Phodo 'CAT' Archive

    Update 11-Oct-2011: Answers to Quant. Questions are given below: 1(a) 19! = 2^X × 3^Y × 5^Z × 7^A × 11^B ×13^C × 17^D × 19^E 20! = 2² × 5 × 2^X × 3^Y × 5^Z × 7^A × 11^B ×13^C × 17^D × 19^E = 2^(X+2) × 3^Y × 5^(Z+1) × 7^A × 11^B ×13^C × 17^D × 19^E Thus the ratio will be (x+2+1) (z+1+1) : (x+1) (z+1). X = Number of 2’s in 19! = 9 + 4 + 2 + 1 = 16 Z = Number of 5’s in 19! = 3 Thus the ratio will be (16+2+1) (3+1+1) : (16+1) (3+1) = 19 × 5 : 17 × 4 = 95 : 68   2 (d) The four circles could be centered at the four vertices of a square, but that is not necessary.  The data in the question is consistent with the condition that the quadrilateral formed by the 4 centers is a rhombus rather than a square.  The shaded area would be the area of the rhombus minus the area of the 4 sectors (which add up to the area of the one of the circles). As the area of the rhombus cannot be determined, the area of the shaded portion cannot be determined.   3 (a) Since the discount percentages are 11.11% i.e. , 14.28% i.e.  and 16.67% i.e.  and also since the marked price of all 3 goods are the same, the smallest possible integral value of the marked price will be 126 (which is LCM of 9, 7 and 6).     Now, the profit percentages are 16.67% i.e. , 12.5% i.e.  and 33.33% i.e. .   As we can see, the selling prices must be multiples of 7, 9 and 4 to keep the values integral. There are two values that are multiples of 7 (112 and 105), one multiple of 9 (108) and two multiples of 4 (112 and 108).   Thus, to keep the values integral, the 12.5% profit has to go to Good 2 (as that is the only one with selling price that is a multiple of 9).   This means, the 33.33% profit has to go to Good 1 and 16.67% profit has to go to Good 3.     Thus, least possible sum of all the Cost Price = 84 + 96 + 90 = 270.   4 (a)   On, double rationalizing R.H.S. we get R.H.S. as   Thus on comparing we get, P=(7/11)  

5(d)

f(x+2)=(x+2)(x+1)/2 Option (a) :  f(x) +f(x) = (X² - x+2)/2 which is not f(x+2) Option (b) and (c) are cubic functions, and thus cannot be the answer.     Update 09-Oct-2011: Please find new set of questions. 1. Find the ratio of the number of factors of 20! to that of 19! a) 95 : 68                      b) 85 : 68                      c) 95 : 64                      d) 85 : 64   2.

        In the above figure, every pair of adjacent circles touches each other and the radius of each of the circles is 7 cm.  What is the area of the shaded portion?     a) 42 cm²                                             b) 21 cm²                                            c) 54 cm²                                             d) Cannot be determined   3.  A shopkeeper marks 3 goods at the same price. He gives discounts of 11.11%, 14.28% and 16.67% on them. Because of this, he ends up making a profit of 16.67%, 12.5% and 33.33% on them (not necessarily in the same order). What is the least possible sum of the cost prices of all the 3 goods, given that all the values (Marked Price, Selling Price and Cost Price) are integers?     a) 270                           b) 280                           c) 290                           d) 300   4.  If                                                                       then the value of P is a)7/11      b)3/11                            c)-1/11                            d) cannot be determined   5. If f(x)= x(x-1)/2, then f(x+2)  equals  

a) f(x)+f(2)                  b) (x+2)*f(x)               c)x*(x+2)*f(x)             d) (x+2)*f(x+1)/x

  Update 09-Oct-2011: Answers to English Comprehension are given below. 1. a) (pitfall means trap/snare) Option (b) is a slight distortion, though major part of the passage is discussing this, because the writer first states, “the method of gradual reform has many merits as compared to the method of revolution, and I have no wish to preach revolution.” Hence, he deals with socialism in general rather than gradual reform alone. Option (c) is too broad – it would be a different essay if these ideas are discussed. The same problem is with option (d) as well.     2. a) “In England, the principal activities of the Fabian society consisted in the furtherance of its goal of socialism through the education of the public along socialist lines by means of meetings, lectures, discussion groups, conferences, and summer schools; carrying out research into political, economic, and social problems; and publishing books, pamphlets, and periodicals.” This is in line with what is stated in option (a).     3. b) B or expropriation is not an aspect of gradual reform, hence not a demerit either. The others are stated in the passage at different places.     4. d) “Economic justice demands a diminution….‘etc. justifies (a).The workers situation justifies (b). 3 is clearly stated in “I think it is at least doubtful whether such measures do anything at all to contribute toward the ideals which inspired the early socialists and still inspire the great majority of those who advocate some form of socialism.”     5. d) “to wit’ (adverb) is an idiom and it means namely or that is to say.  

