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: (B) accb

Filling a, c, c, b gives abca a bcaab c aab c aa b ca = abca abca abca abca abca, the block 'abca' repeated five times. Any other choice breaks this repeating pattern; for example 'ccaa' puts c after 'abca' where the next block must start with a.

Answer: (C) Plagiarism

Misappropriation is the dishonest taking of someone else's money; the matching wrong for writing is plagiarism, passing off someone else's writing as one's own. Theft and deception are general wrongs not specific to writing, and a mistake is not dishonest at all.

Answer: (A) 10%

Candidates who passed in at least one subject = 60 + 70 − 40 = 90%. So those who failed in both = 100 − 90 = 10%. 40% and 30% are the shares who failed in English and in Maths taken one at a time, not those who failed in both.

Answer: (A) 265

In the diagram the Hindi circle contains 70 (Hindi only) + 65 (Hindi and Bengali) + 53 (all three) + 47 (Hindi and English) = 235 persons. Those who do not know Hindi are 500 − 235 = 265, which is also the sum of the remaining regions 120 + 62 + 83. 200, 255 and 201 miss one or more of these regions.

Answer: (C) 48

Each word's code is the sum of its letters' alphabet positions: T + I + E = 20 + 9 + 5 = 34 and N + O + W = 14 + 15 + 23 = 52. So WAX = 23 + 1 + 24 = 48. 47, 46 and 45 are off by miscounting a letter.

Answer: (A) 185

In each figure the bottom number is (sum of the top numbers) × (their difference): (11 + 5) × (11 − 5) = 96 and (15 + 9) × (15 − 9) = 144. So the missing number is (21 + 16) × (21 − 16) = 37 × 5 = 185. The other options do not follow this rule.

Answer: (D) Uncle

The key's answer is (D) Uncle. An uncle does appear in the passage: C's father is A's uncle, and D's father is that uncle's brother. Note: D is one of the two daughters, so she cannot be an uncle; her father is an uncle of A, which makes D A's cousin, option (A), the same relation the key gives for C in Q61.

Answer: (B) 10 km North-East

Net movement is 15 − 9 = 6 km North and 8 km East. The straight-line distance is $\sqrt{6^2 + 8^2} = 10$ km, and he is north and east of the start, i.e. North-East. South-West reverses the direction.

Answer: (D) Cousin

C is the only son of A's uncle, so C is A's cousin. F is E's sister and E is A's brother, so F is A's sister and C is F's cousin too. C is a child of the same generation, so 'uncle' and 'son' are impossible, and C's father is not F's father, so C is not her brother.

Answer: (B) 1

Across the four views (i)–(iv), the face 2 is seen next to 6, 4, 3 and 5. A face cannot be adjacent to its opposite, so the only number left for the face opposite 2 is 1. 4, 5 and 3 are all seen beside 2.