Verbal and Logical Reasoning

Reasoning is worth 7–10 of the 50 mathematics questions in the published pattern, split here between this chapter and the next.

These are the questions where practice beats talent: each type has a fixed method, and the same question shapes recur every year. This chapter covers the verbal side: codes, family relations, directions, ranking and syllogisms.

14.1 Coding and decoding

• Positions: A=1, B=2, … Z=26. The opposite letter of the one at position n is at 27-n (E↔V).
• Shift codes: find the shift on one letter and apply it to the rest. ROSE→TQUG is +2, so LAKE→NCMG. TABLE→UBCMF is +1, so CHAIR→DIBJS.
• Sum codes: add the position values (G=7, O=15, so GO=22).
• Check the first two letters before trusting a pattern; the same shift can be +1, +2, −1 in alternating positions.

14.2 Blood relations and direction sense

• "My mother's only son" is me or my brother; "my father's only son" is me. "Mother's brother" is a maternal uncle; "father's sister's son" is a cousin.
• Work backwards from the person being pointed at, one link at a time, and draw generations as levels.
• Directions: a right turn from North faces East, then South, then West. A left turn from North faces West. A 180° turn reverses. Displacement for legs at right angles is \sqrt{a^2+b^2} (3-4-5, 5-12-13, 8-6-10). At sunrise a person's shadow falls to the west.

(a) Draw the family tree first

(b) Compass rose: N, E, S, W

14.3 Ranking, ordering and seating

• Rank from top T and from bottom B gives a total of T+B-1. Rank from bottom =N-T+1.
• Position from left L and right R gives a row of L+R-1.
• For "taller than" chains, write them as A>B>C and read the extremes.

14.4 Syllogisms and statement–conclusion

• All A are B ⇒ some B are A, but not all B are A. No A is B ⇒ no B is A. Some A are B ⇒ some B are A.
• All A are B, all B are C ⇒ all A are C. Anything beyond the statements (a universal claim from a particular one) is a trap.
• Draw circles: A inside B inside C.

14.5 Eight traps in verbal reasoning

Reasoning questions have one correct method and several tempting shortcuts. These eight traps account for most wrong answers in the model papers, so read each one and test it on a question.

1. Check the rule on at least two letters. A code such as ROSE to TQUG looks like +2, but you must test R to T, O to Q, S to U and E to G before you apply it to LAKE (Fig 14.1). Some codes alternate, for example +1, +2, +1, +2. A rule that fits only the first letter is a guess, not a rule.
2. Opposite letters add to 27, not 26. A is 1 and Z is 26, so the opposite of the letter at position n is at 27-n. E (5) pairs with V (22), and M (13) pairs with N (14). If you use 26-n you will be wrong by one letter in every option.
3. "Only son" and "only child" are different. "My mother's only son" is the speaker (if male) or the speaker's brother, but "my father's only son" is always the speaker himself when he is male. "My father's sister's son" is a cousin, not a brother. Write each phrase as a link on the tree before you look at the options (Fig 14.2).
4. Draw generations on levels. Put grandparents on the top row, parents in the middle and children at the bottom, with a short line for each marriage and each parent–child link. Then move one link at a time. Students who do the whole chain in their heads often swap "uncle" and "cousin".
5. A right turn depends on the direction you face. Facing North, right is East; facing East, right is South; facing South, right is West. A left turn goes the other way round the compass, and a U-turn reverses (Fig 14.3). Track the facing direction after every leg, not just the lengths.
6. Displacement is not distance walked. In the 10 m, 6 m, 2 m walk the distance walked is 18 m but the displacement is only 10 m from the start (Fig 14.3). For legs at right angles use \sqrt{a^2+b^2} and name the direction using the final north–south and east–west moves. A shadow in the morning falls to the west.
7. Rankings overlap by one person. Rank 12 from the top and 30 from the bottom gives 12+30-1=41, not 42 (Fig 14.4). The same L+R-1 rule holds for positions from left and right. To find the rank from the bottom use N-T+1.
8. "All A are B" does not mean "All B are A". In a syllogism accept only a conclusion that is true in every possible picture (Fig 14.5). From "all A are B, some B are C" nothing follows about A and C, because the C circle may lie outside A. Look out for options that turn a "some" statement into an "all" statement.

14.5.1 Worked checks

Q. In a code CAT is written XZG. How is DOG written?

Answer. Each letter is replaced by its opposite, the letter at position 27-n: C(3) becomes X(24), A(1) becomes Z(26), T(20) becomes G(7). So D(4) becomes W(23), O(15) becomes L(12), G(7) becomes T(20). DOG is written WLT.

Q. Ram is 12th from the top and 30th from the bottom of a class. How many students are in the class?

Answer. Ram is counted in both ranks, so the class size is 12+30-1=41. Check: the rank from the bottom is 41-12+1=30, which agrees with the question (Fig 14.4).

Q. A man walks 10 m North, turns right and walks 6 m, then turns right and walks 2 m. How far is he from the start and in which direction?

