Reasoning: previous-year questions

Answer: (A) CZPYQX

Compare the letters of APPLES and BORJHP position by position: A to B (+1), P to O (-1), P to R (+2), L to J (-2), E to H (+3), S to P (-3). The rule is therefore +1, -1, +2, -2, +3, -3. Applying it to BANANA: B+1 = C, A-1 = Z, N+2 = P, A-2 = Y, N+3 = Q, A-3 = X, giving CZPYQX (A). Options B and C keep Z in several places because they apply only a -1 shift to every A. Tip: write A = 1 to Z = 26 and remember that the alphabet wraps around, so one step back from A is Z.

Answer: (B) Bicycle

Car, bus and train are driven by engines or motors, while a bicycle is moved by human muscle power, so the bicycle is the odd one out, as in PSC's key. A second possible grouping exists (car, bus and bicycle run on roads, the train on rails), which is why such questions should be answered by the most basic difference: here, the source of power. Bicycle is also the only two-wheeler and the only vehicle in the list that needs no fuel or electricity.

Answer: (D) 1 km West

Opposite moves cancel out: 500 m North-East and 500 m South-West cancel each other, and 1 km South and 1 km North cancel each other. The only move left is the 1 km walked after 'turning right' while facing South, and a right turn from South faces West. So he ends 1 km West of the start (D). With coordinates: (354, 354), then (354, -646), then (-646, -646), then (-1000, -1000), and finally (-1000, 0). Tip: in direction-sense problems, pair off equal and opposite legs before doing any calculation, and remember that turning right means clockwise (N to E to S to W).

Answer: (B) P

Each letter is three places ahead of the previous one: A (1), D (4), G (7), J (10), M (13), so the next is the 16th letter, P. The letter after that would be S (19). Option A (O) is a jump of only two and option C (Q) a jump of four. Handy aid for letter positions: EJOTY marks the 5th, 10th, 15th, 20th and 25th letters, so P, coming just after O (15), is the 16th.

Answer: (B) South-East

A navigation map in heading-up mode always shows the direction of travel at the top of the screen. If the North arrow points to the bottom-right corner, North lies $135^\circ$ clockwise from the car's heading, so the car is heading $135^\circ$ anticlockwise from North, i.e. South-West. A $90^\circ$ left (anticlockwise) turn from South-West gives South-East (B). Quick check: when you face South-West, your left hand points South-East and your right hand North-West, so option D is what a right turn would give, the common trap. In compass bearings: South-West is $225^\circ$, and $225^\circ - 90^\circ = 135^\circ$, which is South-East.

Answer: (B) Circle

Square, triangle and rectangle are polygons, closed figures made of straight sides meeting at vertices, whereas a circle is a curved figure with no sides or corners, so the circle is the odd one out. A second pattern might be tried (the triangle has three sides while the square and rectangle have four), but it does not separate one figure from the other three, because the circle fits neither group. Always choose the property that isolates exactly one option.

Answer: (C) BAG

RABBIT has the letters R, A, B, B, I, T. RAT (R, A, T), BAT (B, A, T) and BIT (B, I, T) can all be made from these, but BAG needs the letter G, which is not in RABBIT. Method: tick off each letter of the option against the key word, remembering that a letter can be used only as many times as it occurs (here only B occurs twice). Other words that can be formed from RABBIT include BAR, RIB, TAB, BRAT and RABBI.

Answer: (C) Some white X-brand cars with radial tyres are parked here.

Statement 1 says every X-brand car parked here is white, and statement 2 says some of these cars have radial tyres; together they give 'some white X-brand cars with radial tyres are parked here' (C). The statements say nothing about the tyres of other brands, so A and D (which are identical in the booklet) cannot be concluded, and they say only that the X-brand cars here are white, so B ('only white cars are parked here') does not follow, since cars of other brands and colours may also be parked. 'All cars are not X-brand' simply means that some cars are of other brands. Rule: a valid conclusion must not go beyond the group the statements actually speak about.

Answer: (A) A quadrilateral cannot be square unless it has four equal sides, but having four equal sides doesn't guarantee a quadrilateral to be a square.

A necessary condition is one without which the result cannot happen; a sufficient condition is one that by itself guarantees the result. Every square has four equal sides (necessary), but four equal sides do not make a square, because a rhombus also has four equal sides; right angles are needed as well (so the condition is not sufficient). Option A says exactly this. Options B and C reverse the meaning by denying that squares have equal sides, and D denies any connection. In symbols, 'P is necessary for Q' means Q implies P, and 'P is sufficient for Q' means P implies Q.

Answer: (D) All persons with high education has good earnings.

The statement has the form 'if P then Q' (highly educated implies earns well). Option D, 'all highly educated persons have good earnings', is the same statement in other words, so it must be true. Options A and C are the converse ('if Q then P'), the error called affirming the consequent, since a person may earn well without being highly educated. Option B is the inverse ('if not P then not Q'), which also does not follow. The only other statement that is logically equivalent to the original is its contrapositive: 'a person who does not earn well is not highly educated'.

