Concept : numbers of consecutive natural numbers sum to n = (number of odd factors of n ) -1 1000 = 5^3 * 2^3here number of odd factors = 4 and required answer = 4 - 1 = 3

The clock loses 30 minutes per hour. i.e 30 minutes of this faulty clock = 60 minutes of the correct clock From 2 p.m to 6 p.m , total number of hours = 4 hours 4 hours of this faulty clock => 4 x 60/30= 8 hours of original clock So, The correct time when the clock show 6 p.m = 6 p.m + 4 = 10 p.m But The clock stopped 3 hours ago , So present time is 10 p.m + 3 hours = 1 a.m

Q100) A and B play a game of dice between them. The dice consist of colors on their faces (instead of numbers). When the dice are thrown, A wins if both show the same color; otherwise B wins. One dice has 4 red face and 2 blue faces. How many red and blue faces should the other dice have for both the to players have same chances of winning? a) 3 red and 3 blue faces b) 2 red and remaining blue c) 6 red and 0 blue d) 4 red and remaining blue

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