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    Mission IIMpossible

    @Mission IIMpossible

    CAT preparation in itself holds a wonderful opportunity to build and fine tune our managerial qualities. We don’t have to prove to anyone about what we can do. We are not running any race here. It is all about self improvement and getting closer to our dream. Let’s start from where we are today… Let’s give our best and make sure tomorrow we will be closer to our dreams than we are today.

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    Topics created by Mission IIMpossible

    • M

      Gyan Room - Modern Math - Concepts & Shortcuts
      Quant Primer • mission iimpossible • • Mission IIMpossible  

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      Shortcut for Finding the Rank Of A Word
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      Gyan Room - Geometry - Concepts & Shortcuts
      Quant Primer • mission iimpossible • • Mission IIMpossible  

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      Mass point Geometry lecture - @gaurav_sharma
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      Gyan Room - Number Theory - Concepts & Shortcuts
      Quant Primer • mission iimpossible • • Mission IIMpossible  

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      Kaprekar's constant 6174 is known as Kaprekar's constant. Take any four-digit number, using at least two different digits. (Leading zeros are allowed.)Arrange the digits in descending and then in ascending order to get two four-digit numbers, adding leading zeros if necessary.Subtract the smaller number from the bigger number.Go back to step 2 and repeat.The above process will always yield 6174, in at most 7 iterations. The only four-digit numbers for which Kaprekar's routine does not reach 6174 are repdigits such as 1111, which give the result 0000 after a single iteration.
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      Gyan Room - Algebra - Concepts & Shortcuts
      Quant Primer • mission iimpossible • • Mission IIMpossible  

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      A quadratic function f (x ) = ax^2 + bx + c, can be expressed in the standard form : a(x-h)^2 + kby completing the square. The graph of f(x) is a parabola with vertex (h,k); the parabola opens upward if a > 0 or downward if a < 0. Maximum or Minimum Value of a Quadratic Function Let f be a quadratic function with standard form f (x) = a( x − h )^2 + k.The maximum or minimum value of f occurs at x = hIf a > 0, then the minimum value of f is f(h) = k.If a < 0, then the maximum value of is f (h) = k We now derive a formula for the maximum or minimum of the quadratic functionF(x) = ax^2 + bx + c.For either of the two cases (the quadratic having a maxima or a minima), the maxima or the minima,as the case may be, will occur when x = - b/2athe maximum or minimum value is f(-b/2a) = c - b^2/4aremember that - b/2a = sum of roots/2
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      Gyan Room : Arithmetic - Concepts & Shortcuts
      Quant Primer • mission iimpossible • • Mission IIMpossible  

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      If two objects A and B start simultaneously from opposite points and, after meeting, reach their destinations in ‘a’ and ‘b’ hours respectively (i.e. A takes ‘a hrs’ to travel from the meeting point to his destination and B takes ‘b hrs’ to travel from the meeting point to his destination), then the ratio of their speeds is given by:Sa/Sb = √(b/a) i.e. Ratio of speeds is given by the square root of the inverse ratio of time taken. Two trains A and B starting from two points and travelling in opposite directions, reach their destinations 9 hours and 4 hours respectively after meeting each other. If the train A travels at 80kmph, find the rate at which the train B runs. Sa/Sb = √(4/9) = 2/3This gives us that the ratio of the speed of A : speed of B as 2 : 3.Since speed of A is 80 kmph, speed of B must be 80 * (3/2) = 120 kmph A and B start from Opladen and Cologne respectively at the same time and travel towards each other at constant speeds along the same route. After meeting at a point between Opladen and Cologne, A and B proceed to their destinations of Cologne and Opladen respectively. A reaches Cologne 40 minutes after the two meet and B reaches Opladen 90 minutes after their meeting. How long did A take to cover the distance between Opladen and Cologne? Sa/Sb = sqrt(90/40) = 3/2 This gives us that the ratio of the speed of A : speed of B as 3:2. We know that time taken is inversely proportional to speed. If ratio of speed of A and B is 3:2, the time taken to travel the same distance will be in the ratio 2:3. Therefore, since B takes 90 mins to travel from the meeting point to Opladen, A must have taken 60 (= 90*2/3) mins to travel from Opladen to the meeting point(adsbygoogle = window.adsbygoogle || []).push({}); So time taken by A to travel from Opladen to Cologne must be 60 + 40 mins = 1 hr 40 mins [Credits: Veritasprep]