Answer: (A) D, C, A, B

C is older than D but younger than B, so B > C > D. A is "older but not eldest", i.e. A is older than C yet younger than B, giving B > A > C > D. In ascending order of age (youngest first) this is D, C, A, B. Check the other options: (B) puts C before D although C is older; (C) makes A the eldest, which is ruled out; and (D) starts with the eldest, B, so it is not ascending at all. In such questions always note whether ascending or descending order is asked.

Answer: (C) rstr

The series is the block "strs" repeated four times: strs / strs / strs / strs. Writing out the 16 letters, the given ones are s, t, _, s, _, t, r, s, s, _, r, s, s, t, _, s, so the four blanks must be r, s, t and r in that order, i.e. "rstr". Check: st(r)s (s)trs s(t)rs st(r)s. For such questions, count the total number of letters (given letters plus blanks) and look for a repeating block whose length divides that total, here 16 = 4 × 4.

Answer: (C) 11

Each number on one half of the wheel is linked to the number diametrically opposite it by the rule $n \rightarrow 2n+1$: opposite 2 is $2\times2+1=5$, opposite 3 is $2\times3+1=7$, and opposite 4 is $2\times4+1=9$. The sector marked "?" lies opposite 5, so it must be $2\times5+1=11$. In wheel or circle puzzles, first test the relation between opposite sectors, then between adjacent sectors, and only then look for a running series around the rim.

Answer: (D) 44

B did better than A and exactly two students stand between them, so B's rank from the top is $10-3=7$. B is thus 7th from the top and 38th from the bottom, and the total number of students is $7+38-1=44$. The general rule is: total = (rank from top) + (rank from bottom) − 1, because the person concerned is counted twice. Had B been worse than A, B would have been 13th from the top and the total would have been 50, which is not among the options.

Answer: (C) 7

Total teaching periods per day = $3\times6$ (Classes VI, VII, VIII) $+\ 2\times7$ (Classes IX, X) $=18+14=32$. Each teacher can take at most 5 periods, so the number of teachers needed is at least $32\div5=6.4$, i.e. 7 after rounding up. Six teachers could cover only 30 periods, which is short by 2. Seven teachers can cover 35 periods, and since only five classes run at any one time, a workable timetable exists. In "minimum number" questions always round up, never down.

Answer: (D) 835961264

From PARDON = 721890 we get P=7, A=2, R=1, D=8, O=9, N=0. From MERCY = 53164 we get M=5, E=3, R=1, C=6, Y=4 (R is 1 in both, which confirms the code). So DEMOCRACY = D(8) E(3) M(5) O(9) C(6) R(1) A(2) C(6) Y(4) = 835961264. Options (A), (B) and (C) each change one or two digits (a 7 for 6, or 5 and 3 interchanged), so compare the options digit by digit instead of trusting a quick glance.

Answer: (D)

"Books" is the widest class, so it is the large circle. Every Bengali book is a book and every novel is a book, so both small circles must lie wholly inside the large one. Some Bengali books are novels (and some novels are Bengali books), so the two small circles must overlap each other. Only the last diagram shows this. The first diagram would suit two unrelated sub-classes such as "books, novels, dictionaries"; the diagrams in which a small circle crosses the boundary of the large one would wrongly mean that some Bengali books or novels are not books.

Answer: (C) Sunday

Three days before Friday is Tuesday, so the 7th is a Tuesday. Dates that differ by a multiple of 7 fall on the same weekday, so the 14th and the 21st are also Tuesdays. The 19th is two days before the 21st, i.e. a Sunday. Alternatively, from the 7th to the 19th is 12 days, which is one week and 5 days, and five days after Tuesday is Sunday. Read "earlier than" carefully: if you count three days after Friday by mistake you start from Monday and get the wrong day.

Answer: (C) (C, E)

Number the six seats 1 to 6 round the table. Put B at seat 1; A sits opposite at seat 4. B is between C and D, so C and D occupy seats 2 and 6; A is between E and F, so E and F occupy seats 3 and 5. E is next to D (to D's left), so if D is at seat 2, E is at seat 3, which leaves F at seat 5 and C at seat 6. Opposite pairs in a hexagon are 1–4, 2–5 and 3–6, i.e. A–B, D–F and C–E. Hence C and E face each other. The mirror arrangement (D at 6, E at 5) gives the same opposite pairs.

Answer: (A) Mother-in-law

X is the wife of Z, and P is the mother of X, so P is the mother of Z's wife, i.e. Z's mother-in-law. The details about Y (P's brother) and Q (P's husband) are extra information put in to distract; they would make Y the maternal uncle of X, and Q the father of X and father-in-law of Z. In blood-relation questions, pick out only the links that connect the two persons asked about, and draw a small family tree if needed.