ALL INDIA PRELIMS TEST SERIES 2019

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1 Ans:1)(c) Explanation: Let the speed of the bus be 5x and that of the train be 3x. And the distance travelled in the train and bus be 7y and 9y respectively. We know that the time is given by the formula, Dis tan ce Time = Speed Time spent in the bus = 9y/5x Time spent in the train = 7y/3x Ratio of the time spent in the bus to that in the train = 9y/5x : 7y/3x = 27:35 Hence, option (c) is correct. Ans:2)(a) Explanation: Given that the profits of A, B and C are Rs. 3,900, Rs. 5,200 and Rs. 9,100 respectively. Ratio of investments of A, B and C = 3900:5200:9100 = 39:52:91 = 3:4:7. Hence, statement 1 is true. Let Individual contributions of A, B and C be 3x, 4x, and 7x respectively. Total investment of A + B = 3x + 4x = 7x = Investment of C = 50% of total initial investment. Hence, statement 2 is false. Therefore, option (a) is the correct answer. Ans:3)(d) Explanation: Let us assume the manufacturing cost = Rs. 100 Profit = 8% of Rs. 100 = Rs. 8 Selling Price = Rs Rs. 8 = Rs. 108 Due to global fall in crude oil prices, the manufacturing cost of petrol falls by 10%. Reduced manufacturing cost = Rs % of 100 = Rs. 90. Selling Price = Rs Profit = SP CP = Rs. 108 Rs. 90 = Rs. 18. We know that profit percentage = Profit 100% Cost Price (We can understand this logically also. Profit percentage is always on cost price/ manufacturing price. Thus he is gaining Rs. 18 on manufacturing price of Rs. 90. Thus, what is percentage?) Therefore, profit percentage = % = 20% 90 Hence, option (d) is the correct answer. Ans:4)(c) Let the cost price of rice be Rs. 100 per kg. Total cost price = Quantity of Rice Price per kg = = Rs. 75,000. It is given that, the remaining part is 2/5th of the total and was sold at 15% loss. Thus, the first part is 3/5th of the total. Let us assume that 3/5th part is sold at x% profit. Net profit on this part = 3/ x/100 = Rs. 450x. 1 ALL INDIA PRELIMS TEST SERIES 2019 (CSAT - 1) Answer Key Net loss on 2/5th part = 2/ /100 = Rs. 4,500. According to the question, there is no net profit or loss. So, the profit made on 3/5th part must be equal to the loss made on 2/5th part. 450x = Or x = 10% In a single step, it may be said that the profit on the first part is equal to the loss on the second part. Therefore, 750 3/5 x/100 = 750 2/5 15/100. Or x = 10% Hence, option (c) is correct. Ans:5)(d) Explanation: As the price of the article is not known, we cannot determine profit or loss using statement 1. So, statement I can or cannot imply that he made a net profit. Now let us consider statement 2. Giving 10% discount on marked price will bring the selling price of the article to a lower value than the cost price. For example, if the cost price = Rs. 100, Then, Marked price = Rs 110. Selling Price after 10% discount = Rs 110 Rs 11 = Rs 99 < cost price. Also, using formula, Net increase or decrease = a + b + ab/100 for two successive percent increase or decrease. When a% = b% (markup percentage = discount percentage), then: Net increase or decrease = b b b 2 /100 = b 2 /100 As we get a negative value, the shopkeeper must have suffered a net loss. So, statement 2 implies that he made a loss and not profit. Hence option (d) is correct. Ans:6)(d) Explanation: Total matches played = 25 Matches won = 17 Matches lost = = 8 Required Ratio = Matches won : Matches lost = 17 : 8 Hence, option (d) is correct. Ans:7)(a) Explanation: The total number of students appearing in the examination has to be a multiple of 24 (as = 24). Out of the given numbers, only is a multiple of 24. Hence, option (a) is correct. Ans:8)(a) Explanation: We need to calculate the average speed for all the four intervals in the given choices to find the maximum average speed.

