NIACL AO PrelimsPaper 2, booklet 4390128

Test booklet
प्रश्न पुस्तिका
Booklet No.
4390128
Series
A

NIACL AO Prelims Paper 2

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 word closest in meaning to the given word.
    Gratification
    Question 1
    Answer and working

    Answer A

    Gratification (noun) and Satisfaction share their main meaning. None of the other options does.

    Source: WordNet 3.1

  2. Select the one word that can replace the given group of words.
    A companion at play
    Question 2
    Answer and working

    Answer D

    Playmate: a companion at play.

    Source: WordNet 3.1

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

    Answer D

    tirelassly is wrong; it is spelt tirelessly. The others are correct.

  4. Select the one word that can replace the given group of words.
    An actor able to replace a regular performer when required
    Question 4
    Answer and working

    Answer B

    Understudy: an actor able to replace a regular performer when required.

    Source: WordNet 3.1

  5. Select the word closest in meaning to the given word.
    Miscellaneous
    Question 5
    Answer and working

    Answer A

    Miscellaneous (adjective) and Motley share their main meaning. None of the other options does.

    Source: WordNet 3.1

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

    Answer E

    Segment (verb) and Section share their main meaning. None of the other options does.

    Source: WordNet 3.1

  7. Select the word opposite in meaning to the given word.
    Lively
    Question 7
    Answer and working

    Answer A

    The opposite of lively is Dull.

    Source: WordNet 3.1

  8. Select the incorrectly spelt word.
    Question 8
    Answer and working

    Answer D

    sustennance is wrong; it is spelt sustenance. The others are correct.

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

    Answer D

    The correct spelling is attitude.

  10. Select the one word that can replace the given group of words.
    Someone who collects and pays bets at a gaming table
    Question 10
    Answer and working

    Answer A

    Croupier: someone who collects and pays bets at a gaming table.

    Source: WordNet 3.1

  11. Select the one word that can replace the given group of words.
    Resident of a college town not affiliated with the college
    Question 11
    Answer and working

    Answer A

    Townie: resident of a college town not affiliated with the college.

    Source: WordNet 3.1

  12. Select the correctly spelt word.
    Question 12
    Answer and working

    Answer A

    The correct spelling is intelligent.

  13. Select the word closest in meaning to the given word.
    Approximation
    Question 13
    Answer and working

    Answer B

    Approximation (noun) and Estimate share their main meaning. None of the other options does.

    Source: WordNet 3.1

  14. Select the word closest in meaning to the given word.
    Inhabit
    Question 14
    Answer and working

    Answer D

    Inhabit (verb) and Live share their main meaning. None of the other options does.

    Source: WordNet 3.1

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

    Answer D

    commencemment is wrong; it is spelt commencement. The others are correct.

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

    Answer A

    Esteem (verb) and Respect 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.
    Transparency
    Question 17
    Answer and working

    Answer B

    The opposite of transparency is Opacity.

    Source: WordNet 3.1

  18. Select the correctly spelt word.
    Question 18
    Answer and working

    Answer A

    The correct spelling is allegation.

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

    Answer D

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

    Source: WordNet 3.1

  20. Select the incorrectly spelt word.
    Question 20
    Answer and working

    Answer C

    jubalee is wrong; it is spelt jubilee. The others are correct.

  21. Select the word opposite in meaning to the given word.
    Affirm
    Question 21
    Answer and working

    Answer D

    The opposite of affirm is Negate. Corroborate is the trap: it means the same, not the opposite.

    Source: WordNet 3.1

  22. Select the one word that can replace the given group of words.
    Someone who promotes or exchanges goods or services for money
    Question 22
    Answer and working

    Answer C

    Vendor: someone who promotes or exchanges goods or services for money.

    Source: WordNet 3.1

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

    Answer B

    Bask (verb) and Enjoy share their main meaning. None of the other options does.

    Source: WordNet 3.1

  24. Select the incorrectly spelt word.
    Question 24
    Answer and working

    Answer E

    efectively is wrong; it is spelt effectively. The others are correct.

