4 February 2025 · Shift 1

Letter-to-number coding Rule: replace every letter by its position in the English alphabet, increased by 3. Check on BSGN: 2+3=5, 19+3=22, 7+3=10, 14+3=17, which is 5-22-10-17. Check on TAUE: 20+3=23, 1+3=4, 21+3=24, 5+3=8, which is 23-4-24-8. Now PJDQ has positions P =16, J =10, D =4, Q =17. Adding 3 to each: 16+3=19, 10+3=13, 4+3=7, 17+3=20. So PJDQ is coded as 19-13-7-20, i.e. option (b).

Venn diagram of classes Take the three classes two at a time. Some cardiologists are female and some are male, so Female and Cardiologist overlap only partly - neither is inside the other. Some engineers are female and some are male, so Female and Engineer also overlap only partly. A person cannot practise as a cardiologist and as an engineer at the same time, so those two classes have nothing in common and stay completely separate. The required picture is a middle circle cutting the two outer circles, with the two outer circles apart from each other. That is option (a).

Odd letter-cluster out Write the alphabet position of each letter and find the gap between consecutive letters. HJL gives 8, 10, 12 - gaps +2 and +2. FHJ gives 6, 8, 10 and NPR gives 14, 16, 18 - again gaps +2 and +2. SUV gives 19, 21, 22 - gaps +2 and +1, so the second gap is wrong. Hence SUV does not belong to the group - option (b).

Dice - opposite faces Rule: two faces that are seen together in one view can never be opposite each other. In the first view R is seen with L and T, so R is adjacent to L and to T. In the second view R is seen with O and A, so R is adjacent to O and to A as well. R is therefore adjacent to four faces - L, T, O and A - and the only face left over is E. So E lies opposite R. Hence the face opposite E is R - option (d).

Word-code letter matching In this type the digits are not in order, so match the words and the codes as sets. Letters: JAMB and BALM have A, B and M in common; J belongs only to the first word and L only to the second. Digits: 5139 and 9521 have 5, 1 and 9 in common; 3 belongs only to the first code and 2 only to the second. So the three common letters A, B, M use up the three common digits 5, 1, 9. The letter left over in the first word, J, must take the digit left over in the first code, 3; the letter left over in the second word, L, must take the digit left over in the second code, 2. Hence the code for L is 2 - option (c).

Positional letter shift Compare the two given pairs letter by letter; the shift depends on the position in the word, not on the letter itself. CLONE → BLUKU: C-1=B, L+0=L, O+6=U, N-3=K, E-10=U (counting round the alphabet, 5-10=-5, i.e. 21=U). BOUND → AOAKT: B-1=A, O+0=O, U+6=A (since 21+6=27=1), N-3=K, D-10=T (since 4-10=-6, i.e. 20). So the fixed pattern of shifts is -1, 0, +6, -3, -10. Apply it to NICHE: N-1=M, I+0=I, C+6=I, H-3=E, E-10=U. Hence NICHE is written as MIIEU - option (c).

Number series - difference of differences Read the given string as the terms 208, 190, 163, 127, 82, ? Differences: 190-208=-18, 163-190=-27, 127-163=-36, 82-127=-45. The amounts subtracted are 18, 27, 36, 45 - each one is 9 more than the previous one. So the next amount to subtract is 45+9=54. 82-54=28. Hence the missing term is 28 - option (a).

Linear seating arrangement All seven face north, so a person's left is the left side of the drawing; write each clue as a small block, left to right. M is immediately left of P gives M P; O is immediately left of Q gives O Q. R is immediately right of P and immediately left of L gives P R L. N is immediately right of L and immediately left of O gives L N O. Joining M P, P R L, L N O and O Q gives the single row M P R L N O Q. Counting to the left of N: L is first and R is second. Hence R sits second to the left of N - option (c).

Letter-cluster analogy Compare each letter with the letter it becomes. SBCF → RADG: S → R and B → A are one step back; C → D and F → G are one step forward. NVMO → MUNP: N → M and V → U are one step back; M → N and O → P are one step forward. So the rule is -1, -1, +1, +1 on the four letters. Apply it to GUAX: G-1=F, U-1=T, A+1=B, X+1=Y. Hence GUAX is related to FTBY - option (b).

Letter-cluster series Treat the first, second and third letters of the clusters as three separate series. First letters: E(5), H(8), K(11), ?, Q(17) - the step is +3, so the missing letter is 11+3=14, i.e. N. Second letters: H(8), J(10), L(12), ?, P(16) - the step is +2, so the missing letter is 12+2=14, i.e. N. Third letters: O(15), P(16), Q(17), ?, S(19) - the step is +1, so the missing letter is 17+1=18, i.e. R. Hence the missing cluster is NNR - option (d).

