NIACL AO PrelimsPaper 1, booklet 1387940

Test booklet
प्रश्न पुस्तिका
Booklet No.
1387940
Series
D

NIACL AO Prelims Paper 1

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 correctly spelt word.
    Question 1
    Answer and working

    Answer B

    The correct spelling is globally.

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

    Answer D

    Debonair (adjective) and Suave share their main meaning. None of the other options does.

    Source: WordNet 3.1

  3. Select the incorrectly spelt word.
    Question 3
    Answer and working

    Answer B

    gredient is wrong; it is spelt gradient. The others are correct.

  4. Select the one word that can replace the given group of words.
    Someone who dissipates resources self-indulgently
    Question 4
    Answer and working

    Answer D

    Wastrel: someone who dissipates resources self-indulgently.

    Source: WordNet 3.1

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

    Answer A

    unofficeally is wrong; it is spelt unofficially. The others are correct.

  6. Select the word closest in meaning to the given word.
    Remake
    Question 6
    Answer and working

    Answer D

    Remake (verb) and Redo share their main meaning. None of the other options does.

    Source: WordNet 3.1

  7. Select the word closest in meaning to the given word.
    Testy
    Question 7
    Answer and working

    Answer C

    Testy (adjective) and Cranky share their main meaning. None of the other options does.

    Source: WordNet 3.1

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

    Answer B

    Stutter (noun) and Stammer share their main meaning. None of the other options does.

    Source: WordNet 3.1

  9. Select the correctly spelt word.
    Question 9
    Answer and working

    Answer D

    The correct spelling is bulletin.

  10. Select the word opposite in meaning to the given word.
    Leader
    Question 10
    Answer and working

    Answer E

    The opposite of leader is Follower.

    Source: WordNet 3.1

  11. Select the correctly spelt word.
    Question 11
    Answer and working

    Answer E

    The correct spelling is arraignment.

  12. Select the word opposite in meaning to the given word.
    Complain
    Question 12
    Answer and working

    Answer C

    The opposite of complain is Cheer. Kick is the trap: it means the same, not the opposite.

    Source: WordNet 3.1

  13. Select the incorrectly spelt word.
    Question 13
    Answer and working

    Answer D

    inconceivvable is wrong; it is spelt inconceivable. The others are correct.

  14. Select the incorrectly spelt word.
    Question 14
    Answer and working

    Answer D

    excessevely is wrong; it is spelt excessively. The others are correct.

  15. Select the correctly spelt word.
    Question 15
    Answer and working

    Answer A

    The correct spelling is elementary.

  16. Select the word opposite in meaning to the given word.
    Reject
    Question 16
    Answer and working

    Answer C

    The opposite of reject is Accept.

    Source: WordNet 3.1

  17. Select the one word that can replace the given group of words.
    A baseball pitcher who throws the ball with the left hand
    Question 17
    Answer and working

    Answer C

    Southpaw: a baseball pitcher who throws the ball with the left hand.

    Source: WordNet 3.1

  18. Select the one word that can replace the given group of words.
    A person employed to keep watch for some anticipated event
    Question 18
    Answer and working

    Answer B

    Sentry: a person employed to keep watch for some anticipated event.

    Source: WordNet 3.1

  19. Select the word opposite in meaning to the given word.
    Stingy
    Question 19
    Answer and working

    Answer B

    The opposite of stingy is Generous.

    Source: WordNet 3.1

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

    Answer B

    Narrative (noun) and Story share their main meaning. None of the other options does.

    Source: WordNet 3.1

  21. Select the one word that can replace the given group of words.
    A person regarded as arrogant and annoying
    Question 21
    Answer and working

    Answer D

    Snob: a person regarded as arrogant and annoying.

    Source: WordNet 3.1

  22. Select the word closest in meaning to the given word.
    Tranquil
    Question 22
    Answer and working

    Answer D

    Tranquil (adjective) and Placid share their main meaning. None of the other options does.

