BITS PILANI Test 10 – Answer Key & Explanatory Answers

BITS PILANI Test - 10 – Answer Key & Explanatory Answers 1.A batsman in his 12th innings makes a score of 120, and thereby increase his average by 5. The average score after 12th innings is 1) 60 2) 55 3) 65 4) 70 2.The side BC of the ΔABC is extended to the point D. If ∠ ACD = 112° and ∠B = 3/4 ∠A, then the value of ∠B is 1) 64° 2) 48° 3) 46° 4) 50° 3.ΔABC is a right angled triangle, the radius of its circumcircle is 3 cm and the length of its altitude drawn from the opposite vertex to the hypotenuse is 2 cm. Then the area of the triangle is 1) 12 sq cm 2) 3 sq cm 3) 6 sq cm 4) 5 sq cm 4.The height of a tower is 50√3 m. The angle of elevation of a tower from a distance 50 m from its feet is 1) 30° 2) 45° 3) 60° 4) 90° 5.The amount of Rs. 10,000 after 2 years, compounded annually with the rate of interest being 10% per annum during the first year and 12% per annum during the second year, would be (in rupees) 1) 11,320 2) 12,000 3) 12,320 4) 12,500 6.The value of tan80° tan10° + sin270° + sin20° is tan80° tan10° + sin270° + sin20° 1) 0 2) 1 3) 2 4) 5 7.If 100 cats kill 100 mice in 100 days, then 4 cats would kill 4 mice in how many days? 1) 4 days 2) 3 days 3) 40 days 4) 100 days 8.If two circles touch each other internally. The greater circle has its radius as 6 cm and the distance between the centres of the circles is 2 cm. The radius of the other circle is 1) 3 cm 2) 4 cm 3) 2 cm 4) 5 cm 9.An office opens at 10 AM and closes at 5 PM. The lunch interval is 30 minutes. The ratio of lunch interval to the total period of office hours is 1) 1:7 2) 1:14 3) 7:1 4) 14:1 10.A Bookseller allowed 15% discount on the books sold. Sunil purchased books worth Rs.1500. How much will he have to pay to Bookseller. 1) Rs.1200 2) Rs.1250 3) Rs.1275 4) Rs.1300 11.The number of ways of selecting 6 students out of a particular batch of students is the same as the number of ways of selecting 7 students out of the same batch. In how many ways can 10 students be selected from this batch of students? (1) 120 (2) 240 (3) 60 (4) 180 (5) None of these Solution: Let the number of students in the batch be denoted by n. Hence, according to given data, nC6 = nC7. → (n!)/ (6! × ((n–6)!))) = (n!)/(7! × ((n–7)!))) → (n!)/((6!) × (n–7)!) × {1/(n–6)} = (n!)/((6!) × (n–7)!) × {1/(7)} → (n – 6) = 7 → n = 6 + 7 = 13. The number of ways in which 10 students can be selected out of this batch is given by: 13C10 = 13!/(3! × 10!) = (11 × 12 × 13)/(3 × 2) = 286. Hence, the correct answer is option 5. 12. How many integral values of x satisfy the following inequality: {(4x2 + 13x + 3) × (x2 + 12x + 35)} < 0? (1) 4 (2) 2 (3) 3 (4) 1 (5) Infinite set of values