2 In the time period 8:00 AM 9:00 AM: Distance travelled = 100 km Average Speed = Distance/Time = 100 km/1 hour = 100 km/hour In the time period 9:00 AM 10:30 AM: Distance travelled = = 80 km Average Speed = 80 km/1.5 hour = km/hour In the time period 10:30 AM 11:00 AM: Distance travelled = = 40 km Average Speed = 40 km/0.5 hour = 80 km/hour In the time period 9:00 AM 9:30 AM: Distance travelled = = 20 km Average Speed = 20 km/0.5 hour = 40 km/hour Hence, we can see that the maximum speed was during the interval 8:00 AM 9:00 AM = 100 km/hour Hence, option (a) is correct. So the remaining two students, i.e. F and I, are sitting at second and third position in the rightmost column, not necessarily in the same order. The final picture that emerges may be represented as follows: Column I A E B Column II C H D Column III G F/I F/I Ans:11)(c) Explanation: P is standing between Q and R. Hence, following two cases are possible: Case I: Ans:9)(b) Explanation: A, C and G are the students sitting at the front in the three columns Ans:10)(d) Explanation: It cannot be determined that who is sitting just behind G. Hence, answer is (d). Explanation for Q9 and 10: A and B are sitting in the leftmost column and B is not sitting at the front in any column (given in last statement). Also E is sitting just behind A. Thus, A, B and E are sitting in the first column. A is the first student in the leftmost column and E is sitting just behind A and B is sitting behind E. Hence, arrangement of all the three students of the first column may be represented as follows: Column I A Case II: It is given that Q is standing to the left of T. But in the case II, Q is on the left of P. Hence, case II can be rejected. We get the following final arrangement: E B Now, C and D are sitting in the middle column and H is sitting just behind C. D is not sitting at the front, therefore C is the student sitting at the front in the middle column. H is second and D is the third in the middle column. It may be represented as follows: Column I A E B 2 Column II C H D B, D, F, H and I are not sitting at the front in any column. It means that the students sitting at the front in the three columns are out of A, C, E and G. We already know that A and C are sitting in the front of I and II column respectively. E cannot be the sitting at the front in column III, as he is sitting behind A in column I. Thus G is the student sitting at the front in the rightmost column. Thus, S is the one standing on the left of R. Ans:12)(c) Explanation: While going up, speed of Ravi is 6 steps per min and he takes a break of 20 seconds after every 12 steps. Therefore, total time in completing a journey of every 12 steps = 12/6 min + 20 second = 2 min 20 sec = 140 second. That is, for 2 min he is climbing 12 steps and then taking a break of 20 second (total 140 second). Now, 8 min or 480 second can be broken as = Steps taken by Ravi in 8 min or 480 sec = 3 12 steps + 6 steps in last one min = 42 steps While going down, his speed is 14 steps per min, thus time taken by him in coming down = Total number of steps / Speed in steps per min = 42/14 = 3 min

3 Ans:13)(d) Explanation: Let number of sixes be X and number of fours be Y. Contribution of sixes = Contribution of fours 6X = 4Y. (i) Total score = 6X + 4Y = 240 From (i) we can put 4Y = 6X 6X + 6X = 12 X = 240 Or X = 20 Ans:14)(b) Explanation: The typewriter can type 500 letters in 60 seconds. Speed of typing = 500/60 = 25/3 letters per second He takes 30 seconds to change the page. Total time in typing one page plus changing the page = 300/(25/3) + 30 = = 66 second In 11 min, i.e. 660 seconds, the number of pages he can type = 660/66 = 10 pages Note: After typing the 10 th page, when he changes the page, 11 min gets over (i.e. just before he starts typing the 11th page). Ans:15)(c) Explanation: Method 1: Let the deal price be Rs x lacs. Then commission paid by the seller as well as the buyer = 10% of x = Rs 0.1x lacs It is given that after paying commission, Ragini gets Rs 4.5 lacs. Rs 4.5 lacs = Deal price Commission = x - 0.1x = 0.9x Or x = 4.5/0.9 = Rs 5 lacs Ramesh pays the deal price plus commission = x + 0.1x = 1.1x = = Rs 5.5 lacs Method 2: It is given that after paying commission, Ragini