    Source: WordNet 3.1

  23. Select the word closest in meaning to the given word.
    Jailbreak
    Question 23
    Answer and working

    Answer A

    Jailbreak (noun) and Breakout share their main meaning. None of the other options does.

    Source: WordNet 3.1

  24. Select the word closest in meaning to the given word.
    Vista
    Question 24
    Answer and working

    Answer C

    Vista (noun) and View share their main meaning. None of the other options does.

    Source: WordNet 3.1

  25. Select the one word that can replace the given group of words.
    A specialist in the care of babies
    Question 25
    Answer and working

    Answer C

    Pediatrician: a specialist in the care of babies.

    Source: WordNet 3.1

  26. Select the correctly spelt word.
    Question 26
    Answer and working

    Answer B

    The correct spelling is procession.

  27. Select the word closest in meaning to the given word.
    Steadfast
    Question 27
    Answer and working

    Answer A

    Steadfast (adjective) and Firm share their main meaning. None of the other options does.

    Source: WordNet 3.1

  28. Select the word opposite in meaning to the given word.
    Asset
    Question 28
    Answer and working

    Answer E

    The opposite of asset is Liability.

    Source: WordNet 3.1

  29. Select the one word that can replace the given group of words.
    A person appointed by a testator to carry out the terms of the will
    Question 29
    Answer and working

    Answer E

    Executor: a person appointed by a testator to carry out the terms of the will.

    Source: WordNet 3.1

  30. Select the word opposite in meaning to the given word.
    Bless
    Question 30
    Answer and working

    Answer B

    The opposite of bless is Curse.

    Source: WordNet 3.1

Part BReasoning Ability

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

  1. In a row of 52 students, Lata is 15th from the left. What is Lata’s position from the right?
    Question 31
    Answer and working

    Answer A

    Position from the right = total − position from the left + 1 = 52 − 15 + 1 = 38th.

  2. Statements:
    (1) All leaves are birds.
    (2) Some leaves are not boxes.

    Conclusions:
    (I) Some leaves are not birds.
    (II) All birds are boxes.

    Take the statements to be true, however odd they sound. Which conclusion follows?
    Question 32
    Answer and working

    Answer D

    Conclusion I need not hold: every one of the leaves may be birds. Conclusion II need not hold: some birds may lie outside boxes. So: Neither conclusion follows.

  3. Statement: D ≥ B > P ≥ Z < C
    Conclusions: I. Z ≥ D   II. P = C
    Question 33
    Answer and working

    Answer D

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

  4. Statements:
    (1) No rings are cups.
    (2) Some kites are not rings.
    (3) All kites are coins.

    Conclusions:
    (I) Some rings are not cups.
    (II) No cups are rings.

    Take the statements to be true, however odd they sound. Which conclusion follows?
    Question 34
    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.

  5. Which one does not belong with the others?
    Question 35
    Answer and working

    Answer A

    154, 33, 99, 110 are multiples of 11; 118 is not. The odd one is 118.

  6. In a row of 55 students, Neha is 19th from the left. What is Neha’s position from the right?
    Question 36
    Answer and working

    Answer E

    Position from the right = total − position from the left + 1 = 55 − 19 + 1 = 37th.

  7. Statements:
    (1) Some papers are lamps.
    (2) Some fans are lamps.

    Conclusions:
    (I) No lamps are fans.
    (II) No fans are papers.

    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: lamps and fans may overlap. Conclusion II need not hold: fans and papers may overlap. So: Neither conclusion follows.

  8. In the English alphabet, which letter is 4th to the left of the 11th letter from the left?
    Question 38
    Answer and working

    Answer D

    The 11th letter from the left is K (position 11). 4 places to the left: position 7, which is G.

  9. Statement: Y ≤ T ≤ L = E ≤ K
    Conclusions: I. L = Y   II. L > Y
    Question 39
    Answer and working

    Answer C

    L and Y: the chain gives L ≥ Y, so L = Y is not definitely true. L and Y: the chain gives L ≥ Y, so L > Y is not definitely true. Together the two cover every possibility the chain allows. So: Either conclusion I or II follows.