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BITS PILANI Test - 10 – Answer Key & Explanatory Answers Solution: Given equation: {(4x2 + 13x + 3) × (x2 + 12x + 35)} < 0 → Either (4x2 + 13x + 3) < 0 or (x2 + 12x + 35) < 0. i) Consider (4x2 + 13x + 3) < 0 → (4x2 + 12x + x + 3) < 0 → (4x + 1)(x + 3) < 0 → Either (4x + 1) or (x + 3) < 0 If (4x + 1) < 0, then x < -¼. If (x + 3) < 0, then x < -3. Since, only one of them is true, -3 < x < -¼. Thus, x could be (-2 or -1). ii) Consider (x2 + 12x + 35) < 0 → (x2 + 7x + 5x + 35) < 0 → (x + 7)(x + 5) < 0 → Either (x + 7) or (x + 5) < 0 If (x + 7) < 0, then x < -7. If (x + 5) < 0, then x < -5. Since, only one of them is true, -7 < x < -5. Thus, x could be (6). In all, x could take one of the following 3 values: (-2, -1 or 6). Hence, the correct answer is option 3. 13.Anna made 12 telephone calls (local, STD or ISD) in one day. The average call charge for a local call, long distance (STD), international call (ISD) is Rs 4, 8 and 9 respectively. If the total charge for all the calls is Rs 79, what is the total call charge (in Rs) for the call type that cost the most that day? (1) 42 (2) 32 (3) 45 (4) 35 (5) None of these Solution: Let the number of local, STD and ISD calls be denoted by x, y and z respectively. Given: Anna made a total of 12 calls in a day → x + y + z = 12 (1) The total call charge = 4x + 8y + 9z = 79 (2) (2) – (1) × 4 gives: 4y + 5z = 31 → y = (31 – 5z)/4 Here, it is clear that 31 > 5z or z < 6 → z could be (1, 2, 3, 4 or 5). Upon checking, it can be observed that only when z = 3, y has an integral value. Thus, z = 3 and y = 4. Using these values in (1), we get x = 5. The charges for local calls = 4x = 4 × 5 = Rs 20. The charges for STD calls = 8y = 8 × 4 = Rs 32. The charges for local calls = 9z = 9 × 3 = Rs 27. Hence, the total call charge for the call type that cost the most that day (STD calls) = Rs 32. Hence, the correct answer is option 2. 14.ABCD is a parallelogram with co-ordinates of its vertices as follows: A (3, 5); B (x, 4); C (5, –1); D (10, y), where x and y are integers. What is the sum of the co-ordinates of point E, whose co-ordinates are (2x, y+4)? (1) –2 (2) 4 (3) 2 (4) 0 (5) None of these Solution: Given: A (3, 5); B (x, 4); C (5, -1); D (10, y). Since, ABCD is a parallelogram; AC and BD are its diagonals. In a parallelogram, it is known that the diagonals bisect each other. Hence, the mid-point of line AC is same as mid-point of line BD. Mid-point of AC = ((3 + 5)/2, (5 – 1)/2) = (4, 2). Mid-point of BD = ((x + 10)/2, (4 + y)/2) = (4, 2). → (x + 10)/2 = 4 → x = -2. Also, (4 + y)/2 = 2 → y = 0. Co-ordinates of point E (2x, y+4) = (-4, 4). Sum = 0. Hence, the correct answer is option 4. 15. Let XYZ be an equilateral triangle and point P lies outside of this triangle such that XP = YP = 4 cm and ZP = 6 cm. Which of the following could be a possible value of the measure of the side of the equilateral triangle? (1) 4.2 (2) 6.4 (3) 2.6 (4) 3.2 (5) None of these

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BITS PILANI Test - 10 – Answer Key & Explanatory Answers Solution: Given: XYZ is an equilateral triangle of side x, XP = YP = 4 cms and ZP = 6 cms. The data is represented as shown in the following diagram. Since P is at equal distance from X and Y, it lies on the perpendicular bisector of the side XY. Hence, PO is the altitude and XO = OY = y = x/2. Thus, angle POY = angle XOP = 90°. Similarly, angle YOZ = angle ZOX = 90°. In triangle ZOX, Altitude ZO = x√3/2, OP = PZ – ZO = 6 – (x√3/2) In triangle XOP, OP2 + OX2 = PX2 (6 – (x√3/2))2 + (x/2)2 = 42 → 36 + 3x2/4 + x2/4 – 6 x√3 = 16 → x2 – 6√3(x) + 20 = 0 Solving this equation, we get: x = 3√3 ± √7 = 7.84 or 2.55. Hence, the correct answer is option 3. 16. In a square PQRS, point T is the midpoint of side PS, point U is the midpoint of the line RT and point V is the midpoint of the line QU. What is the ratio of the area of the triangle QVS to the area of the square PQRS? (1) 1:8 (2) 1:32 (3) 1:4 (4) 1:16 (5) Cannot be determined uniquely Solution: Given data can be represented as shown in the following diagram. Let SU produced meet side QR at W. Now, it can be seen that triangles RST and SRW are equal triangles. It can be observed from the figure that the Area of triangle QVS = ½ Area of triangle QUS [Since V is mid-point of QU] = ½ (½ Area of triangle QWS) [Since U is mid-point of SW] = ½ ½ (½ Area of triangle QRS) [Since W is mid-point of QR] = ½ ½ ½ (½ Area of square PQRS) [Since SQ is a diagonal] Thus, area of triangle QVS = (1/16) × Area of square PQRS Hence, the correct answer is option 4. 17. During a festival sale, a home appliance listed at Rs 7200 is sold to a retail store dealer after successive discounts of 40% and 20%. The retailer targets a profit of 30% and he plans to allow a maximum discount of 10% to the customer. At what price (in Rs) should he mark the appliance so that he meets his target after giving the discount? (1) 4992 (2) 2496 (3) 4044 (4) 2022 (5) None of these Solution: List price of the appliance = Rs 7200. After successive discounts of 40% and 20%, selling price to the retailer = 0.6 × 0.8 × 7200 = Cost price of the retailer. Since he targets 30% profit, his selling price should be equal to: 1.3 × 0.6 × 0.8 × 7200. But he also has to give a discount of 10% on the marked price to arrive at this selling price. Thus, the marked price is given by: 90% of Marked Price = Selling price of the retailer → 0.9 × Marked Price = 1.3 × 0.6 × 0.8 × 7200 Thus, Marked Price of the retailer = 1.3 × 0.6 × 0.8 × 7200/0.9 = Rs 4992. Hence, the correct answer is option 1. 18. A motorbike of company A gives 25% more mileage (km per litre of petrol) than motorbike of company B. Also, motorbike of company A always uses upgraded variety of petrol that costs 10% more than the normal variety which is used for the motorbike of company B. If both the bikes are driven for equal distances, what percentage less than the money spent on petrol for motorbike of company B is the money spent on petrol for motorbike of company A? (1) 13.64 (2) 12.00 (3) 8.33 (4) 12.50 (5) None of these Solution: Let the distance driven be = D kms. © 2017 ETHNUS

