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Problem Set 9

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  Gamma Classes – Number system problem set For Answer and detailed solution (Problem set 1-8 PDF with video solution can be found in our FB group) Detailed solution will be discussed tonight 10:30 PM (4 August) in a live class  –    Link below Answer key will be posted tonight here at 8:00 PM - Facebook: https://www.facebook.com/groups/GammaClasses/    Link to join the live video solution to these problems : http://bootcampone.wiziqxt.com/online-class/413145  1.C(n) is the number of natural numbers less than n as well as even that can be written as thesum of three consecutive integersD(n) is the number of natural numbers less than n that can be written as the sum of threeconsecutive integersE(n) is the number of natural numbers less than n that can be written as the sum of twoconsecutive integersFind the unit digit of C(200) + D(200) + E(200)?2.For the nine-digit number 2912a7654, we have to maximize the sum of mods given bythesequence |2–9| + |9–1| + …+ |6–5| + |5–4|.Findthe unit digit of a 3 ?a)0b)1c)9d)2 of the above options are true3.From the tablebelow,answerthequestions that follow: W X Y Z   X Y Z W Y Z W Y Z W X Y X, Y, Z, W represents theage of Superman (W), Batman (X), Spiderman (Y)and Goku (Z) in 4parallel universes. Theyall had age which is a multiple of 5.To maintaintheir super-power,they must stay young (50 is considered old for aSuperhero). Sumof agesfor superheroesfallingindiagonal ofthetable is 80. Also giventhat Superman is theeldest ofthem.Findthe sum of age of Superman, Spiderman and Goku?a)30b)35c)40d)Cannot be uniquelydetermined4.Thanoscomesand says that ifheadds upthe age of all 4 superheroes, it is a multiple of4.Then he triesto calculate the minimum possibleage of Batman?a)5b)10c)15d)205.Find the remainder when LCM of 7 3001 + 1 and 7 3001  – 1 is divided by 10?a)0b)2c)4d)6e)8  Gamma Classes – Number system problem set For Answer and detailed solution (Problem set 1-8 PDF with video solution can be found in our FB group) Detailed solution will be discussed tonight 10:30 PM (4 August) in a live class  –    Link below Answer key will be posted tonight here at 8:00 PM - Facebook: https://www.facebook.com/groups/GammaClasses/    Link to join the live video solution to these problems : http://bootcampone.wiziqxt.com/online-class/413145  6. Find the number of digits in 1001 2018 a) 6054   b) 6055   c) 6056 d) 6057 7. Find the number of non-congruent rectangles having maximum possible perimeter of 150   and having integral length and breadth? a) 1 40 0b) 1402c) 1404d) 14068. Teacher writes a rational number (a/b) on the board. i. While   he went away   for   tea   break, one student changed the number such that the   new number written in decimal format became b.a which looked suspicious to   the   teacher. ii. On asking the class, they   said Gamma changed   the numerator and denominator by   79 and 10. iii. Further the   teacher   noticed that the   new number had greater   change   in numerator   than denominators But unfortunately, the teacher couldn’t recollect the number exactly he had written. He has to calculate it, then in how many attempts he can tell- assuming he is 100% efficient in mathematics. a)He can never tellb)1c)2d)More than 2
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