  10. Statements:
    (1) Some phones are flowers.
    (2) No roads are phones.

    Conclusions:
    (I) No phones are roads.
    (II) Some flowers are phones.

    Take the statements to be true, however odd they sound. Which conclusion follows?
    Question 40
    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.

  11. In a certain code, SHIP is written as 104. How is MONEY written in that code?
    Question 41
    Answer and working

    Answer D

    SHIP = 104 is twice the sum of the letters’ positions in the alphabet. For MONEY: 13 + 15 + 14 + 5 + 25 doubled = 144.

  12. Deepak walks 8 km towards the south. He turns right and walks 15 km. He turns right and walks 10 km. He turns right and walks 14 km. Which direction is he facing now?
    Question 42
    Answer and working

    Answer D

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

  13. Statement: Z ≥ E ≥ T = W > S
    Conclusions: I. T < Z   II. T = Z
    Question 43
    Answer and working

    Answer C

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

  14. In a certain code, STAR is written as RSZQ. How is CARPET written in that code?
    Question 44
    Answer and working

    Answer E

    From STAR → RSZQ: each letter moves 1 place back. Applied to CARPET: BZQODS.

  15. If ‘+’ means ‘×’, ‘−’ means ‘÷’, ‘×’ means ‘−’, ‘÷’ means ‘+’, what is the value of 14 − 7 + 9 × 6 ÷ 10?
    Question 45
    Answer and working

    Answer E

    Replace the signs: 14 ÷ 7 × 9 − 6 + 10. Division and multiplication first, then addition and subtraction: 22.

  16. Pointing to a woman in a photograph, Imran said, ‘She is the only daughter of my father’s mother.’ How is the woman related to Imran?
    Question 46
    Answer and working

    Answer E

    My father’s mother’s only daughter is my father’s sister. So the woman is Imran’s aunt.

  17. Statement: R > G > W ≥ S > B
    Conclusions: I. S ≤ R   II. G ≥ B
    Question 47
    Answer and working

    Answer E

    S and R: the chain gives S < R, so S ≤ R is definitely true. G and B: the chain gives G > B, so G ≥ B is definitely true. So: Both conclusions follow.

  18. Statement: A ≤ P ≤ F < M ≥ Q
    Conclusions: I. A < M   II. M ≥ A
    Question 48
    Answer and working

    Answer E

    A and M: the chain gives A < M, so A < M is definitely true. M and A: the chain gives M > A, so M ≥ A is definitely true. So: Both conclusions follow.

  19. Statements:
    (1) No tables are roads.
    (2) Some bottles are not tables.

    Conclusions:
    (I) All roads are bottles.
    (II) Some roads are not bottles.

    Take the statements to be true, however odd they sound. Which conclusion follows?
    Question 49
    Answer and working

    Answer C

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

  20. In a certain code, PLANET is written as KOZMVG. How is TABLE written in that code?
    Question 50
    Answer and working

    Answer B

    From PLANET → KOZMVG: each letter is replaced by its opposite in the alphabet (A ↔ Z, B ↔ Y …). Applied to TABLE: GZYOV.

  21. Pointing to a man in a photograph, Priya said, ‘He is the son of my grandfather’s only son.’ How is the man related to Priya?
    Question 51
    Answer and working

    Answer C

    My grandfather’s only son is my father; his child, other than me, is my brother or sister. So the man is Priya’s brother.

  22. Vijay walks 9 km towards the south. He turns left and walks 2 km. He turns left and walks 12 km. He turns right and walks 2 km. How far is he from the starting point in a straight line?
    Question 52
    Answer and working

    Answer C

    Taking east and north as positive: he ends 4 km east and 3 km north of the start. Straight-line distance = √(4² + 3²) = 5 km.

  23. In the English alphabet, which letter is 5th to the right of the 13th letter from the left?
    Question 53
    Answer and working

    Answer D

    The 13th letter from the left is M (position 13). 5 places to the right: position 18, which is R.