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BITS PILANI Test - 10 – Answer Key & Explanatory Answers Also, let the cost of normal petrol for bike B = Rs x/litre and mileage of Bike B = b kms/litre. So, the number of litres of petrol needed for Bike B = D/b litres. Total cost of petrol to travel ‘D’ kms for bike B = Rs. (D/b) × x. Now, cost of special petrol for bike A = Rs 1.1x/litre and mileage of Bike A = 1.25b kms/litre. So, the number of litres of petrol needed for Bike A = D/1.25b litres. Total cost of petrol to travel ‘D’ kms for bike A = Rs. (D/1.25b) × 1.1 x = (D/b) × x × 1.1/1.25. Therefore, difference in total petrol costs = (D/b) × x × 0.15/1.25 Hence, percentage less in amounts = {(D/b) × x × 0.15/1.25}/ {(D/b) × x} × 100 = 15/1.25 = 12.0% Hence, the correct answer is option 2. Directions for questions 19 and 20: Refer the following data to answer the questions given below. Lakshmi goes out for shopping one day with some money. On a price chart in a particular shop, she notices that the price of a diamond earring is equal to the price of three gold rings, which is also equal to the price of eight silk saris. It is noticed that she buys an equal number of all the three items. 19. How much money (in Rs) does she spend on the silk saris if she spends Rs 72000 on the gold rings? (1) 12000 (2) 24000 (3) 8000 (4) 27000 (5) None of these Solution: Given that the price of 1 diamond earring = 3 gold rings = 8 silk saris and that she spends Rs 72000 on rings. Assume she buys 3 gold rings, then price of each ring = Rs 72000/3 = Rs 24000. Also, price of 8 silk saris would be = Rs 72000. Hence, price of each silk sari = 72000/8 = Rs 9000. Since it is given that she buys equal number of all items, she should have bought 3 silk saris which would cost 3 × 9000 = Rs 27000. Hence, the correct answer is option 4. 20. What is the amount (in Rs) spent on diamond earrings if the total amount she has is spent on earrings and saris only, considering she buys equal number of earrings and saris? (1) 240000 (2) 350000 (3) 120000 (4) 180000 (5) None of these Solution: Let the amount spent on saris = x, then the amount spent on earrings = 8x. Hence, total money spent on earrings and saris only = x + 8x = 9x. Ratio of price per item of earring, ring and sari = 1/8: 1/3: 1 = 24: 8: 3. Given that amount spent on gold rings = Rs 72000. Thus total money spent = (72000/8) × (24 + 8 + 3) = 9000 × 35. Now this total money is spent only on buying earrings and saris only = 9x = 9000 × 35. Hence, money spent on earrings = 8x = 8000 × 35 = Rs 280000. Hence, the correct answer is option 5. 21.If 12x16 = 188 and 14x18 = 248, then find the value of 16x20 = ? 1) 320 2) 360

