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Fine Tune Your Quantitative Skills

http://ankitat.blogspot.com/2009/07/fine-tune-your-quantitative-skills.html

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Fine Tune Your Quantitative Skills

  1. 1. April 2009 Fine Tune Your Quantitative Skills Ankit Sharma
  2. 2. Disclaimer This session is meant for those who are not good in quant. 2
  3. 3. SESSION OBJECTIVE 2. Solve CAT level questions – Without long calculations – Using simple logic – Spotting wrong options… • To score marks sufficient to clear the cut off in quantitative section • To demonstrate that a relaxed state of mind can help us significantly while attempting quant • To demonstrate that all the above is possible without really knowing quant in detail 3
  4. 4. Point To Ponder The psychology of a quant paper setter She/he spends 3-4 hours to make a good question and 1-2 minutes to make 5 options  4
  5. 5. The Ten Commandments 5
  6. 6. Commandment 1 All questions are equally tough for me, hence I will read all of them Reading means: Reading the questions and all the choices 6
  7. 7. Commandment 2 If I am able to eliminate 3 out of 5 options, I will take a chance and mark an answer. 7
  8. 8. Commandment 3 Geometry is easy ! 4. If no figure is given I will draw it roughly to scale. 5. Wherever possible I will assume a particular case for a general case – Hexagon implies a regular hexagon – Quadrilateral/parallelogram implies a square – Right angle triangle with sides 3,4,5 or its multiples 8
  9. 9. Commandment 4 Algebra is my friend ! 4. In all ‘series’ questions, I will add first 2-3 terms and eliminate options. 5. In quadratic equations, I will assume a simple equation satisfying the options & eliminate options. 6. In all a, b, c or questions where n terms are given I will always assume them to be easy numbers like 0,1,-1, 2 etc. 9
  10. 10. Commandment 5 Probability (Hey bhagwan ! aaj subah kiska mooh dekha tha …) is not as bad as it looks. 4. In questions of probability involving ‘n’ trials I will check for n= 1,2 so on 5. Probability of any event lies between the best and the worst case scenarios. Thus, I will take the best and worst case scenarios for anything to happen or not to happen. 10
  11. 11. Commandment 6 Graph questions are not as ugly as they look, in fact in CAT, like in life, looks are deceiving. The more intimidating they look, the easier they are! 11
  12. 12. Commandment 7 Bring your relaxed brain with you for the exam, there are some really easy questions, we just need to be patient with. 12
  13. 13. Commandment 8 I will use all ‘illegitimate methods’  at my disposal to find the answer. 13
  14. 14. Commandment 9 I will not be afraid of any question in quant, however lengthy or scary it looks. 14
  15. 15. Commandment 10 CAT is like a festival. It occurs every year. So enjoy the festival and its preparation. 15
  16. 16. Applications 16
  17. 17. Application 1 - Question If ab X cd = 1073 and ba X cd = 2117, find the value of (ab + cd) given that ab, ba and cd are all two digit positive integers. 1.66 2.65 3.63 4.67 5.69 17
  18. 18. Application 1 - Solution If ab X cd = 1073 and ba X cd = 2117, find the value of (ab + cd) given that ab, ba and cd are all two digit positive integers. 1.66 2.65 3.63 4.67 5.69 ab and cd are odd because ab X cd = odd, Thus ab + cd = even, Hence, choice 2,3,4,5 are incorrect. Answer: Choice 1 (37 & 29) 18
  19. 19. Application 2 - Question If the points (1, 2), (4, 5), (8, 9) and (x, y) are vertices of a parallelogram, then find (x, y). 1.(1, 5) 2.(5, 12) 3.(7, 13) 4.(5, 7) 5. Data Insufficient 19
  20. 20. Application 2 - Solution If the points (1, 2), (4, 5), (8, 9) and (x, y) are vertices of a parallelogram, then find (x, y). 1.(1, 5) 2.(5, 12) 3. (7, 13) 4. (5,7) 5. Data Insufficient 3 of the 4 given points lie on the same line y = x + 1. Hence, they are Collinear and a parallelogram cannot be formed. Answer: Choice 5 20
  21. 21. Application 3 – Question – CAT 2002 The nth element of a series is represented as Xn = (-1)n Xn-1 If X0 = x and x > 0, then which of the following is always true. 1. Xn is positive if n is even 2. Xn is positive if n is odd 3. Xn is negative if n is even 4. None of these 21
  22. 22. Application 3 – Solution – CAT 2002 The nth element of a series is represented as Xn = (-1)n Xn-1 If X0 = x and x > 0, then which of the following is always true. 1. Xn is positive if n is even 2. Xn is positive if n is odd 3. Xn is negative if n is even 4. None of these Substitute for n = 1,2,3 … X0 = X, X1 = -X, X2 = -X … We find there is no sequence Answer: Choice 4 22