  24. D is the husband of V. V is the sister of Y. How is D related to Y?
    Question 54
    Answer and working

    Answer C

    Follow the links out from Y: V is Y’s sister; D is V’s husband. So D is Y’s brother-in-law.

  25. Statement: C > N > G < P = L
    Conclusions: I. C ≤ G   II. L ≥ G
    Question 55
    Answer and working

    Answer B

    C and G: the chain gives C > G, so C ≤ G is not definitely true. L and G: the chain gives L > G, so L ≥ G is definitely true. So: Only conclusion II follows.

  26. Which number replaces the question mark? 18, 48, 20, 42, ?, 36
    Question 56
    Answer and working

    Answer C

    The rule: two series alternate: 18, 20, 22 … rising by 2, and 48, 42, 36 … falling by 6. The missing term is 22.

  27. Directions for questions 57 to 61

    Six friends, Arun, Bina, Chetan, Divya, Esha and Farhan, sit in a row facing north. Esha sits third to the left of Chetan. Bina and Divya sit next to each other. Bina sits at one of the two ends. Bina sits somewhere to the right of Divya. Exactly one person sits between Divya and Arun.
  28. Who sits at the extreme right end?
    Question 57
    Answer and working

    Answer A

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

  29. Who sits immediately to the right of Chetan?
    Question 58
    Answer and working

    Answer E

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

  30. How many people sit between Arun and Esha?
    Question 59
    Answer and working

    Answer E

    Only one order fits every clue, from the left: Esha, Farhan, Arun, Chetan, Divya, Bina. Between them: 1.

  31. Which pair sits at the two ends of the row?
    Question 60
    Answer and working

    Answer C

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

  32. What is Chetan’s position from the left end?
    Question 61
    Answer and working

    Answer A

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

  33. In a certain code, FISH is written as 42. How is BOTTLE written in that code?
    Question 62
    Answer and working

    Answer D

    FISH = 42 is the sum of the letters’ positions in the alphabet (A = 1 … Z = 26). For BOTTLE: 2 + 15 + 20 + 20 + 12 + 5 = 74.

  34. Which number replaces the question mark? 97, 101, 103, 107, 109, 113, ?
    Question 63
    Answer and working

    Answer B

    The rule: consecutive prime numbers. The missing term is 127.

  35. If ‘+’ means ‘−’, ‘−’ means ‘×’, ‘×’ means ‘÷’, ‘÷’ means ‘+’, what is the value of 30 − 6 × 10 + 17 ÷ 7?
    Question 64
    Answer and working

    Answer B

    Replace the signs: 30 × 6 ÷ 10 − 17 + 7. Division and multiplication first, then addition and subtraction: 8.

  36. Sunil walks 11 km towards the north. He turns left and walks 2 km. He turns left and walks 11 km. He turns left and walks 2 km. He turns right and walks 15 km. How far is he from the starting point in a straight line?
    Question 65
    Answer and working

    Answer B

    Taking east and north as positive: he ends 0 km east and 15 km south of the start. Straight-line distance = √(0² + 15²) = 15 km.

Part CQuantitative Aptitude

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

  1. Solve both equations and compare x and y.
    I. x² − 13x + 12 = 0
    II. y² − 13y + 42 = 0
    Question 66
    Answer and working

    Answer E

    I gives x = 1 or 12. II gives y = 6 or 7. Some x are bigger and some smaller than some y, so no single relation holds: x = y or no relation can be established.

  2. A bag holds 7 red, 6 blue and 5 green balls. One ball is drawn at random. What is the probability that it is red?
    Question 67
    Answer and working

    Answer D

    7 of the 18 balls are red. Probability = 7⁄18.

  3. Directions for questions 68 to 72

    Study the table and answer the questions that follow.

    Cars produced by five plants, in two successive years
    PlantYear 1Year 2
    Plant J7801,092
    Plant K420504
    Plant L340357
    Plant M580870
    Plant N300420
  4. By what percent did Plant J’s figure change from Year 1 to Year 2?
    Question 68
    Answer and working

    Answer B

    Change = 1,092 − 780 = 312. On Year 1: 312 ÷ 780 × 100 = 40% increase.

