Aim-mcat6 Detailed Answers

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All India Test Series MCAT6

AITS CAPSULE

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Section I Q1.

Given AB=2a AP=BQ=a and OA=√2a => angle AOB = 900 So area grazed by goat =2ða2 - 3*(Area of sector AB - area of triangle AOB) = 3(ð/2-1)a2 Hence option D is correct. Difficulty Level: Hard Q2. The equation can be written as |2-|x|| = 3-|x|

From the graph its both curves intersect at 4 points Hence option E is correct. Difficulty Level: Moderate Q3. Let x be the volume removed from the mixture and replaced by liquid B and a be the initial volume of A in original mixture. M is the volume of original mixture. The new percentage of volume of A is P = a(1-x/M)

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The volume of A left will be minimum after the intersection of M3 and M1. The volume in M1 will be = 64(1-x/32) The volume in M2 will be = 48(1-x/48) The volume in M3 will be = 32(1-x/64) At the intersection of M3 and M1 the value of x = 64/3 = 21.33 All values of x greater than it will have Volume of A least in M. Hence option E is correct. Difficulty Level: Hard Q4. Let the polynomial be Ax2 +Bx+C =0 From the condition we get, A[(a-b)2 +(b-c)2 +(c-a)2] +B(a-b+b-c+c-a) + 3C = 2C 3A(a2 +b2+c2) = -C C/A = -3(a2 +b2+c2) Hence option E is correct. Difficulty Level: Easy Q5. Let T be the point of tangency and TD =x Therefore AT2 = AP2 – PT2 = 36-4 = 32 AT=4√2 Now AD2 = AB2 + BD2 = ( 4√2+x)2 = 82 + x2 Solving x= 2√2 Hence option A is correct. Difficulty Level: Easy Q6. (b+ac) – (a+bc) = (c-1)(a-b) and (c+ab)-(b+ac) = (1-a)(c-b) So that inequalliteis equal to (c-1)(a-b)≥0 and (1-a)(c-b) ≥0 If a<1
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For 3 steps number of ways = 3, For 4 steps number of ways = 5 So the number of ways for n steps be f(n) then f(n) = f(n-1)+f(n-2) For 10 steps we will get 89 ways. Essentially these are Fibonacci numbers Hence option A is correct. Difficulty Level: Moderate Q9. The given lines being parallel tangents to a circle, the diameter of the circle is equal to the distance between these lines, so that the required radius is ½ * (4+7/2)/√(9+16) = 15/20 = 3/4 Hence option C is correct. Difficulty Level: Easy Q10. After first over i.e 6 balls 8th batsman will be notout. After the the batsman getting not-out will be y+2 where y is number of balls till previous over. After 2 overs 14th batsman will be notout This process will continue till 38th batsman is notout. Hence option C is correct. Difficulty Level: Easy Q11. is prime for r=0,1,2,3,4 32 Now 2 -1 = (216 +1) (28 +1) (24 +1) (22 +1) (21 +1) (21 -1) Thus 5 factors are prime and 6th factor is 1 which is not prime Hence option B is correct. Difficulty Level: Hard Q12. For common ratio 1 the three terms of G.P are sides of the triangle. Let ar2 ar and a be the sides of the triangle. Now for common ratio > 1 From triangle's inequality ar2 < ar +a since a >0 => r2 -r -1 <0 =>(-√5+1)/2 < r <(√5 +1)/2 since r>1 => 11 Similar to case 1 we get 1 1<1/r<(√5 +1)/2 => (√5 -1)/2
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Difficulty Level: Easy Q13. Previous date which is palindrome is 31 aug 1380 ie. 08311380 So sum of digits is 24. Hence option D is correct. Difficulty Level: Moderate Q14. If we open the cuboid we will get the shape get the minimum length as below.

