Wednesday, July 14, 2010

Challenging P6

Row 1                       2

Row 2                 4    6    8

Row 3          10  12  14  16  18

Row 4    20  22  24  26  28  30  32

a) What is the largest number on Row 10?
b) 288 is the largest number in a certain row. Which row is it?


Row 1 --> 1 = 1 x 2 - 1
Row 2 --> 3 = 2 x 2 - 1
Row 3 --> 5 = 3 x 2 - 1
Row 4 --> 7 = 4 x 2 - 1

Row N --> N x 2 - 1 = 2 N - 1

Row 1 --> 2 x 1
Row 2 --> .......... 2 x (1 + 3)
Row 3 --> .......... 2 x (1 + 3 + 5)
Row 4 --> .......... 2 x (1 ++ 3 + 5 + 7)

Row N --> .......... 2 x [1 + 3 + 5 + 7 + .... (2 N - 1)]
               = 2 x {[1 + (2 N - 1)] x N/2}
               = 2 N x N

Row 10 --> 2 x 10 x 10 = 200

a) The largest number in Row 10 is 200.


2 N x N --> 288
N x N--> 288/ 2 = 144
                          = 12 x 12 -- Row 12

b) 288 is the largest number in Row 12.

3 comments:

  1. Please kindly provide your intelligence...

    In a stadium, 20 % of the people are performers for the concert and the rest are spectators. 72 % of the spectators are males and there are 220 more male spectators then female spectators. How many male spectators must leave the stadium so that 37.5 % of the people in the stadium are male spectators?


    My answer is 276 but don't know whether my answer is correct...

    ReplyDelete
  2. My answer is 201 male spectators must leave the stadium.

    ReplyDelete
  3. 201 is my ans as well

    ReplyDelete