  5. What is the total for Plant L over the two years?
    Question 69
    Answer and working

    Answer A

    340 + 357 = 697.

  6. Plant J’s Year 2 figure is what percent of Plant K’s Year 2 figure?
    Question 70
    Answer and working

    Answer E

    1,092 ÷ 504 × 100 = 216.67%.

  7. What is the average Year 2 figure of the five?
    Question 71
    Answer and working

    Answer B

    Sum of Year 2 = 3,243. ÷ 5 = 648.6.

  8. What is the ratio of Plant L’s Year 1 figure to Plant M’s Year 2 figure?
    Question 72
    Answer and working

    Answer E

    340 : 870 = 34 : 87.

  9. A boat covers 34 km downstream in 2 hours and 39 km upstream in 3 hours. What is the speed of the stream?
    Question 73
    Answer and working

    Answer A

    Downstream speed = 34 ÷ 2 = 17 km/h; upstream = 39 ÷ 3 = 13 km/h. Stream = (17 − 13) ÷ 2 = 2 km/h.

  10. Which number replaces the question mark? 17, 23, 32, 44, 59, 77, ?
    Question 74
    Answer and working

    Answer E

    The rule: the differences grow by 3: 6, 9, 12, 15, 18, 21. The missing term is 98.

  11. The average weight of 6 people goes up by 3.5 kg when a new person takes the place of one who weighs 55 kg. What does the new person weigh?
    Question 75
    Answer and working

    Answer A

    The total rises by 6 × 3.5 = 21 kg, so the new person weighs 55 + 21 = 76 kg.

  12. What is 8% of 1,200?
    Question 76
    Answer and working

    Answer E

    8% of 1,200 = 1,200 × 8/100 = 96.

  13. What is the mean proportional between 25 and 9?
    Question 77
    Answer and working

    Answer C

    Mean proportional = √(25 × 9) = √225 = 15.

  14. A train 120 m long crosses a platform 210 m long in 22 seconds. What is the speed of the train?
    Question 78
    Answer and working

    Answer C

    It must cover its own length and the platform: 120 + 210 = 330 m in 22 s, so 15 m/s = 15 × 18/5 = 54 km/h.

  15. Find the wrong number in the series: 3, 7, 15, 31, 63, 135, 255
    Question 79
    Answer and working

    Answer E

    The rule: each term is the previous × 2 + 1. The term in place of 135 should be 127, so the wrong number is 135.

  16. What is √841 + √289 − √144?
    Question 80
    Answer and working

    Answer D

    29 + 17 − 12 = 34.

  17. Simplify: 1⁄8 + 1⁄12 + 1⁄4
    Question 81
    Answer and working

    Answer B

    Over the common denominator 24: the sum is 11⁄24. Adding tops and bottoms separately (3/24) is the trap.

  18. Solve both equations and compare x and y.
    I. x² − 7x − 44 = 0
    II. y² − 2y − 80 = 0
    Question 82
    Answer and working

    Answer E

    I gives x = −4 or 11. II gives y = −8 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.

  19. Solve both equations and compare x and y.
    I. x² − 9x = 0
    II. y² − 1 = 0
    Question 83
    Answer and working

    Answer E

    I gives x = 0 or 9. II gives y = −1 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.

  20. Solve both equations and compare x and y.
    I. x² − 15x + 50 = 0
    II. y² − 10y − 24 = 0
    Question 84
    Answer and working

    Answer E

    I gives x = 5 or 10. II gives y = −2 or 12. Some x are bigger and some smaller than some y, so no single relation holds: x = y or no relation can be established.

  21. Find the wrong number in the series: 10, 14, 23, 39, 64, 94, 149
    Question 85
    Answer and working

    Answer C

    The rule: the differences are squares: 4, 9, 16, 25, 36, 49. The term in place of 94 should be 100, so the wrong number is 94.

