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

@aafalke [solution credits - Sayantan Ghatak] CP = 100MP = (100 + 4n)Discount = (100 + 4n) x (n + 10)/100SP = (100 + 4n) - (100 + 4n) x (n + 10)/100 = 130(100 + 4n) [1 - (n+10)/100] = 130(100 + 4n) [ (90 - n)/100] = 1309000 + 360n - 100n - 4n^2 = 13000n^2 - 65n + 1000 = 0(n - 40)(n - 25) = 0n = 40 or n = 25As it is given that n is a multiple of 8, n = 40New SP = (40 + 10) + 100 = 150MP = (100 + 4 x 40) = 260Discount = (110 x 100)/260 = 550/13 = 42.3%

Q30) On a particular day, exactly six persons – Amar, Bhanu, Chetan, Dinesh, Gaurav and Jitesh – visited a doctor for consultation, not necessarily in the same order. Each person paid a different amount to the doctor as consultation fee and each person consulted the doctor at a different time. At the end of the day, the doctor noticed that, except for the first two persons, the rest of the persons paid a consultation fee, which was equal to the average of the consultation fees paid by the previous two persons. The following information is known about the fees paid and the order in which they consulted the doctor: The consultation fee paid by each person (in Rs.) was not necessarily an integer and no person paid more than Rs.2500.Bhanu paid Rs.1000, which was the lowest among all the six persons, and she consulted the doctor immediately before Gaurav, who did not pay the highest amount.Amar paid Rs.100 more than Dinesh, who consulted the doctor before both Amar and Jitesh. What is the highest amount (in Rs.) paid for consultation by any of the six persons? Who was the last person to consult the doctor? What is the total amount paid by all the six persons combined? Who among the six persons paid the second lowest amount for consultation?