NIACL AO PrelimsPaper 4, booklet 8766076

Test booklet
प्रश्न पुस्तिका
Booklet No.
8766076
Series
C

NIACL AO Prelims Paper 4

Questions
100
Maximum marks
100
Minutes allowed
60

Roll No. assigned when you start

Instructions निर्देश

  1. This booklet has 100 questions in 3 parts: A. English Language (30), B. Reasoning Ability (35), C. Quantitative Aptitude (35).
  2. Each part has its own clock. When it runs out, that part closes and the next opens.
  3. Each question has 5 options and one right answer. A right answer earns 1 mark. A wrong answer costs 0.25. A question left blank scores nothing.
  4. Fill one bubble per question on the answer sheet. Unlike a real sheet, you can clear it and change your mind.

Scripting is off, so this page is a printed paper: answer on paper, then open each question’s working.

Part AEnglish Language

30 questions, 1 mark each, 0.25 off for a wrong answer

  1. Select the incorrectly spelt word.
    Question 1
    Answer and working

    Answer D

    innovattive is wrong; it is spelt innovative. The others are correct.

  2. Select the word closest in meaning to the given word.
    Forage
    Question 2
    Answer and working

    Answer D

    Forage (verb) and Scrounge share their main meaning. None of the other options does.

    Source: WordNet 3.1

  3. Select the word closest in meaning to the given word.
    Viable
    Question 3
    Answer and working

    Answer B

    Viable (adjective) and Feasible share their main meaning. None of the other options does.

    Source: WordNet 3.1

  4. Select the incorrectly spelt word.
    Question 4
    Answer and working

    Answer D

    concievable is wrong; it is spelt conceivable. The others are correct.

  5. Select the incorrectly spelt word.
    Question 5
    Answer and working

    Answer E

    inadmisible is wrong; it is spelt inadmissible. The others are correct.

  6. Select the correctly spelt word.
    Question 6
    Answer and working

    Answer B

    The correct spelling is vegetable.

  7. Select the correctly spelt word.
    Question 7
    Answer and working

    Answer A

    The correct spelling is admirable.

  8. Select the word closest in meaning to the given word.
    Tenacity
    Question 8
    Answer and working

    Answer E

    Tenacity (noun) and Perseverance share their main meaning. None of the other options does.

    Source: WordNet 3.1

  9. Select the word closest in meaning to the given word.
    Canny
    Question 9
    Answer and working

    Answer E

    Canny (adjective) and Clever share their main meaning. None of the other options does.

    Source: WordNet 3.1

  10. Select the one word that can replace the given group of words.
    Someone who takes the place of another person
    Question 10
    Answer and working

    Answer D

    Surrogate: someone who takes the place of another person.

    Source: WordNet 3.1

  11. Select the word opposite in meaning to the given word.
    Domestic
    Question 11
    Answer and working

    Answer B

    The opposite of domestic is Foreign.

    Source: WordNet 3.1

  12. Select the word closest in meaning to the given word.
    Larceny
    Question 12
    Answer and working

    Answer C

    Larceny (noun) and Theft share their main meaning. None of the other options does.

    Source: WordNet 3.1

  13. Select the one word that can replace the given group of words.
    Someone who dissipates resources self-indulgently
    Question 13
    Answer and working

    Answer C

    Waster: someone who dissipates resources self-indulgently.

    Source: WordNet 3.1

  14. Select the word opposite in meaning to the given word.
    Stimulate
    Question 14
    Answer and working

    Answer B

    The opposite of stimulate is Stifle.

    Source: WordNet 3.1

  15. Select the one word that can replace the given group of words.
    An attendant who loads guns for someone shooting game
    Question 15
    Answer and working

    Answer E

    Loader: an attendant who loads guns for someone shooting game.

    Source: WordNet 3.1

  16. Select the word closest in meaning to the given word.
    Apparent
    Question 16
    Answer and working

    Answer B

    Apparent (adjective) and Plain share their main meaning. None of the other options does.

    Source: WordNet 3.1

  17. Select the word opposite in meaning to the given word.
    Expand
    Question 17
    Answer and working

    Answer B

    The opposite of expand is Contract.

    Source: WordNet 3.1

  18. Select the one word that can replace the given group of words.
    A person who is voluntarily absent from home or country
    Question 18
    Answer and working

    Answer A

    Expatriate: a person who is voluntarily absent from home or country.

    Source: WordNet 3.1

  19. Select the correctly spelt word.
    Question 19
    Answer and working

    Answer A

    The correct spelling is additional.