  22. A bus goes from Pune to Nashik at 30 km/h and returns by the same road at 42 km/h. What is its average speed for the whole journey?
    Question 86
    Answer and working

    Answer D

    For equal distances, average speed = 2xy/(x + y) = 2 × 30 × 42 ÷ 72 = 35 km/h. The plain average, 36, ignores that the slower leg takes longer.

  23. Which number replaces the question mark? 11, 15, 24, 40, 65, 101, ?
    Question 87
    Answer and working

    Answer A

    The rule: the differences are squares: 4, 9, 16, 25, 36, 49. The missing term is 150.

  24. A shopkeeper marks his goods 60% above the cost price and allows a discount of 15%. What is his profit or loss percent?
    Question 88
    Answer and working

    Answer B

    Take CP = 100. Marked price = 160. After 15% off: 160 × 85/100 = 136. So 36% profit.

  25. The sum of the present ages of a father and his son is 82 years. 6 years ago, the father was 6 times as old as the son. How old is the son now?
    Question 89
    Answer and working

    Answer E

    Let the son be s. Then (82 − s − 6) = 6(s − 6), so 112 = 7s and s = 16 years.

  26. Simplify: 1⁄6 + 1⁄2 + 1⁄4
    Question 90
    Answer and working

    Answer D

    Over the common denominator 12: the sum is 11⁄12. Adding tops and bottoms separately (3/12) is the trap.

  27. 63 litres of a mixture contains milk and water in the ratio 6 : 1. How much water must be added to make the ratio 3 : 1?
    Question 91
    Answer and working

    Answer B

    Milk = 54 l, water = 9 l. For 3 : 1, water must be 54 × 1/3 = 18 l. Add 18 − 9 = 9 litres.

  28. A sum of money at simple interest amounts to ₹21,600 in 4 years and to ₹24,900 in 6 years. What is the sum?
    Question 92
    Answer and working

    Answer B

    Interest for 2 years = 24,900 − 21,600 = ₹3,300, so ₹1,650 a year. Interest for 4 years = ₹6,600. Sum = 21,600 − 6,600 = ₹15,000.

  29. 145 is what percent of 1,160?
    Question 93
    Answer and working

    Answer C

    145 ÷ 1,160 × 100 = 12.5%.

  30. What is √625 + √841 − √196?
    Question 94
    Answer and working

    Answer C

    25 + 29 − 14 = 40.

  31. A and B together can do a job in 7 days. A alone can do it in 8 days. In how many days can B alone do it?
    Question 95
    Answer and working

    Answer E

    B’s one day = 1/7 − 1/8 = 1/56. B alone takes 56 days.

  32. Which number replaces the question mark? 1, 4, 13, 40, ?, 364
    Question 96
    Answer and working

    Answer A

    The rule: each term is the previous × 3 + 1. The missing term is 121.

  33. Solve both equations and compare x and y.
    I. x² − 13x + 36 = 0
    II. y² − 6y + 8 = 0
    Question 97
    Answer and working

    Answer B

    I gives x = 4 or 9. II gives y = 2 or 4. No x is smaller than any y, and one value of each is equal: x ≥ y.

  34. A trader buys a bicycle for ₹1,275 and sells it for ₹1,530. What is the profit or loss percent?
    Question 98
    Answer and working

    Answer E

    Profit = ₹255. As a percent of the cost price: 255 ÷ 1,275 × 100 = 20% profit.

  35. ₹30,000 amounts to ₹36,300 in 2 years at compound interest, compounded annually. What is the rate of interest?
    Question 99
    Answer and working

    Answer B

    (1 + R/100)² = 36,300/30,000 = 1.21, so 1 + R/100 = 1.1 and R = 10%. Dividing the interest equally between the years (simple interest) gives a wrong answer.

  36. Simplify: 20 + 5 × 10 − 42 ÷ 6
    Question 100
    Answer and working

    Answer C

    Division and multiplication first: 5 × 10 = 50 and 42 ÷ 6 = 7. Then 20 + 50 − 7 = 63.