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

    Answer A

    fatelly is wrong; it is spelt fatally. The others are correct.

  26. Select the word closest in meaning to the given word.
    Captivity
    Question 26
    Answer and working

    Answer A

    Captivity (noun) and Imprisonment share their main meaning. None of the other options does.

    Source: WordNet 3.1

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

    Answer B

    The opposite of upload is Download.

    Source: WordNet 3.1

  28. Select the one word that can replace the given group of words.
    Poor and often mischievous city child
    Question 28
    Answer and working

    Answer A

    Urchin: poor and often mischievous city child.

    Source: WordNet 3.1

  29. Select the word opposite in meaning to the given word.
    Stingy
    Question 29
    Answer and working

    Answer B

    The opposite of stingy is Generous.

    Source: WordNet 3.1

  30. Select the word closest in meaning to the given word.
    Adieu
    Question 30
    Answer and working

    Answer D

    Adieu (noun) and Goodbye share their main meaning. None of the other options does.

    Source: WordNet 3.1

Part BReasoning Ability

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

  1. Statements:
    (1) No leaves are kites.
    (2) All stones are kites.

    Conclusions:
    (I) Some stones are not leaves.
    (II) Some kites are not stones.

    Take the statements to be true, however odd they sound. Which conclusion follows?
    Question 31
    Answer and working

    Answer A

    Conclusion I holds in every diagram the statements allow. Conclusion II need not hold: every one of the kites may be stones. So: Only conclusion I follows.

  2. S is the brother of E. E is the husband of N. How is S related to N?
    Question 32
    Answer and working

    Answer D

    Follow the links out from N: E is N’s husband; S is E’s brother. So S is N’s brother-in-law.

  3. Statements:
    (1) Some clouds are not planes.
    (2) All trees are planes.

    Conclusions:
    (I) No trees are clouds.
    (II) Some trees are clouds.

    Take the statements to be true, however odd they sound. Which conclusion follows?
    Question 33
    Answer and working

    Answer C

    Conclusion I need not hold: trees and clouds may overlap. Conclusion II need not hold: trees and clouds need not overlap at all. But the two cannot both be false: in every diagram exactly one of them is true. So: Either conclusion I or II follows.

  4. Asha walks 9 km towards the west. She turns right and walks 9 km. She turns right and walks 10 km. She turns right and walks 6 km. She turns left and walks 10 km. In which direction is she from the starting point?
    Question 34
    Answer and working

    Answer C

    Taking east and north as positive: she ends 11 km east and 3 km north of the start, which is to the North-east.

  5. In a certain code, BRICK is written as DPKAM. How is LADDER written in that code?
    Question 35
    Answer and working

    Answer A

    From BRICK → DPKAM: letters in odd places move 2 forward, letters in even places move 2 back. Applied to LADDER: NYFBGP.

  6. Statements:
    (1) No books are birds.
    (2) No birds are lamps.
    (3) All lamps are rivers.

    Conclusions:
    (I) No rivers are books.
    (II) Some rivers are not birds.

    Take the statements to be true, however odd they sound. Which conclusion follows?
    Question 36
    Answer and working

    Answer B

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

  7. Statement: G > J = Y < S < F
    Conclusions: I. Y < F   II. F ≥ J
    Question 37
    Answer and working

    Answer E

    Y and F: the chain gives Y < F, so Y < F is definitely true. F and J: the chain gives F > J, so F ≥ J is definitely true. So: Both conclusions follow.

  8. In a certain code, PENCIL is written as NCLAGJ. How is STONE written in that code?
    Question 38
    Answer and working

    Answer D

    From PENCIL → NCLAGJ: each letter moves 2 places back. Applied to STONE: QRMLC.