Answer. After the first right turn he faces East and after the second he faces South. His position is 6 m east and 10-2=8 m north of the start. The distance is \sqrt{6^2+8^2}=10 m, towards the north-east (Fig 14.3).

Q. Statements: all pens are books; some books are cups. Does "some pens are cups" follow?

Answer. No. Pens lie inside books, but the cups that are books may all sit outside the pens, so nothing definite follows about pens and cups. This is case (b) of Fig 14.5.

Practice questions

Set A — Recall (20 questions)

1. If A=1, B=2, …, the sum of the values of the letters in CAB isa5b6c7d9
2. The letter opposite to E in the alphabet (A↔Z) isaUbWcTdV
3. If each letter is replaced by the next, CAT is writtenaDBUbBZScDAUdCBU
4. If MIND is coded NJOE, then BOOK is codedaCPQLbAPNJcCPPLdCQPL
5. Pointing to a man, a woman says, "He is the son of my mother's only son." The man is herasonbnephewcbrotherdcousin
6. My father's only sister's son is myacousinbunclecbrotherdnephew
7. Facing north, a person turns right and then right again. He now facesanorthbeastcwestdsouth
8. A man walks 3 km east and then 4 km north. His distance from the start isa7 kmb1 kmc5 kmd12 km
9. A student is 7th from the top and 14th from the bottom. The class hasa20 studentsb21 studentsc22 studentsd19 students
10. All pens are books and all books are bags. Which conclusion follows?aAll bags are pensbAll books are penscSome bags are not booksdAll pens are bags
11. "No A is B" impliesaall B are Abno B is Acsome A are Bdsome B are A
12. In the morning, a man's shadow falls towards theaeastbnorthcwestdsouth
13. If ROSE is TQUG, then LAKE isaNCMGbMBLFcJYICdNDMH
14. Pointing to a girl, Ram says, "She is the daughter of my father's only son." The girl is Ram'sasisterbniececmotherddaughter
15. A person facing east turns left through 90°. He now facesasouthbeastcnorthdwest
16. A mother's brother is called aapaternal unclebmaternal uncleccousindnephew
17. Ram is 10th from the left and 15th from the right in a row. The row hasa24 personsb25 personsc23 personsd26 persons
18. "Some A are B" impliesaall A are Bbno A is Bcsome B are Adall B are A
19. The direction opposite to north-east isanorth-westbsouth-eastcnorthdsouth-west
20. If Z=1, Y=2, …, A=26, the value of C isa3b24c23d25

Set B — Understanding (12 questions)

1. If TABLE is coded UBCMF, then CHAIR is codedaDHBJSbBGZHQcDIBJSdDJBIS
2. In a code, the value of a word is the sum of its letter positions (A=1). The value of NO isa29b28c30d27
3. A man walks 10 m north, turns right and walks 6 m, then turns right again and walks 10 m. His distance from the start isa26 mb10 mc16 md6 m
4. A man walks 8 km west and then 6 km south. His distance from the start isa14 kmb10 kmc2 kmd48 km
5. A is B's sister, C is B's mother, D is C's father and E is D's mother. A is related to D asadaughterbniececgranddaughterdsister
6. Pointing to a photograph, Rita says, "He is the son of the only son of my grandfather." The man is Rita'sabrotherbuncleccousindfather
7. In a class of 40, Hari ranks 12th from the top. His rank from the bottom isa27thb28thc30thd29th
8. A person facing north turns 90° left and then turns 180°. He now facesawestbeastcnorthdsouth
9. Statements: All roses are flowers. Some flowers fade. Conclusions: I. Some roses fade. II. All flowers are roses. Which follows?aneither I nor IIbonly Iconly IIdboth I and II
10. Find the odd one out: 8, 27, 64, 100a8b27c100d64
11. Find the odd one out: Delhi, Kathmandu, Colombo, MumbaiaDelhibKathmanducColombodMumbai
12. Ram is taller than Hari and Hari is taller than Sita. The shortest isaRambSitacHaridcannot be determined

Set C — Application (8 questions)

1. A man walks 5 km east and then 12 km north. His shortest distance from the start isa17 kmb7 kmc60 kmd13 km
2. If letters are replaced by their positions, the sum for DOG (D=4, O=15, G=7) isa26b24c28d22
3. Hari is 15th from the top and 20th from the bottom. The class hasa35 studentsb36 studentsc34 studentsd33 students
4. All lawyers are graduates and Ramesh is a lawyer. Which conclusion follows?aRamesh is not a graduatebRamesh is a graduatecAll graduates are lawyersdSome graduates are not lawyers
5. A is the brother of B, B is the sister of C and C is the father of D. D is A'sasonbbrotherccousindnephew or niece
6. A person facing east turns through 180° and then turns left. He now facesasouthbnorthceastdwest
7. Find the odd one out: 3, 5, 7, 9, 11a3b5c9d11
8. Pointing to a woman, a man says, "Her mother is the only daughter of my mother." The woman is the man'sasisterbniececdaughterdmother