Paper folding and cutting The sheet is folded once - the right half is turned over on to the left half - so the paper now lies in two layers. Every cut made on the folded piece therefore appears twice on the open sheet: once where it was actually cut and once as its mirror image across the fold. The semicircular notch on the top edge and the one on the bottom edge each open out into two notches, giving two notches above and two below. The rectangular piece was cut with one of its sides lying on the fold itself, so its two halves join on unfolding into a single rectangle in the middle of the sheet. The open sheet therefore shows two notches on the top edge, two on the bottom edge and one rectangular hole at the centre, which is option (b).

Alphabetical rearrangement The word GRACEFUL has the eight letters G, R, A, C, E, F, U, L. Arranged in English alphabetical order they read A, C, E, F, G, L, R, U. Compare the two words position by position: G-A, R-C, A-E, C-F, E-G, F-L, U-R, L-U. No position carries the same letter in both words, so the number of letters that stay in place is none.

Syllogism All three statements are of the type 'All … are walls', so gabions, concretes and bridges are each a group lying completely inside the group of walls. Two groups placed inside one larger group are not forced to touch each other - they may sit entirely apart, as drawn above. So 'Some bridges are gabions' is only a possibility and never a certainty; conclusion (I) does not follow. For exactly the same reason 'Some concretes are bridges' need not be true, so conclusion (II) does not follow either. Hence neither conclusion (I) nor (II) follows.

Mirror image MN is a vertical mirror standing to the right of the figure, so the image is obtained by turning the figure left-to-right; whatever is on top stays on top. Now examine the figure itself: the inverted triangle, the dot inside it and the rectangle below are all placed symmetrically about the vertical centre line of the square. A figure that is already symmetrical about a vertical line reflects into itself, so the mirror image must look exactly like the given figure. Only option (d) reproduces it completely - the dot inside the triangle, and the two slanting lines running from the upper corners of the rectangle down to the middle of its lower side. In (a) the slanting lines start from the top centre instead, (b) has lost both slanting lines and (c) has lost the dot, so none of them can be the image.

Interchange of signs In the given equation $50-9÷1+63\times 7$, interchange $÷$ with $\times$ and interchange + with -. The equation becomes $50+9\times 1-63÷7$. Solve it by BODMAS - division and multiplication come first: $9\times 1=9$ and $63÷7=9$. So the value is 50+9-9=50, and the question mark stands for 50.

Figure series Read each figure of the series column by column. The left column always carries the same five marks - the dollar sign, the percent sign, two triangles and a circle - so the missing figure must still show five marks there. The middle and right columns change turn by turn: first the topmost U of the middle column becomes an O, then one more U appears at the top of the right column, and so on. The fourth figure shows two O's in the middle column and one U on the right, so the change now due is on the right - the missing figure keeps O, O, U, U, U in the middle and shows two U's on the right. Only option (b) matches on all three columns; option (a) is an earlier figure of the same series, and options (c) and (d) drop a mark from the left column.

Missing letters series The series is built from five groups of four letters each, and exactly one letter is missing from every group. Read the groups column-wise. The first letters run L, O, R, U, X - each one is +3 from the letter before it. The second letters run H, K, N, Q, T, the third letters K, N, Q, T, W and the fourth letters M, P, S, V, Y - every column again moves forward by 3. Reading the blanks in order gives L (group 1), K (group 2), Q (group 3), V (group 4) and Y (group 5). So the required combination of letters is LKQVY.

Number series The series is $4,6,10,18,34,?$ Take the consecutive differences: 6-4=2, 10-6=4, 18-10=8 and 34-18=16. The number being added doubles every time - $2,4,8,16$ - so the next number to be added is 32. Hence the missing term is 34+32=66.

Two-row seating arrangement Row 1 (D, E, O, S) faces south, so for those four people 'left' points east; row 2 (F, A, R, M) faces north, so for them 'left' points west. 'Only D sits to the left of E' means exactly one person stands on E's left, so in row 1's own left-to-right order the first two seats are D and E. 'Only one person sits between D and O' then puts O in the third seat and S in the fourth: row 1 reads D, E, O, S from its own left. 'Only R sits to the left of A' puts R first and A second in row 2, and 'only one person sits between A and F' puts F in the fourth seat, leaving M third: row 2 reads R, A, M, F from its own left. Now redraw both rows from west to east. Row 1 faces south, so its own left-to-right order runs east to west and becomes S, O, E, D; row 2 faces north, so its order is already west to east, R, A, M, F. Two people in the same column of this picture are the ones sitting opposite each other, so the facing pairs are S-R, O-A, E-M and D-F. Hence E and M face each other.

Blood relation coding Break the chain 'N @ E $ J @ S' into the three links it contains and decode each symbol. 'N @ E' means N is the daughter of E, so E is a parent of N. 'E $ J' means E is the husband of J, so E and J are a married couple and J is a woman. 'J @ S' means J is the daughter of S, which only tells us about the older generation. N is the daughter of E, and J is E's wife, so N is the daughter of J as well. Therefore J is the mother of N.