3) 316

4) 318

22.One morning, Raju walked towards the sun. After some time he turned left and again to his left. Which direction is he facing? 1) North 2) South 3) East 4) West 23.One or two statements are given followed by two conclusions/assumptions, I and II. You have to consider the statement to be true, even if it seems to be at variance from commonly known facts. You are to decide which of the given conclusions/assumptions can definitely be drawn from the given statement. Indicate your answer. Statements: 1. If people are intelligent, they should be creative. Assumptions: I. Creativity and intelligence are related. II. Creative people are intelligent. 1) Only conclusion I follows 2) Only conclusion II follows 3) Both conclusion I and conclusion II follow 4) Neither conclusion I nor conclusion II follows © 2017 ETHNUS

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BITS PILANI Test - 10 – Answer Key & Explanatory Answers 24.Select the related word/letters/number from the given alternatives. Cell : Cytology:: Birds: ? 1) Odontology 2) Mycology 3) Ornithology 4) Etymology 25.Select the related word/letters/number from the given alternatives. DHLP:WSOK::FJNR: ? 1) UQMI 2) TPLH 3) SOKG 4) VRNJ 26.Select the related word/letters/number from the given alternatives. 2:10::26:? 1) 50 2) 36 3) 42 4) 20 27. For the following questions Find the odd word/letters/number pair from the given alternatives. 1) EHJ 2) JML 3) PSR 4) VYX 28. For the following questions Find the odd word/letters/number pair from the given alternatives. 1) Tomcat 2) Baby 3) Fawn 4) Cub 29. For the following questions Find the odd word/letters/number pair from the given alternatives. 1) 11 2) 17 3) 19 4) 21 30.Arrange the following words as per order in the dictionary. 1.Patriot 2.Pastor 3 Patron 4. Pattern 5. Pastern 1) 5,2,3,1,4 2) 5,2,1,3,4 3) 5,2,4,1,3 4) 5,2,4,3,1 Directions for questions 31 to 35: Refer the following data to answer the questions given below. The following two tables which represent the “odds against” and “odds in favour” for eight international soccer teams from Manchester United, Chelsea, Liverpool, Arsenal, Barcelona, Real Madrid, AC Milan and Bayern Munich by two experts A and B. Any team that wins a match is awarded two points for that match and there are no draws.

Expert A: “Odds against winning” Mancheste Chelse Against à r United a Mancheste 1:4 r United Chelsea 3:4 Liverpool 1:2 2:3 Arsenal 1:5 1:3 Barcelona 2:5 3:7 Real 4:5 5:8 Madrid AC Milan 1:3 3:4 Bayern 5:7 2:3 Munich

Liverpool

Arsenal

Barcelon a

Real Madrid

AC Milan

Bayern Munich

1:2

4:5

3:5

1:5

2:3

2:7

1:3 1:4 2:5

2:3 3:4 1:3

4:7 3:5 2:3 -

3:8 1:3 1:5 3:4

1:4 1:2 1:3 1:2

1:3 1:3 1: 6 1:2

2:3

4:5

1:4

-

1:3

1: 5

1:2

2:3

1:2

2:3

-

1: 4

2:3

5:6

1:2

4:5

3:4

-

For example: The odds against winning for Liverpool against Bayern Munich are 1/3 according to the expert A.

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BITS PILANI Test - 10 – Answer Key & Explanatory Answers Expert B: “Odds in favour” of winning Manchest Chels Against er United ea Manchester 2:3 United Chelsea 1:3 Liverpool 2:5 3:8 Arsenal 2:3 3:5 Barcelona 1:2 2:5 Real Madrid 1:5 1:4 AC Milan 1:2 1:2 Bayern Munich 1:4 3:4