gets Rs 4.5 lacs and commission paid is 10% of the deal price. Thus Ragini s net earnings is 90% of the deal price. Rs 4.5 lacs = 90% of deal price Deal price = /90 = Rs 5 lacs Total amount spent by Ramesh = Deal price + Commission (10% of deal price) = /100 = Rs 5.5 lacs Ans:16)(c) Let one side of the original cube = x The surface area of the original cube = 6x 2 The cube is cut into eight similar cubes as shown below: = 12x 2 Hence, required ratio = 12x 2 /6x 2 = 12/6 = 2/1 or 2:1 The cube in question is a cube. Hence, there are 8 smaller cubes and all of them are corner cubes. We know that out of the total of 6 faces every corner cube has 3 faces exposed. Thus, in case of every corner cube only half of the total surface area is exposed while being a part of the original bigger cube. Thus, required ratio = Total Surface area of 8 individual smaller cubes/surface area of original cube = Total Surface area of one smaller cube/exposed Surface area of one smaller cube while being a part of the original bigger cube = 2/1 or 2:1 Ans:17)(c) Explanation: Total distance = = 300 m Total speed = total distance/ total time = 300/12 m/sec = 25m/sec Let speed of slower train be x. Hence, the speed of the faster train = x+0.5x= 1.5x Now, x+1.5x= 25m/sec Or x = 10m/sec Speed of the faster train = m/sec = 15 m/sec = km/hr= 54 km/hr Note: When we have to convert unit of speed from m/sec into km/hr we have to multiply by 18/5 or 3.6. Opposite is When we have to convert unit of speed from km/hr into m/sec we have to divide by 18/5 or multiply by 5/18 Ans:18)(b) Explanation: Let Deepika's monthly salary be y. The amount that she saves = y = Rs Here we have to understand that, when Deepika is spending 20% remaining is 80%. When she spends 40% remaining is 60 %. And when she spends 15% remaining is 85 %. Thus we have to multiply by 0.8, 0.6 and Finally, solving for y, we get y = Rs. 8,500 Ans:19)(c) Explanation: Number of chocolates that each student gets = (20/100) 60 = 12 Total number of chocolates = = % of 720 = % of the students = 60/10 = chocolates are distributed among 6 students. Hence, number of chocolates that each student gets = 216/6 = 36 chocolates. As shown in the figure, one side of the smaller cube = x/2 Surface area of one smaller cube = 6(x/2) 2 = 3x 2 /2 Total surface area of 8 similar cubes = 8 3x 2 /2 3 Ans:20)(d) Let the required ratio = x : 1 Quantity of milk and water in x litres of A will be 4x/7 and 3x/7 litres respectively. Similarly, Quantity of milk and water in 1 litre of B will be 4/9 and 5/9 litres respectively. Now, Total quantity of milk in the new mixture = total quantity of water in the new mixture 4x/7 + 4/9 = 3x/7 + 5/9 x = 7/9 This means both mixtures should be mixed in the

4 ratio (7/9):1 = 7:9 Container A contains milk and water in the ratio of 4:3, i.e. 7 parts (4 parts of milk and 3 of water). Container B contains milk and water in the ratio of 4: 5, i.e. 9 parts (4 parts of milk and 5 of water). If we assume every part to be of the same volume, then we can see that mixing the 7 parts of A and the 9 parts of B will lead to the formation of a solution having 8 parts of milk (4+4) and 8 parts of water (3+5). Hence, we can see that A and B must be mixed in the ratio of 7:9. Ans:21)(a) Let PR = x They are meeting at point R, means within same time A travels PR and B travels PQ+QR. When time is same, distance travelled is proportional to speed. PR : (PQ + QR) = 12:16 PR : ( PR) = 12:16 x/(168-x) = 12/16=3/4 x= 72 km In such situations, Distance travelled by A, i.e. PR = 2D (a/(a+b)) And Distance travelled by B, (PQ + QR) = 2D (b/(a+b)) Where D = PQ, a= speed of A, b = speed of B Hence, PR = 2 84 (12/(12+16)) = /28 = 72 km Ans:22)(b) 5 pens are gained on selling 15 pens. Profit %= 5/15*100= % Let the CP of one pen be Rs. x. Now, SP of 15 pen = CP of 20 pen = 20x Total CP of 15 pen = 15x Hence, profit = [(SP CP)/CP] 100 = [(20x 15x)/15x] 100 = 100/3 = 33.33% Ans:23)(b) Explanation: Let CP = Rs. x 135x/ x/100 = x/100 = 1600 x = Rs. 16,000 Ans:24)(c) Explanation: Let the present age of Anshul = x years. Then, his grandfather s present age = x + 50 years. After 6 years, age of anshul and his grandfather will become x + 6 and x + 56 respectively. As we know that after 6 years, the sum of their ages is 152, we get: (x + 6) + (x + 56) = 152 2x + 62 = 152 2x = 90 x = 45 years. So, the present age of Anshul = 45 years. And his grandfather s age = = 95 years. Ans:25)(c) Explanation: Since loss = 15% and SP = 0.85 CP. Therefore, CP = 18.7/0.85 = Rs. 22 lakh Now, gain = 15% and SP = 1.15 CP Therefore, SP = = Rs lakh Ans:26)(d) Make number of toffees equal in both sale and purchased. 