  9. Sana walks 12 km towards the south. She turns left and walks 11 km. She turns right and walks 8 km. She turns left and walks 9 km. She turns right and walks 10 km. Which direction is she facing now?
    Question 39
    Answer and working

    Answer E

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

  10. V is the mother of E. L is the brother of V. How is L related to E?
    Question 40
    Answer and working

    Answer E

    Follow the links out from E: V is E’s mother; L is V’s brother. So L is E’s uncle.

  11. Statements:
    (1) All fans are planes.
    (2) Some tables are planes.
    (3) Some roads are tables.

    Conclusions:
    (I) Some planes are tables.
    (II) Some roads are not tables.

    Take the statements to be true, however odd they sound. Which conclusion follows?
    Question 41
    Answer and working

    Answer A

    Conclusion I holds in every diagram the statements allow. Conclusion II need not hold: every one of the roads may be tables. So: Only conclusion I follows.

  12. Statements:
    (1) Some coins are clouds.
    (2) All coins are planes.

    Conclusions:
    (I) No coins are clouds.
    (II) All clouds are planes.

    Take the statements to be true, however odd they sound. Which conclusion follows?
    Question 42
    Answer and working

    Answer D

    Conclusion I need not hold: coins and clouds may overlap. Conclusion II need not hold: some clouds may lie outside planes. So: Neither conclusion follows.

  13. Directions for questions 43 to 47

    Seven friends, Arun, Bina, Chetan, Divya, Esha, Farhan and Gopal, sit in a row facing north. Gopal sits immediately to the right of Bina. Arun sits third to the right of Divya. Bina does not sit at either end. Divya sits immediately to the left of Farhan. Chetan and Gopal sit next to each other.
  14. Who sits second to the right of Bina?
    Question 43
    Answer and working

    Answer C

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

  15. Who sits at the extreme right end?
    Question 44
    Answer and working

    Answer E

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

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

    Answer B

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

  17. Who sits exactly between Esha and Bina?
    Question 46
    Answer and working

    Answer D

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

  18. Which pair sits at the two ends of the row?
    Question 47
    Answer and working

    Answer C

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

  19. Statement: Q = W = H ≤ U ≤ N
    Conclusions: I. N = H   II. N > H
    Question 48
    Answer and working

    Answer C

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

  20. In a certain code, BOOK is written as JNNA. How is BREAD written in that code?
    Question 49
    Answer and working

    Answer D

    From BOOK → JNNA: the word is written backwards and each letter moves 1 back. Applied to BREAD: CZDQA.

  21. Find the wrong number in the series: 8, 19, 38, 85, 173, 349, 701
    Question 50
    Answer and working

    Answer D

    The rule: each term is the previous × 2 + 3. The term in place of 38 should be 41, so the wrong number is 38.

  22. Which number replaces the question mark? 27, 64, 125, 216, 343, ?
    Question 51
    Answer and working

    Answer D

    The rule: the terms are 3³, 4³, 5³ …. The missing term is 512.

  23. Statement: K > X ≥ D = J > Z
    Conclusions: I. Z < K   II. K ≥ D
    Question 52
    Answer and working

    Answer E

    Z and K: the chain gives Z < K, so Z < K is definitely true. K and D: the chain gives K > D, so K ≥ D is definitely true. So: Both conclusions follow.

  24. In the English alphabet, which letter is 3rd to the right of the 18th letter from the right?
    Question 53
    Answer and working

    Answer E

    The 18th letter from the right is I (position 9). 3 places to the right: position 12, which is L.

  25. In the English alphabet, which letter is 4th to the right of the 14th letter from the left?
    Question 54
    Answer and working

    Answer D

    The 14th letter from the left is N (position 14). 4 places to the right: position 18, which is R.

  26. Statement: H > R > P > C ≥ F
    Conclusions: I. F ≤ P   II. C ≤ R
    Question 55
    Answer and working

    Answer E

    F and P: the chain gives F < P, so F ≤ P is definitely true. C and R: the chain gives C < R, so C ≤ R is definitely true. So: Both conclusions follow.