2 2 So minimum length of the string required = √c +(3a+2b) Putting the values we get string length = √(64 + 225) = 17 Hence option A is correct. Difficulty Level: Moderate Q15. Define the following variables: w=width of Canal, s1=speed of first swimmer, s2=speed of second swimmer, t1=time until Swimmers meet the first time, t2=time until swimmers meet the second time Now we can arbitrarily say that both swimmers are 700 mts from the shore of original of the first swimmer at time t1. The following equations can be inferred from the information given: (1) w=t1*(s1+s2) (2) s1*t1=700 (3) w+300=s1*t2 (4) 2w-300=s2*t2 Adding equations (3) and (4) we get: (5) 3w=t2*(s1+s2) Substituting s1+s2=w/t1 from equation (1) we get: 3w=t2*r/t1 3w*t1=r*t2 (6) 3*t1=t2 Combining equations (3) and (6): (7) w+300=3*s1*t1 Combining equations (2) and (7): w + 300=2100 w = 1800 Hence option B is correct. All Content © Copyright 2009 MindInsight.com

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Difficulty Level: Moderate Q16.

AB=2km AC=4km Let PQ be the tower Angle PCQ =45 So PC= h Angle PBQ = 30 degree BP=h√3 Angle PC and BP are perpendiculars on AC and AB respectively, since boys are closes to the tower. Therefore AB2 + BP2 = AC2 + PC2 => 4 + 3h2 = 16 + h2 => 2h2 = 12 => h=√6 Hence option A is correct. Difficulty Level: Moderate Q17. Let p be the probability that just one bateria eventually dies out, and all its n decendants. The probablity of n amoba all dying out is p . After the first turn there are four possibilities for the number of bacteria left, 0, 1, 2, 3 2 3 with probabilites of eventually dying out of 0, p, p , and p . With each outcome being 2 3 equally likely the probability of all bacterias eventually dying out is 1/4*[ 1 + p + p + p 2 3 2 3 2 ]. So p = 1/4*[ 1 + p + p + p ] or 1 -3p + p + p = 0. This reduces to (p - 1)(p + 2p 1) = 0. The solutions for p are 1, (√2-1), and (-√2-1). The only one which satisfies the constraints of the problem is √2-1. Hence option E is correct. Difficulty Level: Hard Q18. The general term of the series is = n2 /(2n-1)*(2n+1) = n2 /(4n2-1) = (1+ 1/(4n2-1))/4 = 1/4+(1/(2n-1) -1/(2n+1))/4 So sum of the series (n=1 to n=500) = 500/4 + (1-1/1001)/8 = 125250/1001 Hence option C is correct. All Content © Copyright 2009 MindInsight.com

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Difficulty Level: Hard Q19. (3m+1)2 + (3m-1)2 = 20 => 18m2 +2 = 20 => m2 = 1 => m=1,-1 So two values possible Hence option C is correct. Difficulty Level: Easy Q20. If x is a positive multiple of 6 that ends with a 4, then the next multiples of 6 end with a 0 (x + 6), a 6 (x + 12), a 2 (x + 18), an 8 (x + 24), a 4 (x + 30), so the next multiple of 6 that ends with a 4 is x+30. So any 30 consecutive positive integers must contain exactly one integer with the desired properties. How many such integers lie between 10000 and 99999? Since we have 90000 consecutive positive integers, we find 90000 ÷ 30 = 3000 such integers amongst them. Hence option D is correct. Difficulty Level: Moderate