6 toffees for Rs 5 is equal to 30 toffees for Rs. 25 Similarly, 5 toffees for Rs 6 is equal to 30 toffees for Rs. 36 Therefore, CP = Rs. 25, SP = Rs. 36 Profit = SP CP = = Rs. 11 Hence, gain percent = Profit/CP 100 = 11/ = 44% CP = Rs 5/6 SP = Rs 6/5 Gain percent = (6/5 5/6)/ (5/6) 100 = 44% Ans:27)(c) Let the required ratio of time be x:y:z Ratio of investments (capital time) = ratio of profits 4x:3y:2z = 5:3:4 Using first two terms, 4x/3y = 5/3 x/y = 5/4 Using last two terms, 3y/2z = 3:4 y/z = 1/2 = 4/8 Hence, x:y:z = 5:4:8 If C1: C2: C3 is the ratio of capitals and P1: P2: P3 is the ratio of profits, then Ratio of time = P1/C1: P2/C2: P3/C3 = 5/4: 3/3: 4/2 = 5/4: 1: 2 = 5:4:8 Ans:28)(a) Explanation: Let the length of each train be l metres and their speeds be x m/s and y m/s respectively. According to the question, 6= l /x ; 3= l /y Thus, x = l /6 and y = l /3 Thus, x + y = l /6 + l /3 = 3 l / 6= l /2. When they move towards each other, their relative speed will be x + y and total length to be crossed will be 2 l So, Time to cross each other = total distance/ relative speed= 2 l /(x+y) Now replacing values for x and y we get: 2 l /(x + y) = 2 l /( l /2) = 4 seconds Ans:29)(c) Explanation: Cost price of first set of erasers = Rs. 1/4 per eraser Cost price of second set of erasers = Rs. 1/5 per eraser After mixing, cost price of each eraser = ½ (1/4 +1/5) = Rs. 9/40 As per question, selling price of one eraser after mixing = Rs. 1/4 Gain percentage = [(selling price - cost price)/ cost price] 100= [(1/4-9/40)/(9/40)] 100= 100/9% Ans:30)(b) Let x be the gain percentage on the rest of the products. 4

5 As no profit or loss occurs, Loss amount = Gain amount Or (1/4) (40/100) = (1-1/4) (x/100) Or (1/4) (40/100) = (3/4) (x/ 100) Or x = 40/3 = 13.33% gain It is given that, 1/4 th part of the products are sold at 40% loss. Thus, Rs 3000 products are sold at loss. Total loss= 3000 (40/100)= 1200 Now this loss is to be recovered from remaining sales of Rs So profit percentage has to be = (1200/9000) 100 = 13.33% Ans:31)(c) Explanation: Per Capita Food Production in any specific year = Total food production in that year/total Population present in the year For year 2001, per capita food production = 38/105 = 0.36 For year 2002, per capita food production = 41/108 = 0.38 For year 2003, per capita food production = 45/100 = 0.41 Thus, the trend is fluctuating. Hence, option (c) is correct. Ans:32)(a) Explanation: Assume that the total expense of the company = Rs Then, Other costs = Rs. 50 It is given that power constitutes 50% of other costs Now, Power cost = 50% of the other costs = 50% of 50 = Rs. 25. Decrease in power cost = 10% of original rate = 10% of 25 = Rs Hence, the percentage decrease in expenses = (2.5/100) 100 = 2.5%. Ans:33)(b) Explanation: It is clear from the statement given in the question that each person shakes hands with 7 persons (excluding himself/herself and two of his/her neighbors). So, we may erringly infer that total number of handshakes = 10 7 But in this process every A shaking hands with B and B shaking hands with A is counted separately (assuming A and B are two persons). So, the total number of handshakes may be obtained by dividing this by two. Total number of handshakes = (10 7)/2 = 35 Hence, option (b) is correct. Ans:34)(d) Explanation: It s evident that the train A has a constant speed, while train B has a constant acceleration. Thus, the speed of train B will keep on increasing with time. As we cannot be sure about the relative speeds of trains A and B at any given point or period of time, we cannot arrive at any of the conclusions drawn in the first three statements. Though as the speed of train B is constantly increasing, we can say for sure that after some time it will have a larger speed than train A, even if it was