  27. In a row of 51 students, Vikram is 20th from the left. What is Vikram’s position from the right?
    Question 56
    Answer and working

    Answer A

    Position from the right = total − position from the left + 1 = 51 − 20 + 1 = 32nd.

  28. T is the mother of R. M is the brother of T. W is the son of M. How is W related to R?
    Question 57
    Answer and working

    Answer D

    Follow the links out from R: T is R’s mother; M is T’s brother; W is M’s son. So W is R’s cousin.

  29. Sunil walks 2 km towards the south. He turns left and walks 12 km. He turns right and walks 14 km. How far, and in which direction, is he from the starting point?
    Question 58
    Answer and working

    Answer E

    Taking east and north as positive: he ends 12 km east and 16 km south of the start. Distance = √(12² + 16²) = 20 km. 20 km, south-east.

  30. Statement: T ≤ P < M > V > R
    Conclusions: I. V < T   II. T < V
    Question 59
    Answer and working

    Answer D

    V and T: the signs between them point both ways, so no relation can be fixed, so V < T is not definitely true. T and V: the signs between them point both ways, so no relation can be fixed, so T < V is not definitely true. So: Neither conclusion follows.

  31. If ‘+’ means ‘−’, ‘−’ means ‘×’, ‘×’ means ‘÷’, ‘÷’ means ‘+’, what is the value of 14 ÷ 4 − 11 + 18 × 6?
    Question 60
    Answer and working

    Answer A

    Replace the signs: 14 + 4 × 11 − 18 ÷ 6. Division and multiplication first, then addition and subtraction: 55.

  32. Which one does not belong with the others?
    Question 61
    Answer and working

    Answer E

    61, 19, 37, 73 are prime; 33 = 3 × 11. The odd one is 33.

  33. In a class, Kabir ranks 7th from the top and 5th from the bottom. How many students are in the class?
    Question 62
    Answer and working

    Answer C

    Kabir is counted in both ranks, so the total is 7 + 5 − 1 = 11.

  34. In a certain code, RIBBON is written as PQDDKT. How is PAPER written in that code?
    Question 63
    Answer and working

    Answer C

    From RIBBON → PQDDKT: the word is written backwards and each letter moves 2 forward. Applied to PAPER: TGRCR.

  35. Statement: C ≤ H ≤ D = B ≤ K
    Conclusions: I. B = C   II. B > C
    Question 64
    Answer and working

    Answer C

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

  36. If ‘+’ means ‘÷’, ‘−’ means ‘+’, ‘×’ means ‘−’, ‘÷’ means ‘×’, what is the value of 34 − 10 ÷ 12 + 8 × 12?
    Question 65
    Answer and working

    Answer D

    Replace the signs: 34 + 10 × 12 ÷ 8 − 12. Division and multiplication first, then addition and subtraction: 37.

Part CQuantitative Aptitude

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

  1. What is √361 + √196 − √676?
    Question 66
    Answer and working

    Answer A

    19 + 14 − 26 = 7.

  2. The population of a town is 69,675. It grows by 20% every year. What will it be after 2 years?
    Question 67
    Answer and working

    Answer A

    69,675 × (1 + 20/100)² = 69,675 × 1.44 = 1,00,332. Growing 20% on 69,675 twice, not 40% once.

  3. A bus goes from Pune to Nashik at 90 km/h and returns by the same road at 110 km/h. What is its average speed for the whole journey?
    Question 68
    Answer and working

    Answer A

    For equal distances, average speed = 2xy/(x + y) = 2 × 90 × 110 ÷ 200 = 99 km/h. The plain average, 100, ignores that the slower leg takes longer.

  4. Simplify: 1⁄4 + 1⁄4 + 2⁄5
    Question 69
    Answer and working

    Answer B

    Over the common denominator 60: the sum is 9⁄10. Adding tops and bottoms separately (8/26) is the trap.

  5. What is the fourth proportional to 4, 8 and 68?
    Question 70
    Answer and working

    Answer E

    4 : 8 = 68 : x, so x = 8 × 68 ÷ 4 = 136.