  23. 23. Application 4 – Question – CAT 2003 Given that -1 ≤ v ≤ 1, -2 ≤ u ≤ -0.5 and -2 ≤ z ≤ -0.5 and w = vz/u, then which of the following is necessarily true 1. -0.5 ≤ w ≤ 2 2. -4 ≤ w ≤ 4 3. -4 ≤ w ≤ 2 4. -2 ≤ w ≤ -0.5 23
  24. 24. Application 4 – Solution – CAT 2003 Given that -1 ≤ v ≤ 1, -2 ≤ u ≤ -0.5 and -2 ≤ z ≤ -0.5 and w = vz/u, then which of the following is necessarily true 1. -0.5 ≤ w ≤ 2 2. -4 ≤ w ≤ 4 3. -4 ≤ w ≤ 2 4. -2 ≤ w ≤ -0.5 U is always negative. For minimum value of w, vz should always be maximum positive. This means vz is 2. For maximum value of w, vz should be the smallest negative. This means vz is -2. Consider decimal value of W, to find the extreme values. Answer: Choice 2 24
  25. 25. Application 5 – Question – CAT 2004 If f(x) = x3 -4x + p, and f(0) and f(1) are of opposite signs, then which of the following is necessarily true 1. -1 < p < 2 2. 0 < p < 3 3. -2 < p < 1 4. -3 < p < 0 25
  26. 26. Application 5 – Solution – CAT 2004 If f(x) = x3 -4x + p, and f(0) and f(1) are of opposite signs, then which of the following is necessarily true 1. -1 < p < 2 2. 0 < p < 3 3. -2 < p < 1 4. -3 < p < 0 Substitute x = 0,1 f(0) = p, f(1) = -3 + p From the above we can infer that p cannot be negative. From -3 we know that p cannot be greater than 3. Answer: Choice 2 26
  27. 27. Application 6 – Question Bag A contains 6 white balls and 4 black balls and bag B contains 3 white balls and 2 black balls. A white ball is picked from bag A and put into bag B. Then, 3 balls are picked from bag B and put into bag A. Find the probability that a ball picked now from bag A is black. 1. 1/4 2. 1/3 3. 7/12 4. 5/12 5. 11/24 27
  28. 28. Application 6 – Solution Probability will lie between the best and the worst case scenario. White Black Bag A 6-1=5 4 Bag B 3+1=4 2 3 balls are transferred from bag B to bag A. Best Case 2 black and 1 white ball from B to A Worst Case 3 white balls from B to A White Black P(Black Ball) Best Case 5+1=6 4+2=6 6/12 Worst Case 5+3=8 4+0=4 4/12 The answer should lie between the best and the worst case. This eliminates option 1,2 and 3. Answer: Choice 4 28
  29. 29. Application 7 – Question – CAT 2005 Then x equals. (2 Marks) 1. 3 2. (√13 - 1) / 2 3. (√13 + 1) / 2 4. √13 29
  30. 30. Application 7 – Solution – CAT 2005 Then x equals. (2 Marks) 1. 3 2. (√13 - 1) / 2 3. (√13 + 1) / 2 4. √13 The above can be written as X2 = 4 + √(4-x) The first term is √4 which is greater than 2. The second term is √(4 + 2) which means the value of x must be less than 3. √13 = around 3.6 1. 3 2. 1.3 3. 2.3 4. 3.6 Answer: Choice 3 30
  31. 31. Application 8 – Question – CAT 2006 Let f(x) = max(2x + 1, 3 – 4x), where x is any real number. Then the minimum possible value of f(x) is. 1. 1/3 2. 1/2 3. 2/3 4. 4/3 5. 5/3 31
  32. 32. Application 8 – Solution – CAT 2006 Let f(x) = max(2x + 1, 3 – 4x), where x is any real number. Then the minimum possible value of f(x) is. 1. 1/3 2. 1/2 3. 2/3 4. 4/3 5. 5/3 We know that f(x) would be minimum at the point of intersection of these curves. 2x + 1 = 3 – 4x  6x = 2  x = 1/3 Hence, min f(x) = 5/3 Answer: Choice 5 32
  33. 33. Application 9 – Question MTNL has 1500 subscribers in ‘Paradise’ and they earn a revenue of Rs.300 from each subscriber. They wish to maximize their revenue but for every increase in revenue of Rs.1 per subscriber, one subscriber drops out. What will be the maximum revenue of MTNL. 1. Rs.810,000 2. Rs.640,000 3. Rs.570,000 4. Rs.720,000 5. None of these 33
  34. 34. Application 9 – Solution MTNL has 1500 subscribers in ‘Paradise’ and they earn a revenue of Rs.300 from each subscriber. They wish to maximize their revenue but for every increase in revenue of Rs.1 per subscriber, one subscriber drops out. What will be the maximum revenue of MTNL. 1. Rs.810,000 2. Rs.640,000 3. Rs.570,000 4. Rs.720,000 5. None of these For every increase in revenue the subscriber base falls by same amount. Therefore (1500 – x) + (300 + x) = 1800 is a constant. When the sum of 2 numbers is constant, the product of the 2 is maximum when they are equal.  (1500 – x) = (300 + x) = 900 Therefore, f(x)max = 900 * 900 Answer: Choice 1 34
  35. 35. Application 10 – Question – CAT 2005 If x = (163 + 173 + 183 + 193), then x divided by 70 leaves a remainder of 1. 0 2. 1 3. 69 4. 35 35
  36. 36. Application 10 – Solution – CAT 2005 If x = (163 + 173 + 183 + 193), then x divided by 70 leaves a remainder of 1. 0 2. 1 3. 69 4. 35 X is a even number. Why ?? (a + b) always divides a3 + b3 Therefore, (163 + 193) and (173 + 183)are divisible by 35. Hence, x is divisible by 70. Answer: Choice 1 36
  37. 37. All The Best http://ankitat.blogspot.com/2009/07/fine-tune-your- quantitative-skills.html 37

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