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Section II Q21. Each student has at least one true/false answer in common with every other student. So if one of them gets five correct answers then each student got at least one correct answer. From II, total number of correct answers obtained by all the students can be 1 + 2 + 3 + 4 + 5 =15. Now maximum number of correct answers can be +2(A or B), +2(A or B), +4(T), +4(T), +3(T) = 15, hence Anand should have all correct answers. But then Bhanu and Dipu will have same marks, same for Charu and Ekta. Hence no one gets five correct answers. Then from II number of correct answers must be 0 + 1 + 2 + 3 + 4 = 10. Anand, Charu and Dipu can not get 0 marks because total number of correct answers can not be required 10 if answer for both Q3 and Q4 is false. Hence Bhanu or Ekta got 0 marks. If Bhanu got 0 marks then correct answers for T/F questions are Q3-F, Q4-T, Q5-F. Then Charu, Dipu and Ekta will have at least two answers correct. Anand is with one correct answer in true/false section and hence he gets 1 mark if none of his multiple choice sections are correct. But in this case we get total marks as +1(C), +1(C), +1(F), +4(T), +2(F) = 9. Hence it is Ekta who got 0 marks and not Bhanu. Ekta got 0 marks hence correct answers for T/F section are Q3-T, Q4-F, Q5-F. Anand got 1 marks hence Q1-B, Q2-B/C. If Q2-C, then we have sum of marks as +2(B), +1(C), +1(F), +4(T), +2(F) = 10. Hence, Dipu got maximum correct answers i.e 4. Hence option D is correct. Difficulty Level: Hard Q22. ‘A’ and the person who paddled twice, each paddled at least in one return trip. From I and IV, B, C and D each paddled on one forward trip. From I and III, C was in the boat when B paddled on a forward trip. C was in the boat on two forward trips, C must have paddled on a return trip. Hence C paddled twice. Hence option C is correct. Difficulty Level: Moderate

Q23. The man who goes every two days, man went to the health club for the first time this month on the 1st or 2nd of this month and the man who goes every three days went to the gym for the first time on 1st,2nd or 3rd.The man who goes every seven days went to the gym for the first time this month on either 5th or 6th. Two cases are possible: Case A: Ali went on Monday (1st), Dara went on Wednesday (3rd) and Gama went on Friday (5th). Possible dates are: Ali: 1,3,5,7,9,11,13,15,17,19,21,23,25,27,29,31 Dara: 3,6,9,12,15,18,21,24,27,30 Gama: 5,12,19,26 Case B: Dara went on Wednesday(1st), Gama went on Friday(3rd) and Ali(6th) went on Monday. Ali: 1,3,5,7,9,11,13,15,17,19,21,23,25,27,29,31 All Content © Copyright 2009 MindInsight.com

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Dara: 3,6,9,12,15,18,21,24,27,30 Gama: 6,13,20,27 Case A is eliminated and from case B we have common date for all three as 27. Hence option E is correct. Difficulty Level: Moderate Q24. Case I: If Arjun is speaking truth, he is the only one from pandva family or Bhima is the only one from Kaurva family. Case II: If Arjun is lying, he cannot be the only one of the three members from Kaurva family. Also, Bhima cannot be the only one of the three from Pandva family. So Duryodhna is the only one from Pandva family or all three are members of Kaurava family. Hence Arjun is member of Pandva family from case I and from Kaurava family from case II. Hence Bhima is member of Kaurava family from both case I and II. Hence Duryodhana is member of either family from case I and either family from case II. Hence we know Bhima belongs to Kaurava family. Hence option B is correct. Difficulty Level: Moderate

Q25. For first two rounds analyzing from table: Germany and Argentina have both won their matches while New Zealand and South Africa have lost both theirs. Germany’s round 2 match has to be vs. South Africa, since Pakistan can not lose 2-1. In round 2 Germany beat South Africa by 2 goals to 1. Hence option D is correct. Difficulty Level: Moderate

Q26. Team Pakistan won one round and lost one. And GF/GA is 2/1. Hence it won 2-0 and lost 0-1. So, Argentina beat Pakistan by 1-0. Hence option B is correct. Difficulty Level: Moderate Q27. From the statements from (a), (b), (c) given in the problem four teams (Spain, Argentina, Germany and Pakistan) appear to win their matches in the fifth round. However, there are only three matches per round and hence only three teams can win their matches in any round. Hence, the data set appears to be inconsistent. Hence option E is correct. Difficulty Level: Moderate All Content © Copyright 2009 MindInsight.com