  20. Select the word closest in meaning to the given word.
    Prosper
    Question 20
    Answer and working

    Answer E

    Prosper (verb) and Thrive share their main meaning. None of the other options does.

    Source: WordNet 3.1

  21. Select the word closest in meaning to the given word.
    Avert
    Question 21
    Answer and working

    Answer A

    Avert (verb) and Avoid share their main meaning. None of the other options does.

    Source: WordNet 3.1

  22. Select the one word that can replace the given group of words.
    Someone who assists a priest or minister in a liturgical service
    Question 22
    Answer and working

    Answer A

    Acolyte: someone who assists a priest or minister in a liturgical service.

    Source: WordNet 3.1

  23. Select the incorrectly spelt word.
    Question 23
    Answer and working

    Answer D

    judiciery is wrong; it is spelt judiciary. The others are correct.

  24. Select the word opposite in meaning to the given word.
    Persuasive
    Question 24
    Answer and working

    Answer E

    The opposite of persuasive is Dissuasive.

    Source: WordNet 3.1

  25. Select the correctly spelt word.
    Question 25
    Answer and working

    Answer D

    The correct spelling is chandelier.

  26. Select the word opposite in meaning to the given word.
    Uptown
    Question 26
    Answer and working

    Answer E

    The opposite of uptown is Downtown.

    Source: WordNet 3.1

  27. Select the word opposite in meaning to the given word.
    Unilateral
    Question 27
    Answer and working

    Answer E

    The opposite of unilateral is Multilateral.

    Source: WordNet 3.1

  28. Select the word closest in meaning to the given word.
    Neat
    Question 28
    Answer and working

    Answer C

    Neat (adjective) and Orderly share their main meaning. None of the other options does.

    Source: WordNet 3.1

  29. Select the one word that can replace the given group of words.
    A student who attends a course but does not take it for credit
    Question 29
    Answer and working

    Answer D

    Auditor: a student who attends a course but does not take it for credit.

    Source: WordNet 3.1

  30. Select the correctly spelt word.
    Question 30
    Answer and working

    Answer D

    The correct spelling is accomplice.

Part BReasoning Ability

35 questions, 1 mark each, 0.25 off for a wrong answer

  1. In the English alphabet, which letter is 9th to the right of the 16th letter from the right?
    Question 31
    Answer and working

    Answer D

    The 16th letter from the right is K (position 11). 9 places to the right: position 20, which is T.

  2. Statement: M ≥ L < C < S = T
    Conclusions: I. L < S   II. T > M
    Question 32
    Answer and working

    Answer A

    L and S: the chain gives L < S, so L < S is definitely true. T and M: the signs between them point both ways, so no relation can be fixed, so T > M is not definitely true. So: Only conclusion I follows.

  3. If ‘+’ means ‘×’, ‘−’ means ‘+’, ‘×’ means ‘÷’, ‘÷’ means ‘−’, what is the value of 7 + 7 − 5 ÷ 16 × 4?
    Question 33
    Answer and working

    Answer E

    Replace the signs: 7 × 7 + 5 − 16 ÷ 4. Division and multiplication first, then addition and subtraction: 50.

  4. Which number replaces the question mark? 7, 14, 28, 56, ?, 224
    Question 34
    Answer and working

    Answer C

    The rule: each term is the previous × 2. The missing term is 112.

  5. If ‘+’ means ‘÷’, ‘−’ means ‘×’, ‘×’ means ‘+’, ‘÷’ means ‘−’, what is the value of 26 × 6 ÷ 6 + 6 − 3?
    Question 35
    Answer and working

    Answer A

    Replace the signs: 26 + 6 − 6 ÷ 6 × 3. Division and multiplication first, then addition and subtraction: 29.

  6. In a certain code, RIBBON is written as IRYYLM. How is TRAIN written in that code?
    Question 36
    Answer and working

    Answer A

    From RIBBON → IRYYLM: each letter is replaced by its opposite in the alphabet (A ↔ Z, B ↔ Y …). Applied to TRAIN: GIZRM.

  7. Statements:
    (1) Some doors are not tables.
    (2) Some tables are kites.

    Conclusions:
    (I) Some tables are not kites.
    (II) Some kites are doors.

    Take the statements to be true, however odd they sound. Which conclusion follows?
    Question 37
    Answer and working

    Answer D

    Conclusion I need not hold: every one of the tables may be kites. Conclusion II need not hold: kites and doors need not overlap at all. So: Neither conclusion follows.

