12 February 2025 · Shift 2

Syllogism Put all three statements into one figure: the Words circle cuts the Paragraphs circle, the Paragraphs circle lies wholly inside Essays, and the Stories circle stays completely outside Essays. Conclusion (I): every paragraph is an essay and no essay is a story, so no paragraph can be a story. (I) does not follow. Conclusion (II): only some words are paragraphs, so the remaining words may lie outside the Essays circle altogether. (II) does not follow. Neither conclusion follows, so option (b) is correct.

Venn diagram of classes A table can be made of wood and a table can be made of steel, so the Table circle must cut both the Wood circle and the Steel circle. No piece of wood is steel and no piece of steel is wood, so those two circles must stay completely apart. Only a chain of three circles shows all three facts at once: Wood cuts Table, Table cuts Steel, and Wood never touches Steel. That is exactly option (b), so option (b) is correct.

Number coding 'AUNT' → '8793' and 'NUTS' → '3598'. The two words share the letters U, N and T, and the two codes share the digits 8, 9 and 3, so those three digits stand for U, N and T in some order. In AUNT the only letter left over is A and the only digit left over is 7, so A = 7. In NUTS the only letter left over is S and the only digit left over is 5, so S = 5. The code for S is therefore 5, so option (c) is correct.

Letter-cluster analogy Compare the first pair letter by letter: R → U, S → V, T → W, R → U. Every letter moves 3 places forward in the alphabet. The second pair obeys the same rule: W → Z, X → A, Y → B, W → Z, the alphabet being counted cyclically. Applying +3 to FGHF gives F → I, G → J, H → K, F → I, that is IJKI, so option (c) is correct.

Number series Take the gap between one term and the next: 39-32=7, 44-39=5, 51-44=7, 56-51=5. The gaps alternate +7, +5, +7, +5, so the next gap must again be +7. Hence the missing term is 56+7=63, so option (d) is correct.

Odd letter-cluster Write the alphabet position of each letter and look at the gaps inside every cluster. GZS: $7\to 26\to 19$, that is -7 each time (7-7=0, which is Z when the count is cyclic). OHA: $15\to 8\to 1$, again -7 each time. IBU: $9\to 2\to 21$, again -7 each time (2-7=-5, which is U when the count is cyclic). FYT: $6\to 25$ is -7, but $25\to 20$ is only -5; a -7 step from Y would give R, not T. FYT is the only cluster that breaks the $-7,-7$ rule, so option (c) is correct.

Number coding 'HAMS' → '5607' and 'MASK' → '0578'. The two words share the letters A, M and S, and the two codes share the digits 5, 0 and 7, so those three digits stand for A, M and S in some order. In HAMS the only letter left over is H and the only digit left over is 6, so H = 6. In MASK the only letter left over is K and the only digit left over is 8, so K = 8. The code for K is therefore 8, so option (c) is correct.

Circular seating For people facing the centre, a person's left is the clockwise side and the right is the anticlockwise side. Fix G's seat. Two people sit between G and I counted from G's right, so I is the third seat anticlockwise from G. Two people sit between I and H as well, so H is three seats from I; three seats clockwise from I is G's own seat, so H takes the seat three places anticlockwise from I. Three people sit between G and K, so K is four seats from G; four seats clockwise from G is already I's seat, so K sits four seats anticlockwise from G. Three seats are still empty and M must sit immediately clockwise of J (that is, on J's left); only one of the empty pairs is adjacent in that order, which fixes J and M and leaves the last seat for L. Counting from L towards L's right, that is anticlockwise, we meet H, then G, then M, so two people sit between L and M and option (a) is correct.

Interchange of signs Change the signs first: every - becomes $÷$, every $÷$ becomes -, every $\times$ becomes + and every + becomes $\times$. So $19+24-6\times 8÷6$ turns into $19\times 24÷6+8-6$. By BODMAS the multiplication and the division come first: $19\times 24=456$. $456÷6=76$. Now the addition and the subtraction: 76+8-6=78. The value in place of the question mark is 78, so option (b) is correct.

Blood relations Q is P's son and R is P's child as well, so Q and R are brother and sister. R is the wife of S and T is the son of S, so T is the son of R too. Q is therefore the brother of T's mother, that is T's mother's brother, so option (b) is correct. He cannot be T's brother, because Q belongs to R's generation and T to the next one.

Linear seating Number the seats 1 to 7 from the left end. No one sits to the left of X, so X takes seat 1. Four people sit between X and N, so N takes seat 6. Only three people sit to the right of L, so L takes seat 4. Seats 2, 3, 5 and 7 are left. M sits immediately to the left of W, and 2-3 is the only pair of neighbouring free seats, so M takes seat 2 and W seat 3. O is not an immediate neighbour of L, so O cannot take seat 5; O goes to seat 7 and Y to seat 5. The row reads X, M, W, L, Y, N, O, so O sits at the right-most end and option (d) is correct.