Update 06-Oct-2011: Today we have a passage in English Comprehension. Please find below. Recommended time: 10 mins

Beginning of Question Set

Passage 1

  In its early days, socialism was a revolutionary movement of which the object was the liberation of the wage-earning classes and the establishment of freedom and justice. The passage from capitalism to the new régime was to be sudden and violent: capitalists were to be expropriated without compensation, and their power was not to be replaced by any new authority. Gradually a change came over the spirit of socialism. In France, socialists became members of the government, and made and unmade parliamentary majorities. In Germany, social democracy grew so strong that it became impossible for it to resist the temptation to barter away some of its intransigence in return for government recognition of its claims. In England, the principal activities of the Fabian society consisted in the furtherance of its goal of socialism through the education of the public along socialist lines by means of meetings, lectures, discussion groups, conferences, and summer schools; carrying out research into political, economic, and social problems; and publishing books, pamphlets, and periodicals.   The method of gradual reform has many merits as compared to the method of revolution, and I have no wish to preach revolution. But gradual reform has certain dangers, to wit, the ownership or control of businesses hitherto in private hands, and by encouraging legislative interference for the benefit of various sections of the wage-earning classes. I think it is at least doubtful whether such measures do anything at all to contribute toward the ideals which inspired the early socialists and still inspire the great majority of those who advocate some form of socialism. Let us take as an illustration such a measure as state purchase of railways. This is a typical object of state socialism, thoroughly practicable, already achieved in many countries, and clearly the sort of step that must be taken in any piecemeal approach to complete collectivism. Yet I see no reason to believe that any real advance toward democracy, freedom, or economic justice is achieved when a state takes over the railways after full compensation to the shareholders.   Economic justice demands a diminution, if not a total abolition, of the proportion of the national income which goes to the recipients of rent and interest. But when the holders of railway shares are given government stock to replace their shares, they are given the prospect of an income in perpetuity equal to what they might reasonably expect to have derived from their shares. Unless there is reason to expect a great increase in the earnings of railways, the whole operation does nothing to alter the distribution of wealth. This could only be effected if the present owners were expropriated, or paid less than the market value, or given a mere life-interest as compensation. When full value is given, economic justice is not advanced in any degree. There is equally little advance toward freedom. The men employed on the railway have no more voice than they had before in the management of the railway, or in the wages and conditions of work. Instead of having to fight the directors, with the possibility of an appeal to the government, they now have to fight the government directly; and experience does not lead to the view that a government department has any special tenderness toward the claims of labor. If they strike, they have to contend against the whole organized power of the state, which they can only do successfully if they happen to have a strong public opinion on their side. In view of the influence which the state can always exercise on the press, public opinion is likely to be biased against them, particularly when a nominally progressive government is in power. There will no longer be the possibility of divergences between the policies of different railways. Railway men in England derived advantages for many years from the comparatively liberal policy of the North Eastern Railway, which they were able to use as an argument for a similar policy elsewhere. Such possibilities are excluded by the dead uniformity of state administration.     1. Which of the following is the best title for the passage? a) Pitfalls of socialism b) Pitfalls of Gradual Reform towards Socialism c) Socialism and Economic Justice d) Socialism and Democracy     2. It can be inferred from the passage that the Fabians, in order to achieve socialism … a) preferred reform against revolution, and conciliatory bargaining against antagonism. b) preferred reform against revolution, and expropriation of property as against conciliatory bargaining. c) preferred revolution against reform, and conciliatory bargaining  against expropriation. d) preferred revolution against reform, and a sudden and violent change to socialism.     3. Which of the following reasons is/are advanced by the writer as the demerits of gradual reform? A. State ownership or control of businesses after full compensation to share holders. B. Expropriation of shares. C. The government machinery becomes a formidable adversary for the workers. D. The uniformity of the state administration.   a) A, B and C                b) A, C and D                c) B only                       d) None of these     4. It is the writer’s belief that a piecemeal approach to collectivism does not … a) ensure economic justice                                 b) further the cause of democracy