  8. J is the son of F. F is the brother of N. How is J related to N?
    Question 38
    Answer and working

    Answer D

    Follow the links out from N: F is N’s brother; J is F’s son. So J is N’s nephew.

  9. In a certain code, FLOWER is written as DJMUCP. How is DESK written in that code?
    Question 39
    Answer and working

    Answer B

    From FLOWER → DJMUCP: each letter moves 2 places back. Applied to DESK: BCQI.

  10. Statement: A < L < H < Z > F
    Conclusions: I. A ≤ Z   II. L ≤ F
    Question 40
    Answer and working

    Answer A

    A and Z: the chain gives A < Z, so A ≤ Z is definitely true. L and F: the signs between them point both ways, so no relation can be fixed, so L ≤ F is not definitely true. So: Only conclusion I follows.

  11. Directions for questions 41 to 45

    Seven friends, Arun, Bina, Chetan, Divya, Esha, Farhan and Gopal, sit in a row facing north. Exactly one person sits between Divya and Gopal. Esha sits immediately to the left of Arun. Chetan sits third to the left of Gopal. Exactly 3 people sit between Arun and Gopal. Arun sits somewhere to the right of Farhan.
  12. Who sits exactly between Arun and Divya?
    Question 41
    Answer and working

    Answer E

    Only one order fits every clue, from the left: Farhan, Esha, Arun, Chetan, Divya, Bina, Gopal. Chetan.

  13. How many people sit between Divya and Farhan?
    Question 42
    Answer and working

    Answer D

    Only one order fits every clue, from the left: Farhan, Esha, Arun, Chetan, Divya, Bina, Gopal. Between them: 3.

  14. What is Chetan’s position from the left end?
    Question 43
    Answer and working

    Answer A

    Only one order fits every clue, from the left: Farhan, Esha, Arun, Chetan, Divya, Bina, Gopal. 4th.

  15. Who sits immediately to the right of Chetan?
    Question 44
    Answer and working

    Answer B

    Only one order fits every clue, from the left: Farhan, Esha, Arun, Chetan, Divya, Bina, Gopal. Divya.

  16. Who sits at the extreme right end?
    Question 45
    Answer and working

    Answer D

    Only one order fits every clue, from the left: Farhan, Esha, Arun, Chetan, Divya, Bina, Gopal. Gopal.

  17. Which one does not belong with the others?
    Question 46
    Answer and working

    Answer C

    25, 361, 256, 144 are perfect squares; 269 is not. The odd one is 269.

  18. In a certain code, TRAIN is written as OJBSU. How is TABLE written in that code?
    Question 47
    Answer and working

    Answer E

    From TRAIN → OJBSU: the word is written backwards and each letter moves 1 forward. Applied to TABLE: FMCBU.

  19. Kabir walks 13 km towards the north. He turns left and walks 8 km. He turns left and walks 13 km. How far is he from the starting point in a straight line?
    Question 48
    Answer and working

    Answer D

    Taking east and north as positive: he ends 8 km west and 0 km north of the start. Straight-line distance = √(8² + 0²) = 8 km.

  20. Statement: W ≥ C ≥ A ≤ D ≤ M
    Conclusions: I. D ≥ C   II. W > A
    Question 49
    Answer and working

    Answer D

    D and C: the signs between them point both ways, so no relation can be fixed, so D ≥ C is not definitely true. W and A: the chain gives W ≥ A, so W > A is not definitely true. So: Neither conclusion follows.

  21. Statements:
    (1) Some stones are rings.
    (2) All doors are stones.

    Conclusions:
    (I) Some doors are not rings.
    (II) All doors are rings.

    Take the statements to be true, however odd they sound. Which conclusion follows?
    Question 50
    Answer and working

    Answer C

    Conclusion I need not hold: every one of the doors may be rings. Conclusion II need not hold: some doors may lie outside rings. But the two cannot both be false: in every diagram exactly one of them is true. So: Either conclusion I or II follows.

  22. Pointing to a man in a photograph, Kavita said, ‘He is the only son of my mother’s father.’ How is the man related to Kavita?
    Question 51
    Answer and working

    Answer C

    The only son of my mother’s father is my mother’s brother. So the man is Kavita’s uncle.

  23. Which number replaces the question mark? 11, 18, 27, 38, 51, 66, ?
    Question 52
    Answer and working

    Answer E

    The rule: the terms are 3², 4², 5² … plus 2. The missing term is 83.