Liverpool

Arsenal

Barcelona

Real Madrid

AC Milan

Bayern Munich

3:5

1:3

1:2

4:5

1:2

3:4

5:8 2:3 1:2 2:5 3:5 1:3

2:5 1:3 1:3 1:8 2:5 1:4

3:5 1:2 2:3 1:5 2:5 3:5

3:4 3:5 7:8 4:5 5:6 2:3

1:2 2:5 3:5 3:5 1:6 1:3

1:4 2:3 3:4 2:5 1:3 2:3 -

For example: The odds in favour of winning for Bayern Munich against Liverpool are 1/3 according to the expert B. 31. If Manchester United, Barcelona and AC Milan played a three nation tourney, in which each team played one match against the other two, who will be the winner according to the expert A’s expectation? (1) Manchester United (2) AC Milan (3) Barcelona (4) (2) or (3) (5) Indeterminate Solution: The expected points for Manchester United would be = (1/3) × 2 + (2/5) × 2 = 22/15 ≅ 1.5 (i.e., the probability of Manchester United winning against AC Milan × 2 points + winning against Barcelona × 2 points) The expected points for AC Milan would be = (1/2) × 2 + (2/3) × 2 = 14/6 ≅ 2.33 The expected points for Barcelona would be = (1/2) × 2 + (3/5) × 2 = 22/10 = 2.2 The highest expectation is for AC Milan. Hence, the correct answer is option 2. 32. Chelsea and Liverpool played a five match series. If a person calculated the expectation of winning for these two teams based on the expectations of expert B for the first two matches and expectations of expert A for the last three matches, then which of the following statements is true? (1) Liverpool wins the series (2) Chelsea wins the series (3) Both Liver pool and Chelsea have equal chances for winning the series (4) Chelsea wins all the five matches (5) Liverpool wins exactly four matches Solution: Odds in favour of Chelsea winning against Liverpool according to expert B = 5/8. Odds against Chelsea winning against Liverpool according to expert A = 1/3 Odds in favour of Chelsea winning against Liverpool according to expert A = 2/3. If a five match series is played the clear favourite to win is Chelsea Hence, the correct answer is option 2. 33. A knock-out tournament was played among Manchester United, AC Milan, Liverpool and Arsenal. Who has the greatest probability of winning the tournament according to expert B’s expectations, given that Manchester United played Arsenal and AC Milan played Liverpool in the first round? (1) Manchester United (2) Liverpool (3) AC Milan (4) Arsenal (5) Indeterminate Solution: Probability for Manchester United winning can be calculated as it winning the first round and then winning against AC Milan or Liverpool. Note: To calculate the probability of Manchester United winning we have to do (Probability of Manchester United winning against Arsenal) × (Probability of Manchester United winning against Liverpool) × (Probability of Manchester United winning against AC Milan) + (Probability of Manchester United winning against Arsenal) × (Probability of Liverpool winning against AC Milan) × (Probability of Manchester United winning against Liverpool) Hence the probability for Manchester United to win = © 2017 ETHNUS

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BITS PILANI Test - 10 – Answer Key & Explanatory Answers [(1/3) × (3/5) × (1/2)] + [(1/3) × (2/5) × (3/5)] =27/150 For the AC Milan to win = [(3/5) × (1/3) × (1/2)] + [(3/5) × (2/3) × (2/5)] =39/150 For the Arsenal to win = [(2/3) × (3/5) × (3/5)] + [(2/3) × (2/5) × (2/3)] =94/225 For the Liverpool to win = [(2/5) × (1/3) × (2/5)] + [(2/5) × (2/3) × (1/3)] =32/225 We can also see that the sum of the probability is 1. Since the highest probability of winning is for Arsenal, option 4 is the answer. Hence, the correct answer is option 4. 34.In the next world cup the teams Manchester United, Chelsea, Liverpool and Arsenal are put in group A and the other teams in group B. In the first round each team plays exactly one match against the other three teams in its group. The top team from each group goes the second round. Which two teams are most likely to go in to the second round, if Expert A’s expectations are taken into consideration? (1) Arsenal and Bayern Munich (2) Manchester United and Bayern Munich (3) Arsenal and Real Madrid (4) Chelsea and Real Madrid (5) Indeterminate Solution: By observation the odds against Arsenal winning against the three teams Manchester United, Chelsea and Liverpool are 1/5, 1/3 and 1/4 respectively. This implies that the probability of Arsenal winning are 4/5, 2/3 and 3/4 against the other three teams and hence is most likely to go into the next round. Similarly is the case with Real Madrid whose odds in favour of winning Barcelona, AC Milan and Bayern Munich would be 3/4 , 2/3 and 4/5 respectively. Hence, the correct answer is option 3. 35. In the next world cup the teams Barcelona, Real Madrid, AC Milan and Bayern Munich are put in group A and the other teams in group B. In the first round each team plays exactly one match against the other three teams in its group. The top team from each group goes the second round. Which two teams are most likely to go in to the second round, if Expert B’s expectations are taken into consideration? (1) Real Madrid and Liverpool (2) Manchester United and Bayern Munich (3) Arsenal and AC Milan (4) Real Madrid and Chelsea (5) Indeterminate Solution: By observation again, we see that probabilities of winning are the lowest for Liverpool and Real Madrid in the two groups Hence, the correct answer is option 1. Directions for questions 36 to 40: Refer the following data to answer the questions given below. There are some pebbles kept on a table. Sreepriya and Sreevidya are playing a game where they pick up pebbles alternately from the pebbles kept on the table. The rule of the game is that each person has to pick up atleast one pebble in her turn and no person can pick up more than six pebbles in each turn. The person who picks up the last pebble from the table is the loser and the other person is the winner. Solutions to 36 to 40: The minimum number of pebbles one can pick is 1 and the maximum number of pebbles is 6. The controlling number (CN) of pebbles in this game is 7, (i.e. the Min + Max. pebbles one can pick). We also know that the person picking up the last pebble is the loser. Hence, anyone trying to win the game has to ensure that he/she leaves 1 + 7 (1 plus the controlling number of pebbles), i.e., 8 pebbles on the table. The pebbles that have to be picked to be assured of a win are 9th, 16th [9 + 7], 23rd [16 + 7], 30th [23 + 7].. …pebbles. We can write this in the general for as 7k + 2, where k = 0, 1, 2, 3,…… 36. If the rule deciding the winner of the game is changed such that the person clearing the table wins the game, the other rules remaining the same, then how many pebbles should Sreepriya pick up when it is her turn to ensure a win for herself given that there are nineteen pebbles on the table? (1) 5 (2) 4 (3) 3 (4) 6 (5) It is not possible for Sreepriya to win the game © 2017 ETHNUS