c) help realize the ideals of early socialists         d) All of the above

    5. ” But gradual reform has certain dangers, to wit, the ownership or control …” “to wit” in the context means which of the following? a) to come to know       b) with humour              c)to reason                   d) namely   End Of  Question Set    1st October Here are the 5 questions for the day : 1) At an Independence Day ceremony, 77 students from Arya Vidya Mandir were standing in a rectangular formation with 7 rows of 11 students each. Each of these students is now given some flowers such that the number of flowers with students in each row and each column is in Arithmetic Progression. If the number of flowers with the fourth and the tenth students in the third row is 25 and 61 respectively and that with the sixth student of the seventh row is 65, find the average number of flowers with all the students.   a) 33                             b) 42                             c) 44                             d) 49   2) Which of the following digit will be at hundred’s place of 2¹⁰⁰⁰?   a) 5                              b) 3                              c) 9                               d) 7   3)Whenever Rakesh, a shop owner, sees Rajesh coming to his shop, he increases the price of each item by 34.44% because Rajesh has a habit of bargaining to take 10% extra quantity and pay only 90% of amount quoted for marked price. How much profit does Rakesh earn in doing this?   a) 8%                            b) 9%                          c) 10%                          d) 11%   4) How many such natural numbers x exist such that (x+36)/(x-36)  is an integer? a) 24                             b) 22                             c) 12                             d) 8   5)Rakesh and Suresh start walking from A to B with the speed of 19 kmph and 9 kmph respectively. But Suresh increases his speed by 2 kmph after every hour and thus both of them reach B at the same time. Find the total distance between A and B.   a) 190 km                      b) 209 km                    c) 228 km                      d) 247 km   Update: Please find Solutions below   Ans 1.(c) Since the number of flowers in the rows and also in the columns are in A.P., the number of flowers with the sixth student in the fourth row (the centre-most student in the rectangle) would represent the average number of flowers with all the students.   1. As shown in the table below, there are 5 students between the fourth and the tenth students of the third rows, and the difference between the flowers with them is 36.   So, each person in that row must have 6 more flowers than the person on his left.   2. Now, in the sixth column there are 3 students between the third student and the seventh student and the difference between the flowers with them is 28. Hence, the number flowers with each person in that column will be 7 more than the person ahead of him.       As we can see, the number of flowers with the sixth student in the fourth row is 44, which is the average number of flowers with all the students.   Ans 2(a) To find hundred’s place we need to divide by 1000, since on dividing by 1000, we will get remainder of 3 digits, which will help us in getting hundred’s place.   = (2^1000)/1000   = (2^997/125)   = ((2^10)^99)*(2^7)/125   =1024*128/125   = 24*3/125   =72/125   Since we have divided by 8, we need to multiply back by 8.   = 72*8/125*8   =  576/1000   Thus, hundreds place’s is 5   Ans 3 (c) If Rakesh increases the price of item by 34.44% which means it increases by (31/90).   Thus,  MP/CP = 121/90   Thus, 0.9(M.P.) = 1.21(C.P.)   Rakesh pays 10% of mark price and takes 10% extra, thus looking at the above equation Rakesh earns 10% profit.   Ans 4 ( b) (x+36) /(x-36) = I (say)   I  –  1= 72/ (x-36)   Thus, x  –  36 should be factor of 72 = 2³ x 3²   Thus, x – 36 = ± 1, ± 2, ± 3, ± 4, ± 6, ± 8, ± 9, ± 12, ± 18, ± 24, ± 36, ± 72,   Thus there are 22 values of x except – 36 and – 72 since for these two values x will not be natural.   Ans 5 (b) 19n = Σ(9 +2n) 19n = Σ9 + 2Σn 19n = 9n +2n(n-1)/2 10n = n (n – 1) n = 11 Alternatively, initially difference between speed is 10 kmph that will be at par after 5 hours and at 6^th hour it will be exactly 19 kmph and thus to cover up the lost in initial 5 hour it will have to travel for more 5 hours. Thus, 11 hours.   Now, if it has travel for 11 hours total distance travel will be 209 km.