  6. A bag holds 6 red, 5 blue and 3 green balls. Two balls are drawn at random without replacement. What is the probability that both are red?
    Question 71
    Answer and working

    Answer B

    Ways to pick 2 red: 15. Ways to pick any 2: 91. Probability = 15⁄91.

  7. A boat covers 105 km downstream in 5 hours and 76 km upstream in 4 hours. What is the speed of the boat in still water?
    Question 72
    Answer and working

    Answer B

    Downstream speed = 105 ÷ 5 = 21 km/h; upstream = 76 ÷ 4 = 19 km/h. Boat = (21 + 19) ÷ 2 = 20 km/h.

  8. Simplify: 1⁄2 + 1⁄4 + 1⁄5
    Question 73
    Answer and working

    Answer E

    Over the common denominator 40: the sum is 19⁄20. Adding tops and bottoms separately (5/20) is the trap.

  9. Solve both equations and compare x and y.
    I. x² − 25 = 0
    II. y² + 2y − 48 = 0
    Question 74
    Answer and working

    Answer E

    I gives x = −5 or 5. II gives y = −8 or 6. Some x are bigger and some smaller than some y, so no single relation holds: x = y or no relation can be established.

  10. A shopkeeper marks an article 50% above its cost price and allows a discount of 15%. If the article was sold for ₹2,550, what was its cost price?
    Question 75
    Answer and working

    Answer E

    SP = CP × 1.5 × 0.85 = CP × 1.28. So CP = 2,550 ÷ 1.28 = ₹2,000.

  11. Solve both equations and compare x and y.
    I. x² + 11x + 30 = 0
    II. y² + 8y = 0
    Question 76
    Answer and working

    Answer E

    I gives x = −6 or −5. II gives y = −8 or 0. Some x are bigger and some smaller than some y, so no single relation holds: x = y or no relation can be established.

  12. What is the average of the first 31 natural numbers?
    Question 77
    Answer and working

    Answer D

    Sum = 31 × 32/2, so the average is (31 + 1)/2 = 16.

  13. Solve both equations and compare x and y.
    I. x² + 7x + 12 = 0
    II. y² + y − 72 = 0
    Question 78
    Answer and working

    Answer E

    I gives x = −4 or −3. II gives y = −9 or 8. Some x are bigger and some smaller than some y, so no single relation holds: x = y or no relation can be established.

  14. 250 is what percent of 2,000?
    Question 79
    Answer and working

    Answer C

    250 ÷ 2,000 × 100 = 12.5%.

  15. Which number replaces the question mark? 125, 216, 343, 512, 729, ?
    Question 80
    Answer and working

    Answer C

    The rule: the terms are 5³, 6³, 7³ …. The missing term is 1,000.

  16. A sum of money becomes three times itself in 8 years at simple interest. What is the rate of interest per annum?
    Question 81
    Answer and working

    Answer D

    The interest earned is 2 times the principal in 8 years. Rate = 2 × 100 / 8 = 25%.

  17. What is the value of 57² − 29²?
    Question 82
    Answer and working

    Answer C

    a² − b² = (a + b)(a − b) = 86 × 28 = 2,408.

  18. Which number replaces the question mark? 4, 8, 17, 33, 58, 94, ?
    Question 83
    Answer and working

    Answer D

    The rule: the differences are squares: 4, 9, 16, 25, 36, 49. The missing term is 143.

  19. 70 litres of a mixture contains milk and water in the ratio 6 : 1. How much water must be added to make the ratio 2 : 5?
    Question 84
    Answer and working

    Answer C

    Milk = 60 l, water = 10 l. For 2 : 5, water must be 60 × 5/2 = 150 l. Add 150 − 10 = 140 litres.

  20. A bus goes from Pune to Nashik at 60 km/h and returns by the same road at 84 km/h. What is its average speed for the whole journey?
    Question 85
    Answer and working

    Answer E

    For equal distances, average speed = 2xy/(x + y) = 2 × 60 × 84 ÷ 144 = 70 km/h. The plain average, 72, ignores that the slower leg takes longer.