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BITS PILANI Test - 10 – Answer Key & Explanatory Answers Solution: The winning strategy in this case is that the person picking the last pebble wins. Hence, that person should pick (controlling number + 1 number) of pebbles. ∴Winning strategy = (7k + 1)th pebble is to picked up. ∴ (7k + 1)th pebble is closest to 19 is 15. ∴Five pebbles have to be picked (i.e., 19th, 18th, 17th, 16th, 15th) Hence, the correct answer is option 1. 37. If Sreevidya starts the game first, then what is the least number of pebbles greater than twenty at the beginning of the game to ensure a win for Sreepriya? (1) 22 (2) 26 (3) 25 (4) 24 (5) 23 Solution: Number of pebbles on the table should be greater than 20. Winning strategy is 7k + 2 pebble, which has to be picked. The number greater than 20 satisfying this is 23. If Sreevidya makes the first move (with the number of pebbles on the table being 23 or greater) then Sreevidya can ensure that she picks the 23rd pebble to win. However if there are 22 pebbles on the table, then Sreevidya will not win irrespective of the strategy she uses. Hence, the correct answer is option 1 38. Sometime during the game when it was Sreepriya’s turn, there were thirty nine pebbles on the table. Without Sreepriya’s realizing it, Sreevidya wanted to surreptitiously remove some pebbles from the table. What is the least number of pebbles should she remove to ensure her own win irrespective of what moves Sreepriya makes later? (1) 1 (2) 3 (3) 2 (4) 4 (5) 5 Solution: Number of pebbles = 39. Winning strategy = 7k + 2 pebble is to be picked. 7k + 2 pebble in this case is 37. Hence Sreevidya should surreptitious remove 3 pebbles (39th, 38th and 37th). Hence, the correct answer is option 2. 39. At one stage during the game, when there twenty seven pebbles on the table and it was Sreevidya’s turn. If she picked up one pebble, then which of the following statements is true? (Assume that Sreepriya does not make any mistake and plays her every turn to win) (1) Sreevidya will anyway win the game. (2) Sreepriya will anyway win the game. (3) Sreevidya will anyway loose the game. (4) If Sreepriya plays her every turn to win without any mistakes, she will surely win the game. (5) Data insufficient to decide the winner Solution: Number of pebbles = 27. Winning strategy = pick the (7k +2)th pebble The 7k + 2 pebble in this case is 23rd pebble. ∴To win Sreevidya should pick 5 pebbles (i.e., 27th, 26th, 25th, 24th, 23rd pebble). Hence the strategy adopted in this case is wrong. Only the correct moves of Sreepriya will ensure her own win. Hence, the correct answer is option 4 40. If, at some stage of the game there are seventeen pebbles on the table, and it is Sreepriya’s turn to pick up the pebbles, then how many should she pick up to ensure her win irrespective of what Sreevidya does in later steps? (1) 1 (2) 5 (3) 4 (4) 3 (5) 2 Solution: The number of pebbles on the table is 12. To be assured of the win Sreepriya should ensure that she picks up the (7k + 2) pebbles, which in this case are the 17th and 16th pebbles. Hence, Sreepriya should pick up just two pebbles. Hence, the correct answer is option 5.

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