moving slower than train A in the beginning. Ans:35)(d) Explanation: The population of the given bacteria type, at any given point of time, can be represented as 2 x, where x is a whole number. It s an exponential function which is aptly represented by the curve D. Ans:36)(d) Explanation: Assume that the number of pages in the original book = n Sum of all the page numbers = n = n(n+1)/2. Average of all the page numbers = n(n+1)/2n = (n+1)/2 As n is even, n+1 has to be odd and therefore, (n+1)/2 cannot be an integer. Thus, the average of all the page numbers of a book having even number of pages cannot be an integer. So, the average coming out to be 26 is not possible. Hence, option (d) is correct. Note: The information regarding one page being removed and the average of the remaining page numbers of the book being 25 is redundant, i.e. it s not required to solve the question. Ans:37)(a) Explanation: There is zero probability of this scenario as if one letter is placed in wrong envelope then it is obvious that one other letter would also be in wrong envelope. To make it more clear, let s say there are 5 envelopes A, B, C, D and E and five letters corresponding to these envelopes. One letter, say belonging to A, is wrongly placed in the envelope B. Now, there is no way for the letter belonging to B to be placed in the correct envelope (as the envelope belonging to B has already been used by A). Therefore, exactly one letter can never be placed in the wrong envelope. Hence, option (a) is correct. Ans:38)(d) Explanation: The first ten prime numbers, which are the roll numbers of students, are 2, 3, 5, 7, 11, 13, 17, 19, 23 and 29. Total possible ways in which two roll numbers can be selected = 10 C2 The product of the roll numbers can end in 0 only if the selected roll numbers are 2 and 5. Hence, there is only one possibility for this. Required probability = 1/ 10 C2= 1/45 Hence, option (d) is correct. Ans:39)(c) Explanation: We can see that D and B are diagonally opposite to each other. Ans:40)(c) Explanation: If the positions of E and B are interchanged, then the person opposite to E will be F. 5

6 Explanation for Questions 39 and 40 Using statements 2 and 5, we get two possible cases: Now, using statement 1 we may eliminate Case II represented above, as A is not on the left of anyone in Case II. Now, as per statement 4, B is sitting opposite to F. Adding it on to Case I, we get: Ans:44)(b) Explanation: Required number of ways = Total number of ways in which 3 persons can be selected Number of ways of not including any opposition party leader = 10 C3 6 C3 = = 100 Ans:45)(c) Explanation: To post a letter, we need to select one envelop out of 9 and one stamp out of 8. Thus, Number of ways of posting a letter = 9 C1 8 C1 = 9 8 = 72 Ans:46)(a) Explanation: In first bounce, the height achieved by the ball = 10 3/4; in second bounce= 10 3/4 3/4 and so on. This is a case of geometric progression As per statement 3, there is only one person to the right of H. Hence, we get: Ans:41)(a) Explanation: From figures (x) and (y) we conclude that the number 1, 2, 3 and 4 appear adjacent to 6. Thus, the number 5 will appear on the face opposite to 6. Therefore, when six is at the bottom, 5 will be at the top. Hence, (a) is the correct answer. Ans:42)(d) Explanation: The water image of any object is the inverted image obtained by turning the object upside down. On observing the options we can see that the figure given under option (d) is the appropriate answer. It has been shown below: Different distances covered by ball are: 10, (2 10 3/4), (2 10 3/4 3/4), (2 10 3/4 3/4 3/4) Not counting the first drop of 10 m, we have GP series with a = 10 3/4, r = 3/4 and n = 3. Sum = a (1 r n )/ (1 r) = [10 3/4] [(1 (3/4) 3 /(1/4)] = /64 As per the figure, total distance covered by the ball = 10 (first drop) + 2 sum of series for three terms = /64 = 45 (approximately). Ans:47)(d) Explanation: The original figure is represented below: Ans:43)(b) Explanation: The original folded piece of paper is as follows: On observing the options we can see that the figure given under option (d) is indeed embedded in the original figure. It has been represented below: On unfolding its layers it will look as shown below: Ans:48)(a) Explanation: The neutrons produced and the nucleus broken, both will be in geometric progression. In the 1 st second one nucleus is broken, two nucleus are broken in the 2 nd second, 6