  24. Sana walks 15 km towards the north. She turns right and walks 9 km. She turns left and walks 14 km. She turns left and walks 5 km. She turns right and walks 12 km. Which direction is she facing now?
    Question 53
    Answer and working

    Answer A

    Each right turn is a quarter turn clockwise, each left anticlockwise. The last leg runs North.

  25. S is the sister of K. K is the father of D. How is S related to D?
    Question 54
    Answer and working

    Answer B

    Follow the links out from D: K is D’s father; S is K’s sister. So S is D’s aunt.

  26. Statements:
    (1) All papers are kites.
    (2) No kites are coins.
    (3) Some coins are tables.

    Conclusions:
    (I) No tables are coins.
    (II) Some coins are not kites.

    Take the statements to be true, however odd they sound. Which conclusion follows?
    Question 55
    Answer and working

    Answer B

    Conclusion I need not hold: tables and coins may overlap. Conclusion II holds in every diagram the statements allow. So: Only conclusion II follows.

  27. In a class, Anjali ranks 23rd from the top and 7th from the bottom. How many students are in the class?
    Question 56
    Answer and working

    Answer A

    Anjali is counted in both ranks, so the total is 23 + 7 − 1 = 29.

  28. In the English alphabet, which letter is 7th to the left of the 20th letter from the left?
    Question 57
    Answer and working

    Answer B

    The 20th letter from the left is T (position 20). 7 places to the left: position 13, which is M.

  29. Pooja walks 14 km towards the south. She turns right and walks 10 km. She turns left and walks 15 km. She turns right and walks 10 km. She turns right and walks 12 km. In which direction is she from the starting point?
    Question 58
    Answer and working

    Answer B

    Taking east and north as positive: she ends 20 km west and 17 km south of the start, which is to the South-west.

  30. Statement: D < C ≥ K ≥ V ≥ R
    Conclusions: I. R = C   II. R < C
    Question 59
    Answer and working

    Answer C

    R and C: the chain gives R ≤ C, so R = C is not definitely true. R and C: the chain gives R ≤ C, so R < C is not definitely true. Together the two cover every possibility the chain allows. So: Either conclusion I or II follows.

  31. Statements:
    (1) Some tables are bags.
    (2) Some tables are watches.

    Conclusions:
    (I) Some bags are not watches.
    (II) All bags are tables.

    Take the statements to be true, however odd they sound. Which conclusion follows?
    Question 60
    Answer and working

    Answer D

    Conclusion I need not hold: every one of the bags may be watches. Conclusion II need not hold: some bags may lie outside tables. So: Neither conclusion follows.

  32. In a certain code, PENCIL is written as SHQFLO. How is MONEY written in that code?
    Question 61
    Answer and working

    Answer A

    From PENCIL → SHQFLO: each letter moves 3 places forward. Applied to MONEY: PRQHB.

  33. Statements:
    (1) No shirts are bags.
    (2) All flowers are bags.
    (3) No clocks are flowers.

    Conclusions:
    (I) Some flowers are bags.
    (II) Some shirts are not flowers.

    Take the statements to be true, however odd they sound. Which conclusion follows?
    Question 62
    Answer and working

    Answer E

    Conclusion I holds in every diagram the statements allow. Conclusion II holds in every diagram the statements allow. So: Both conclusions follow.

  34. Statement: P ≤ A < S < L > H
    Conclusions: I. S ≥ P   II. L > P
    Question 63
    Answer and working

    Answer E

    S and P: the chain gives S > P, so S ≥ P is definitely true. L and P: the chain gives L > P, so L > P is definitely true. So: Both conclusions follow.

  35. Statements:
    (1) Some lamps are kites.
    (2) All kites are flowers.

    Conclusions:
    (I) Some lamps are not flowers.
    (II) All lamps are flowers.

    Take the statements to be true, however odd they sound. Which conclusion follows?
    Question 64
    Answer and working

    Answer C

    Conclusion I need not hold: every one of the lamps may be flowers. Conclusion II need not hold: some lamps may lie outside flowers. But the two cannot both be false: in every diagram exactly one of them is true. So: Either conclusion I or II follows.

  36. In a class, Vikram ranks 15th from the top and 29th from the bottom. How many students are in the class?
    Question 65
    Answer and working

    Answer E

    Vikram is counted in both ranks, so the total is 15 + 29 − 1 = 43.