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Q28. From the statements from (a), (b), (c) given in the problem four teams (Spain, Argentina, Germany and Pakistan) appear to win their matches in the fifth round. However, there are only three matches per round and hence only three teams can win their matches in any round. Hence, the data set appears to be inconsistent. Hence option E is correct. Difficulty Level: Moderate Q29. Since the number of persons per household can be assumed to be a constant, the ratio of x1 to x2 is the same as the ratio of the number of property crimes per 1000 households in 1975 to that in 2000. This value is 560/180= 3:1 Hence option A is correct. Difficulty Level: Moderate Q30. Let the number of households in thousands be T1 in 2000 and T2 in 2050. The total number of property crimes in 2000 is, therefore, T1 × 180. This will reduce to T1 × 180 × 0.71 × 0.71. The number of property crimes per thousands households in 2050 is T1 × 180 × 0.71 × 0.71/T2. Since the number of persons per household remains constant, the ratio of T1/ T2 is the same as the ratio of the populations. The ratio of the populations is (157+ 2.3 × 50)/ (157 +2.3 × 100). The required answer comes out to be approximately 63. Hence option A is correct. Difficulty Level: Moderate

Q31. Let x be the number of aggravated assaults per thousand population. The number of robberies is x – 1.8 and the number of simple assaults is 3x. From the graph, we get the sum of all the three as 27. Hence x – 1.8 + x + 3x = 27, giving x = 5.76 and x – 1.8 = 3.96. The total number of robberies is, therefore, (3.96/1000) × (157 + 2.3 × 50) ×10^6 = 1.1 × 10^6. Hence option A is correct. Difficulty Level: Moderate Q32. Population in 1975 = 157 + 2.3*25 = 214.5 Population in 2000 = 157 + 2.3*50 = 272 Y1 = 214.5 x 48 x 1000 Y2 = 272 x 28 x 1000 Y2 – y1 = -2680 x 1000 Hence option E is correct. All Content © Copyright 2009 MindInsight.com

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Difficulty Level: Easy Q33. The number of property crimes in 2000 was 180 × H where H is the number of households in thousands in 2000. The number of violent crimes in 1975 was 49 x P1 where P1 is the population in 1975 in thousands. Therefore, 180 x ( H / 49.P1) = 1.45 which gives P1/H = 3.67/1.45 The quantity required is P2/H where P2 is the population in 2000. But P2/ P1 = (157+2.3x50)/(157+2.3x25) = 272/214.5 So, P2/H = (272/214.5) x (3.67/1.45) = 3.2 (approx) Hence option B is correct. Difficulty Level: Moderate Q34. Visually, we see US has reported more than 21,000,000 cases. Hence option B is correct. Difficulty Level: Easy Q35. Bahamas, Belgium and Denmark Hence option C is correct. Difficulty Level: Easy Q36. West Germany = 222, France = 555 So, Required ratio = 222:555 = 2:5 Hence option D is correct. Difficulty Level: Easy Q37. Bahamas, Burundi, French Guyana and US. Hence option B is correct. Difficulty Level: Easy Q38. Let P = population of Zambia in 1996 Rate of AIDS cases = 4/10000 4/10000 x P = 286,000 hence P = 715,000(in thousands) Hence option D is correct. Difficulty Level: Easy

Q39. Only I and II are true. Hence option A is correct. All Content © Copyright 2009 MindInsight.com

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Difficulty Level: Moderate Q40. Ethiopia, Israel and Yugoslavia. Hence option D is correct. Difficulty Level: Easy

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Section III Q41. Refer to the paragraph I, passage I, many statements have been made for objectivist design. From those, we can deduce that option B is correct statement. Hence, correct answer is option B. Difficulty Level: Easy Q42. Refer to the paragraph II, passage I, statements A and B are wrong, but statement C holds true. Hence, correct answer is option C. Difficulty Level: Easy Q43. From first few lines of paragraph III, it is quite clear that statement A is true. Hence, correct answer is option A. Difficulty Level: Easy Q44. In the last paragraph, few theories have been discussed. According to those theories, statements A to D, all are incorrect. Hence, correct answer is option E. Difficulty Level: Moderate Q45. Refer to the paragraph I, passage II, author emphasizes the potential of culture as a strong social and economic resource for the community. Hence, correct answer is option B. Difficulty Level: Easy Q46. Refer to the paragraph II, passage II, we can easily spot that option A is correct. In options B and C, use of the word “only” is incorrect since culture can be one of the ways, not the sole way. Hence, correct answer is option A. Difficulty Level: Moderate Q47. Refer to the paragraph III, passage II, statements A to D, all are incorrect. Hence, correct answer is option E. Difficulty Level: Easy Q48. From the passage, we can deduce that defensive mechanism of releasing phenols by the trees to counter lepidopteran caterpillars population has counter effect on trees since phenols control virus attack on lepidopteran caterpillars. All Content © Copyright 2009 MindInsight.com