7 four in the 3 rd second, eight in the 4 th second, sixteen in the 5 th second and thirty two in the 6 th second. Hence, total number of nucleuses broken in 6 seconds = = 63. Number of ways of choosing such a team = Number of ways of choosing 6 bowlers out of 6 and 5 batsmen out of 7 = 6 C6 7 C5 = 1 21 = 21. Hence, total ways possible = = 63. Ans:49)(b) Total non-green balls = 8; hence chance of getting one in first draw = 8/12 After first successful draw, non-green balls = 7, also total balls is now 11 Hence, probability of getting non green = 7/11 Final probability = 8/12 7/11 = 14/33 Using combinations Number of ways to choose two non-green balls = 8C2 = 28 Total no. of ways to choose 2 balls = 12 C2 = 66 Probability = 8 C2/ 12 C2 = 14/33 Ans:50)(d) Explanation: Blue balls = 4, green balls = 4 Probability = 2 4/12 4/11 = 8/33 (multiplied by 2 as there are two possibilities green ball 1 st and blue ball 1 st ) Ans:51)(a) Explanation: Number of ways to go from A to C = Number of ways to go from A to B to C + Number of ways to go from A to D to C = = 7 Ans:52)(d) Explanation: From the city A, 5 routes emerge. The probabilities that the person will go towards B and D are 3/5 and 2/5 respectively. The probability of the person leaving B and D is ½ each. Now considering the two cases separately. Probability that the person will reach C from A via B = (3/5) (1/2) = 3/10 Probability that the person will reach C from A via D = (2/5) (1/2) = 2/10 (Note that both the ways emerging out of D reach directly to C. So no matter which route is chosen the probability of a person to reach C once he leaves D will remain 1) So the required probability = 3/10 + 2/10 = 5/10 = 1/2 Ans:53)(d) Explanation: Here we have to select, i.e. it's a question of combination, as the order of the players do not matter. As the team must have at least 5 bowlers, two cases emerge: Case I: Team has 5 bowlers and 6 batsmen. Number of ways of choosing such a team = Number of ways of choosing 5 bowlers out of 6 and 6 batsmen out of 7 = 6 C5 7 C6 = 6 7 = 42. Case II: Team has 6 bowlers and 5 batsmen. 7 Ans:54)(a) Explanation: Here we are supposed to arrange, i.e. it's a question of permutation. However, the 10 red balls are identical. Hence, no matter how we arrange them and the single white ball on the table symmetrically, we will effectively get the same kind of arrangement. Ans:55)(c) Explanation: In every row the right hand side number is the cube of the number on the left minus that number, i.e. if the number on the left is n, then the number on the right will be n 3 n = n(n 2-1) So, the missing number = = = 120 Ans:56)(b) Explanation: To draw a line we need two points which may be joined. If the 19 points were non-collinear, then the number of straight lines that can be drawn = 19 C2 Number of straight lines that can be formed using 5 points = 5 C2 However, these five points are collinear. So, now 5C2 has to be considered to be 1, as only one line can be drawn using these points. The number of straight lines formed = 19 C2 5 C2 + 1 = = 162 Ans:57)(d) Explanation: Probability that Ria can solve a problem = 1/2 So, probability that Ria can t solve a problem = 1 ½ = ½ Probability that Tina can solve a problem = 2/3 Probability that Tina can t solve a problem = 1 2/3 = 1/3 Method I: Probability that the problem is solved = 1 - Probability that the problem is not solved = 1 (Probability that neither Ria nor Tina solve the problem) = 1 (1/2 1/3) = 1 1/6 = 5/6 Ans:58)(b) Explanation: It is given that last 3 digits are randomly dialed. Then, each of the digits can be selected out of 10 digits in 10 ways, out of which only one will be correct in each case. Required probability = Ans:59)(b) Explanation: Let the number of rooms at the lowest floor (ground floor) be x. Number of rooms is always an integer. The number of rooms at each floor is 2/3 rd of the number of rooms situated at the next higher floor. We can also say, the number of rooms at each floor is 3/2 times the number of rooms situated at the next lower floor.

