The only figure with a middle circle cutting both end circles while the end circles themselves stay separate is option (c).

Number series, odd differences Write down the difference between each pair of consecutive terms. 880-879=1, 883-880=3, 888-883=5, 895-888=7. The differences are the consecutive odd numbers $1,3,5,7$, so the next difference is 9. Missing term =895+9=904. Hence the correct option is (c).

Dice, opposite faces In view I the face W touches U (top) and V (left), so W is adjacent to U and V. In view II the same face W touches Y (top) and Z (left), so W is adjacent to Y and Z. A cube face touches exactly four faces, and W already touches U, V, Y and Z. The only letter left is X, so X and W lie on opposite faces. The face opposite X therefore carries W, option (a).

Word-code matching Line the two statements up and look for what they share. The sentences 'here I come' and 'I am going' have exactly one word in common - 'I'. Their codes 'Is rc tp' and 'rc as bo' have exactly one code in common - 'rc'. A code that appears in both lines must stand for the word that appears in both lines. So 'I' is coded as 'rc', option (a).

Figure series, counting Count the triangles: the first box has 9, the second 8 and the third 7, so one triangle is lost at every step. Look at where the loss happens: the middle column and the right column never change, and the triangle that disappears is always the lowest one still standing in the left column. The left column starts with three triangles (rows 2, 3 and 4) and has already lost the row-4 one and then the row-3 one. The fourth figure therefore loses the last left-column triangle and keeps 6: one in row 1, one in row 2 and two in each of rows 3 and 4. That figure is option (a).

Letter-cluster analogy Compare NSBX with QQZA position by position: N $\to$ Q is +3, S $\to$ Q is -2, B $\to$ Z is -2 (wrapping past A), X $\to$ A is +3 (wrapping past Z). The second pair obeys the same rule: O +3= R, K -2= I, I -2= G, R +3= U, giving RIGU. Apply $+3,-2,-2,+3$ to DTAF: D (4)+3=7= G, T (20)-2=18= R, A (1)-2=25= Y, F (6)+3=9= I. So DTAF is related to GRYI, option (d).

Syllogism, conclusions 'All actors are writers' puts the whole Actor circle inside Writers. 'Some writers are dancers' and 'Some dancers are stars' are only partial overlaps, so draw them just touching and nothing more. Conclusion (I): Stars meets only Dancers, and Dancers need not reach the Actor circle at all, so 'Some stars are actors' is not forced - it does not follow. Conclusion (II): the part of Writers shared with Dancers can lie completely outside the Actor circle, so 'Some dancers are actors' is not forced either. Neither conclusion follows, option (b).

Letter series with blanks Each group holds four letters, so write the five groups one below the other and read each position down its own column. 1st letters: D, G, J, M, P - each step is +3. 2nd letters: G, J, M, P, S - each step is +3. 3rd letters: C, F, I, L, O - each step is +3. 4th letters: E, H, K, N, Q - each step is +3. The blanks come in the order 1st of group 1, 2nd of group 2, 3rd of group 3, 4th of group 4 and 4th of group 5, i.e. D, J, I, N, Q. Hence the correct option is (c).

Paper folding and punching The sheet is folded twice: first the top half comes down on the bottom half, then the right half comes over on to the left half. The punch is made in the quarter that is left. Undo the last fold first. Opening the vertical fold copies the punch into the bottom-right quarter as a left-right mirror image. Now undo the first fold. Opening the horizontal fold copies both punches into the top half as top-bottom mirror images. So the open sheet carries four punches, one per quarter, each one a mirror of its neighbours across the fold lines - the two top punches point downwards and the two bottom punches point upwards. Only option (a) shows this, so it is the answer.

Two-row seating Number the four facing pairs 1 to 4 across the page, so seat 1 of row 1 faces seat 1 of row 2. Row 2 faces north, so its right runs towards seat 4; 'no one sits to the right of S' fixes S in seat 4. Row 1 faces south, so its right runs the other way, towards seat 1; 'no one sits to the right of N' fixes N in seat 1. Only one person sits between S (seat 4) and A, so A takes seat 2. For the south-facing row, left runs towards seat 4, so 'O sits second to the left of T' means T in seat 2 and O in seat 4; E is left with seat 3. M must not face E (seat 3), so M takes seat 1 and D takes seat 3. Seat 4 holds O in row 1 and S in row 2, so O and S face each other - option (d).

Linear seating, one row Number the seats 1 to 7 from left to right; everyone faces north, so their right is towards seat 7. 'No one sits to the right of N' puts N in seat 7. Three people between N and X means the gap is 4 seats, so X sits in seat 3. Two people between X and W means a gap of 3 seats, so W sits in seat 6 (seat 0 does not exist). M is third to the left of L, and Y is immediately right of L; the only fit in the free seats 1, 2, 4, 5 is M in seat 1, L in seat 4 and Y in seat 5, leaving seat 2 for O. Between O (seat 2) and W (seat 6) sit X, L and Y. That is three people, option (b).

Number series, growing gaps Take the difference between consecutive terms. 34-28=6, 44-34=10, 58-44=14, 76-58=18. These differences themselves rise by 4 each time, so the next difference is 18+4=22. Missing term =76+22=98. Hence the correct option is (d).

Mirror image, vertical mirror LM is a vertical line standing to the right of the figure, so the image is the left-right mirror: heights stay where they are and every part swaps its side. The thick black band that runs down the right edge must appear down the left edge. The black band along the bottom, which starts part-way along and reaches the right edge, must start at the left edge and stop part-way along. The small black rectangle in the top-left corner must move to the top-right corner. The two slanting lines fall from the left edge towards the right, so in the image they must fall from the right edge towards the left. Option (a) turns the figure upside down, (c) flips it top-to-bottom and (d) leaves the black bands on their original sides. Only option (b) satisfies every check, so it is the mirror image.

Letter-to-digit coding Put the two words and their codes side by side and strike out what they share. FILE and LIVE share the letters I, L and E; the codes 6312 and 3241 share the digits 3, 1 and 2. So I, L, E use up the digits 3, 1, 2 in some order, and whatever is left in a word must match whatever is left in its code. F is the only letter in FILE that LIVE does not have, and 6 is the only digit in 6312 that 3241 does not have, so F =6. V is the only letter in LIVE that FILE does not have, and 4 is the only digit in 3241 that 6312 does not have, so V =4. Hence the correct option is (a).