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Hence, correct answer is option B. Difficulty Level: Moderate Q49. From the paragraph III, it is stated that, “these same chemicals also help caterpillars survive by disabling the droop virus.” Hence, correct answer is option B. Difficulty Level: Easy Q50. After reading the passage, we can find that statement D is correct about lepidopteran caterpillars. Hence, correct answer is option D. Difficulty Level: Moderate Q51. Here, we need to first decide between statement s F and C. Clearly, statement C is the starting statement since it introduces microorganism and their immediate surroundings. Between statements A and B, it is easy to spot that A should come first. Hence, correct answer is option D. Difficulty Level: Moderate Q52. In this question, we have to choose among statements D, E and F for the starting statement. Statements D and F are the continuation of other statements, hence can’t start the paragraph. Statement E is most suited for the starting statement. Hence, correct answer is option A. Difficulty Level: Moderate Q53. Here, clearly statement B is the starting statement. Statement C is most suited to come after B since it talks about the usage of technology which was introduced in statement B. Hence, correct answer is option E. Difficulty Level: Moderate Q54. The original underlined sentence as well as choices B and C are unnecessarily wordy. Choice D is an efficient, direct, and clear expression that retains the meaning of the original. Choice E leaves out essential information from the original. Hence, correct answer is option D. Difficulty Level: Moderate Q55. In the original underlined portion, ‘those’ is incorrect. To express respectively two singular points of view, the noun or pronoun which refers to each must be singular; those All Content © Copyright 2009 MindInsight.com

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is, of course, plural. Only choice D provides a clearly singular reference, one, for each viewpoint. Hence, correct answer is option D. Difficulty Level: Moderate Q56. The underlined portion must name Monarch immediately in order to clarify the comparison between Monarch and King. It is Monarch, not the harpooner, as in choices A or C, and not the prognostications, as in choice B, who is much like King. Choice D has the right structure but has an agreement error between prognostication and their. Hence, correct answer is option E. Difficulty Level: Moderate Q57. In the second paragraph, we read of his recognition that behaviorism is offensive to many people, that it does not have popular appeal. Hence, correct answer is option C. Difficulty Level: Easy Q58. The passage discusses the possible application of ABC’s theory to the field of human affairs and in promoting the development of humankind. Hence, correct answer is option A. Difficulty Level: Easy Q59. Aggravate means ‘to make worse’. aggregate means ‘to collect together or total’. Clearly, aggravate will be used here, covering any crime will make things worse. done means completed. dun means demand repeatedly. In this context, usage of dun is correct. altar means worship table. alter means change. Very easy to spot, alter is correct. elapse means (of time) pass by. lapse means ‘to slip or fall’. We are talking about the time, hence elapse will be used. casual means informal. causal means relating to a cause. Clearly, causal will be used. Hence, correct answer is option C. Difficulty Level: Easy Q60. amend means modify or revise. emend means alter or correct in the text of a written work. Related to text, hence emend is correct. bridal means having to do with a marriage ceremony. All Content © Copyright 2009 MindInsight.com

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bridle is having to do with horseback riding. Use of riders in the sentence points towards bridle. cession means act of ceding (surrendering) to another. session means meeting or term. Cession will be used since here we are talking about treaty. facilitate means make easy. felicitate means congratulate. Clearly, felicitate is correct. hypercritical means excessively critical. hypocritical means deceptive, just pretending to be good. The context points towards deception, hence hypocritical is correct. Hence, correct answer is option A. Difficulty Level: Easy

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