8 Thus, the number of rooms at 1 st floor = 3x/2 Similarly, the number of rooms at 2 nd floor = (3x/2)3/2 = 9x/4 The number of rooms at 3 rd floor = (9x/4)3/2 = 27x/8 The number of rooms at 4 th floor = (27x/8)3/2 = 81x/16 81x/16 must be an integer and smallest value of x for which it is an integer is 16. Thus, smallest possible number of rooms at the lowest floor is 16. Note: Also, using Geometrical Progression we can find the n th term = ar n-1, where a is the first term and r is the common multiplying factor. Thus, the number of rooms at 4 th floor = x(3/2) 4 = 81x/16 Ans:60)(a) Ans:61)(c) Explanation for Questions 60 and 61: The total number of girls in the meet is 3. Thus, total number of boys in the meet is also 3. Let the number of students from one school be y. Thus, the number of students from another school is also y. Now, Total number of students from both the schools = total number of boys + total number of girls Or y + y = Or 2y = 6 Or y = 3 Let the number of boys in first school be b. Thus, the number of boys in second school = 3-b Also, the number of girls in first school = 3-b And so the number of girls in second school = b Now, as each of the two schools is sending at least 1 boy and 1 girl to the meet: b = 1 or 2 Case 1: when b = 1 First School Second School Girls 2 1 Boys 1 2 Students of same sex and same school hug each other. There is only one boy in first school and only one girl in second school, so no hug happens here. Number of hugs = 1 (between two girls of first school) + 1 (between two boys of second school) = 2 Students of same school but different sex handshake with each other. Thus, one boy of first school handshakes with two girls of same school. Similarly, one girl of second school handshakes with two boys of same school. Number of handshakes = = 4 Case 2: when b = 2 First School Second School Girls 1 2 Boys 2 1 Number of hugs = 1 (between two boys of first school) + 1 (between two girls of second school) = 2 Number of handshakes = = 4 Therefore, in both the possible cases there are two hugs and 4 handshakes. Ans:62)(c) Explanation: Mahak gets 200 grams of cake which is equivalent to 40% of cake. 100% of cake = (200/40) 100 = 500 grams Richa s share (30%) = /100 = 150 grams Archana s share (10%) = /100 = 50 grams Divya s share (20%) = /100 = 100 grams Option (a): If Richa gives 40 grams of cake to Archana then: Amount of cake with Archana = = 90 grams and Amount of cake with Richa = = 110 grams. Thus Richa, Archana and Divya will have different quantities of cake. Option (b): By looking at the figure we find that: Mahak s share > Richa s share > Divya s share > Archana s share Hence, option (b) is incorrect. Option (c): Mahak has 40% of cake. If she gives half of her cake to Archana, then she is left with 20% of cake and now Archana, who was already having 10% of cake, has 30% of cake. Thus Archana and Richa have 30% of cake each and Mahak and Divya have 20% of cake each. Thus, two pairs of friends can be formed, where friends in each pair have equal amount of cake. Hence, option (c) is correct. Ans:63)(a) Explanation: HCF (Highest Common Factor) of 16, 16 and 12= 4, thus the dimensions of required identical cube will be 4 cm 4 cm 4 cm. Number of cubes = ( )/ (4 4 4) = 4 4 3= 48 Ans:64)(d) Explanation: In the above figure it s clear that there are three layers of 16 cubes each. All the cubes on the edges of the cuboid will have two or more than two faces painted. The top layer, has 12 cubes on its edges. Similarly bottom layer has 12 cubes on the edges. Middle layer has 4 cubes on the edges. Total number of cubes having two or more than two faces painted = = 28 Ans:65)(c) Explanation: 8

9 In the above figure it s clear that only four inner cubes in the middle layer will have no face painted. Alternative method: All outer cubes will have at least one face painted. We need to calculate the number of cubes which have no face exposed. The cuboid is of the dimensions , i.e. there are four cubes each on the two edges of the cuboid (16/4=4) and one edge of the cuboid has 3 cubes (12/4=3). Number of cubes having no face painted = (4-2) (4-2) (3-2) = 2 2 1= 4 Ans:66)(b) Explanation: Common Factors of 16, 16 and 12 are 4, 2 and 1. [16 = and 12 = 2 2 3] Thus, three kinds of identical cubes, each with dimensions 4cm 4cm 4cm, 2cm 2cm 2cm and 1cm 1cm 1cm, can be cut from the