Part CQuantitative Aptitude

35 questions, 1 mark each, 0.25 off for a wrong answer

  1. The population of a town is 38,025. It grows by 20% every year. What will it be after 2 years?
    Question 66
    Answer and working

    Answer C

    38,025 × (1 + 20/100)² = 38,025 × 1.44 = 54,756. Growing 20% on 38,025 twice, not 40% once.

  2. Solve both equations and compare x and y.
    I. x² + 7x = 0
    II. y² + 6y − 7 = 0
    Question 67
    Answer and working

    Answer E

    I gives x = −7 or 0. II gives y = −7 or 1. Some x are bigger and some smaller than some y, so no single relation holds: x = y or no relation can be established.

  3. What is the average of the first 21 natural numbers?
    Question 68
    Answer and working

    Answer B

    Sum = 21 × 22/2, so the average is (21 + 1)/2 = 11.

  4. Solve both equations and compare x and y.
    I. x² − 18x + 72 = 0
    II. y² + 5y − 6 = 0
    Question 69
    Answer and working

    Answer A

    I gives x = 6 or 12. II gives y = −6 or 1. Every x is greater than every y: x > y.

  5. A bag holds 2 red, 7 blue and 4 green balls. Two balls are drawn at random without replacement. What is the probability that both are red?
    Question 70
    Answer and working

    Answer C

    Ways to pick 2 red: 1. Ways to pick any 2: 78. Probability = 1⁄78.

  6. Directions for questions 71 to 75

    Study the table and answer the questions that follow.

    Books issued by five libraries, in two successive years
    LibraryYear 1Year 2
    Library A420441
    Library B320288
    Library C660528
    Library D380437
    Library E560700
  7. Library D’s Year 2 figure is what percent of Library E’s Year 2 figure?
    Question 71
    Answer and working

    Answer B

    437 ÷ 700 × 100 = 62.43%.

  8. Which one grew the most in percentage terms from Year 1 to Year 2?
    Question 72
    Answer and working

    Answer E

    Growth: Library A 5%, Library B −10%, Library C −20%, Library D 15%, Library E 25%. The highest is Library E.

  9. What is the average Year 2 figure of the five?
    Question 73
    Answer and working

    Answer D

    Sum of Year 2 = 2,394. ÷ 5 = 478.8.

  10. What is the total for Library C over the two years?
    Question 74
    Answer and working

    Answer D

    660 + 528 = 1,188.

  11. What is the ratio of Library B’s Year 1 figure to Library E’s Year 2 figure?
    Question 75
    Answer and working

    Answer C

    320 : 700 = 16 : 35.

  12. 44 litres of a mixture contains milk and water in the ratio 6 : 5. How much water must be added to make the ratio 2 : 3?
    Question 76
    Answer and working

    Answer A

    Milk = 24 l, water = 20 l. For 2 : 3, water must be 24 × 3/2 = 36 l. Add 36 − 20 = 16 litres.

  13. A scooter runs at 126 km/h. What is its speed in metres per second?
    Question 77
    Answer and working

    Answer E

    Multiply by 5/18: 126 × 5/18 = 35 m/s.

  14. Which number replaces the question mark? 4, 5, 9, 18, 34, 59, ?
    Question 78
    Answer and working

    Answer E

    The rule: the differences are squares: 1, 4, 9, 16, 25, 36. The missing term is 95.

  15. Which number replaces the question mark? 8, 27, 64, 125, ?, 343
    Question 79
    Answer and working

    Answer C

    The rule: the terms are 2³, 3³, 4³ …. The missing term is 216.

  16. A train 240 m long crosses a platform 270 m long in 17 seconds. What is the speed of the train?
    Question 80
    Answer and working

    Answer C

    It must cover its own length and the platform: 240 + 270 = 510 m in 17 s, so 30 m/s = 30 × 18/5 = 108 km/h.

  17. Which number replaces the question mark? 6, 15, ?, 56, 92, 141
    Question 81
    Answer and working

    Answer B

    The rule: the differences are squares: 9, 16, 25, 36, 49, 64. The missing term is 31.

  18. ₹8,910 is divided among Ravi, Sunita and Imran in the ratio 1 : 2 : 3. What is Ravi’s share?
    Question 82
    Answer and working

    Answer D

    Total parts = 1 + 2 + 3 = 6. Ravi gets 1/6 × 8,910 = ₹1,485.

  19. 96 is what percent of 2,400?
    Question 83
    Answer and working

    Answer E

    96 ÷ 2,400 × 100 = 4%.