  21. Solve both equations and compare x and y.
    I. x² − 8x − 20 = 0
    II. y² − 14y + 40 = 0
    Question 86
    Answer and working

    Answer E

    I gives x = −2 or 10. II gives y = 4 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.

  22. What is the compound interest on ₹21,875 for 3 years at 20% per annum, compounded annually?
    Question 87
    Answer and working

    Answer A

    Amount = 21,875 × (1 + 20/100)3 = ₹37,800. CI = 37,800 − 21,875 = ₹15,925.

  23. Directions for questions 88 to 92

    Study the table and answer the questions that follow.

    Saplings planted by five villages, in two successive years
    VillageYear 1Year 2
    Village P440352
    Village Q720756
    Village R760798
    Village S580812
    Village T720936
  24. What is the average Year 2 figure of the five?
    Question 88
    Answer and working

    Answer B

    Sum of Year 2 = 3,654. ÷ 5 = 730.8.

  25. By what percent did Village R’s figure change from Year 1 to Year 2?
    Question 89
    Answer and working

    Answer B

    Change = 798 − 760 = 38. On Year 1: 38 ÷ 760 × 100 = 5% increase.

  26. Village Q’s Year 2 figure is what percent of Village R’s Year 2 figure?
    Question 90
    Answer and working

    Answer C

    756 ÷ 798 × 100 = 94.74%.

  27. Which one grew the most in percentage terms from Year 1 to Year 2?
    Question 91
    Answer and working

    Answer B

    Growth: Village P −20%, Village Q 5%, Village R 5%, Village S 40%, Village T 30%. The highest is Village S.

  28. What is the total for Village S over the two years?
    Question 92
    Answer and working

    Answer B

    580 + 812 = 1,392.

  29. What is the value of 96² − 47²?
    Question 93
    Answer and working

    Answer B

    a² − b² = (a + b)(a − b) = 143 × 49 = 7,007.

  30. Find the wrong number in the series: 10, 19, 35, 60, 94, 145, 209
    Question 94
    Answer and working

    Answer A

    The rule: the differences are squares: 9, 16, 25, 36, 49, 64. The term in place of 94 should be 96, so the wrong number is 94.

  31. A is twice as efficient as B. Together they finish a job in 24 days. How long would A take alone?
    Question 95
    Answer and working

    Answer D

    If B does 1 unit a day, A does 2; together 3 units a day for 24 days = 72 units. A alone: 72 ÷ 2 = 36 days.

  32. Which number replaces the question mark? 19, 20, 24, 33, ?, 74
    Question 96
    Answer and working

    Answer B

    The rule: the differences are squares: 1, 4, 9, 16, 25, 36. The missing term is 49.

  33. A shopkeeper marks an article 25% above its cost price and allows a discount of 10%. If the article was sold for ₹675, what was its cost price?
    Question 97
    Answer and working

    Answer E

    SP = CP × 1.25 × 0.9 = CP × 1.13. So CP = 675 ÷ 1.13 = ₹600.

  34. Solve both equations and compare x and y.
    I. x² − 23x + 132 = 0
    II. y² − 6y + 5 = 0
    Question 98
    Answer and working

    Answer A

    I gives x = 11 or 12. II gives y = 1 or 5. Every x is greater than every y: x > y.

  35. The present ages of Asha and her elder brother are in the ratio 7 : 9. After 3 years, the ratio will be 4 : 5. What is Asha’s present age?
    Question 99
    Answer and working

    Answer E

    Ages 7x and 9x. (7x + 3) : (9x + 3) = 4 : 5 gives x = 3. Asha is 7 × 3 = 21 years.

  36. Which number replaces the question mark? 3, 4, ?, 33, 136, 685
    Question 100
    Answer and working

    Answer C

    The rule: each term is the previous × 1 + 1, × 2 + 2, × 3 + 3, and so on. The missing term is 10.