cuboid such that no part of it is wasted. Thus, there are three possible ways. N 3 + 1, where N = position of the element in the series, starting from 0. Thus, the first element = = = 1 Second element = = = 2 Third element = = = 9 Fourth element = = = 28 Fifth element = = = 65 Sixth element = = = 126 Thus, the seventh element = = = 217 Hence, 217 is the required answer. Ans:71)(d) Explanation: We are supposed to find the mirror image of the question figure. On observing the options we can see that the figure given under option (D) is the appropriate answer. It has been shown below: Ans:67)(d) Explanation: The sum of the alphabetical positions of the letters around each star is always st Figure: L + P + U + A + E = = 55 2 nd Figure: K + N + D + S + G = = 55 Similarly in 3 rd Figure: O + C +? + T + C = ? = 55? + 41 = 55? = 14 Hence, N is the required answer. Ans:68)(c) Explanation: The number in the lower segment of the circles is obtained by multiplying the top two numbers and then dividing by 2, 3 and 4 respectively in case of first, second and third circle. 1 st Figure : Number in the lower segment = Figure: Number in the lower segment = Similarly in case of 3 rd Figure: 9 12 Number in the lower segment = 27 4 Hence, 27 is the required answer. Ans:69)(a) Explanation: From all the given figures we conclude that the colours are orange, blue, red and rose appear adjacent to the colour yellow. Thus violet must be opposite to yellow. Hence, option (a) is the correct answer. We can also compare first and second dices and arrive at the same conclusion. Ans:70)(a) Explanation: The original series is: 1, 2, 9, 28, 65, 126,? We can see that the elements in the above series are in the following format: 9 Ans:72)(b) Explanation: Married people are represented by the rectangle, school teachers are represented by triangle and people who live in the joint family are represented by circle. Hence, married teachers who live in a joint family will be represented by the overlapping parts of rectangle, triangle and circle. Therefore letter Q represents the married teachers who live in a joint family. Hence, (b) is the required answer. Ans:73)(c) Explanation: Married people are represented by the rectangle, school teachers are represented by triangle and people who live in the joint family are represented by circle. Hence married people who live in a joint family will be represented by the overlapping parts of rectangle and circle, i.e. S and Q. The school teachers are represented by triangle. Hence, married people who live in a joint family, but are not school teachers will be represented by S. Hence (c) is the required answer. Ans:74)(b) Explanation: Let the value of the memento be Rs. x. Then, pay for seven weeks work = Rs x. 300 x Pay for one week s work = Rs x So, pay for four week s work = Rs. 4..(i) 7 Now, this is equivalent to Rs x...(ii) Equating (i) and (ii) 300 x 4 = 30 + x 7 4x = 7x x = 990 x = Rs. 330 Hence (b) is the required answer. Ans:75)(d)

10 Explanation: We have been provided with the change in prices of shares over the four quarters. However, to calculate the net percentage change, either percentage change in prices must be given or the share price in any quarter (either at the starting of the quarter or at the end of the quarter) of 2015 must be given. As no such information is given, net percentage change cannot be determined. Ans:76)(b) Explanation: Change in price of share A in 2015 over four quarters = = Rs. 40 Change in price of share B in 2015 over four quarters = = Rs. 75 Change in price of share C in 2015 over four quarters = = Rs. 40 Price of share A at the end of quarter 4 = = Rs. 850 Price of share B at the end of quarter 4 = = Rs. 895 Price of share C at the end of quarter 4 = = Rs. 870 Thus, it is evident from above that price of share B is the highest among all at the end of quarter 4. Ans:77)(b) Explanation: Only share B has positive change in share price (change is decreasing but always positive) over all the four quarters. Thus its price is increasing continuously over all the quarters. Other two shares have one or more negative price changes and when there is negative price change, price decreases over the previous quarter. Ans:78)(b) Explanation: Q (-) = S (+) P (+) Ans:79)(d) Explanation: M (+) = B (-) T (-) = S (+) Ans:80)(b) Explanation: P (?) U (-) T (-) = S (+) Z (+) 10