  20. The sum of the present ages of a father and his son is 58 years. 4 years ago, the father was 4 times as old as the son. How old is the son now?
    Question 84
    Answer and working

    Answer E

    Let the son be s. Then (58 − s − 4) = 4(s − 4), so 70 = 5s and s = 14 years.

  21. Simplify: 30 + 14 × 7 − 16 ÷ 8
    Question 85
    Answer and working

    Answer D

    Division and multiplication first: 14 × 7 = 98 and 16 ÷ 8 = 2. Then 30 + 98 − 2 = 126.

  22. Solve both equations and compare x and y.
    I. x² − 4 = 0
    II. y² − 10y − 11 = 0
    Question 86
    Answer and working

    Answer E

    I gives x = −2 or 2. II gives y = −1 or 11. Some x are bigger and some smaller than some y, so no single relation holds: x = y or no relation can be established.

  23. What is the value of 67² − 13²?
    Question 87
    Answer and working

    Answer B

    a² − b² = (a + b)(a − b) = 80 × 54 = 4,320.

  24. Ramesh can finish a piece of work in 30 days and Suresh can finish it in 70 days. Working together, how long will they take?
    Question 88
    Answer and working

    Answer E

    In one day they do 1/30 + 1/70 = 1/21 of the work. Time = 30 × 70 ÷ (30 + 70) = 21 days.

  25. Find the wrong number in the series: 3, 7, 15, 35, 63, 127, 255
    Question 89
    Answer and working

    Answer D

    The rule: each term is the previous × 2 + 1. The term in place of 35 should be 31, so the wrong number is 35.

  26. ₹50,000 amounts to ₹55,125 in 2 years at compound interest, compounded annually. What is the rate of interest?
    Question 90
    Answer and working

    Answer C

    (1 + R/100)² = 55,125/50,000 = 1.1025, so 1 + R/100 = 1.05 and R = 5%. Dividing the interest equally between the years (simple interest) gives a wrong answer.

  27. A boat covers 48 km downstream in 3 hours and 24 km upstream in 2 hours. What is the speed of the boat in still water?
    Question 91
    Answer and working

    Answer D

    Downstream speed = 48 ÷ 3 = 16 km/h; upstream = 24 ÷ 2 = 12 km/h. Boat = (16 + 12) ÷ 2 = 14 km/h.

  28. Simplify: 63 + 4 × 12 − 96 ÷ 8
    Question 92
    Answer and working

    Answer A

    Division and multiplication first: 4 × 12 = 48 and 96 ÷ 8 = 12. Then 63 + 48 − 12 = 99.

  29. Which number replaces the question mark? 5, 11, 23, 47, ?, 191
    Question 93
    Answer and working

    Answer D

    The rule: each term is the previous × 2 + 1. The missing term is 95.

  30. A shopkeeper marks his goods 20% above the cost price and allows a discount of 20%. What is his profit or loss percent?
    Question 94
    Answer and working

    Answer A

    Take CP = 100. Marked price = 120. After 20% off: 120 × 80/100 = 96. So 4% loss.

  31. Simplify: 4⁄5 + 5⁄6 + 4⁄5
    Question 95
    Answer and working

    Answer B

    Over the common denominator 30: the sum is 73⁄30. Adding tops and bottoms separately (17/21) is the trap.

  32. What is √676 + √784 − √324?
    Question 96
    Answer and working

    Answer C

    26 + 28 − 18 = 36.

  33. A shopkeeper marks his goods 60% above the cost price and allows a discount of 20%. What is his profit or loss percent?
    Question 97
    Answer and working

    Answer E

    Take CP = 100. Marked price = 160. After 20% off: 160 × 80/100 = 128. So 28% profit.

  34. A sum of money doubles itself in 20 years at simple interest. What is the rate of interest per annum?
    Question 98
    Answer and working

    Answer D

    The interest earned is 1 times the principal in 20 years. Rate = 1 × 100 / 20 = 5%.

  35. Solve both equations and compare x and y.
    I. x² + 14x + 45 = 0
    II. y² − 2y − 3 = 0
    Question 99
    Answer and working

    Answer C

    I gives x = −9 or −5. II gives y = −1 or 3. Every x is smaller than every y: x < y.

  36. Solve both equations and compare x and y.
    I. x² − 14x + 45 = 0
    II. y² − 8y − 20 = 0
    Question 100
    Answer and working

    Answer E

    I gives x = 5 or 9. II gives y = −2 or 10. Some x are bigger and some smaller than some y, so no single relation holds: x = y or no relation can be established.