Embedded figure List the five strokes of the given figure: a base line running the whole width, a tall vertical rising from the right end of that base, a short horizontal stepping left from the top of that vertical, a diagonal rising to the right from the left end of that step, and a separate short diagonal rising to the right from the left end of the base. Options (b) and (d) are drawn from a stepped outline and an arrow-like shape; neither contains a full-width base joined to a tall right-hand vertical, so both are out at once. Option (a) does have the base, the vertical and the step, but the diagonal in its top-right cell falls from left to right instead of rising, so the stroke that must climb to the right above the step is missing there. In option (c) the top-right cell carries a diagonal that rises to the right, exactly the one the figure needs, and the base, the right-hand vertical, the step and the small rising diagonal at the bottom-left are all present as well. All five strokes are found in option (c) without any rotation, so option (c) is correct.

Number series Take the gap between one term and the next: 335-280=55, 280-228=52, 228-179=49, 179-133=46. The gaps themselves fall by 3 every time, so the next gap is 46-3=43. Hence the missing term is 133-43=90, so option (b) is correct.

Dice - opposite faces Write down the faces each view shows: view I has E on top with G and K beside it, and view II has L on top with E and N beside it. E appears in both views, and in them it is seen touching G, K, L and N - four different faces. A face on a cube touches four faces and is opposite the fifth, so the only face that can lie opposite E is H, the one face never seen next to it. The face opposite H is therefore E, so option (a) is correct.

Rearranging letters The word CABLEWAY uses the letters A, A, B, C, E, L, W, Y. In reverse alphabetical order they read Y, W, L, E, C, B, A, A. Compare the two rows place by place: C/Y, A/W, B/L, L/E, E/C, W/B, A/A, Y/A. Only the 7th place holds the same letter A in both rows. Exactly one letter stays where it was, so option (d) is correct.

Letter-cluster analogy Compare EWRT with LDYA letter by letter: E(5) → L(12), W(23) → D(4), R(18) → Y(25), T(20) → A(1). Each letter moves 7 places forward, the alphabet being counted cyclically, so 23+7=30 becomes 4 (D) and 20+7=27 becomes 1 (A). GYTV → NFAC obeys the same +7 rule, which confirms it. Applying +7 to BTOQ: B(2) → I(9), T(20) → A(1), O(15) → V(22), Q(17) → X(24), that is IAVX, so option (d) is correct.

Dice - opposite faces Write down the faces each view shows: view I has B on top with H and J beside it, and view II has A on top with V and J beside it. J appears in both views, and in them it is seen touching B, H, A and V - four different faces. A face touches four faces and is opposite the fifth, so J must lie opposite N, the one face never seen next to it. The face opposite N is therefore J, so option (d) is correct.

Letter series Compare the first two clusters column by column: C → F is +3, Z → Y is -1, V → U is -1. The same three steps carry FYU to IXT and IXT to LWS, so the rule holds throughout. Apply the steps to LWS: L+3=O, W-1=V, S-1=R. The missing term is OVR, so option (a) is correct.

Figure series Track the trapezium and the star separately; each one climbs exactly one row at every step. The trapezium starts in the middle row of the left column and reaches the top row of the same column in figure 2. A shape that is already in the top row reappears in the bottom row of the NEXT column, which is why the trapezium sits at the bottom of the middle column in figure 3 and climbs to the middle of that column in figure 4. The star does the same one step later: bottom, middle, then the top of the left column in figure 3, and the bottom of the middle column in figure 4. So in figure 5 the trapezium climbs from the middle to the top of the middle column and the star climbs from the bottom to the middle of the same column, one directly below the other. Options (a) and (b) place both shapes in the right-hand column and option (c) puts them side by side along the bottom; only option (d) shows the trapezium in the top row of the middle column with the star just below it in the middle row, so option (d) is correct.

Letter series with blanks The string holds 20 places, so split it into five blocks of four: _DHL / I_JN / KH_P / MJN_ / OLP_. Now read the blocks column by column. First letters: _, I, K, M, O - the run I, K, M, O rises by 2, so the first blank is G. Second letters: D, _, H, J, L - again a rise of 2, so that blank is F. Third letters: H, J, _, N, P - a rise of 2 again, so that blank is L. Fourth letters: L, N, P, _, _ - the same rise of 2 gives R and then T. Reading the blanks in order gives G, F, L, R, T, so option (d) is correct.