IMAT 2014 Q17 [Playing Board]

The diagram below shows the layout of a game playing board with the square board numbered as indicated. The numbers on the board start with 1 on the bottom left and finish with 25 at the top right.


A larger, square playing board is numbered in a similar way and divided into pieces which fit together to make the whole board. One piece of this larger board is shown below:


How many squares are there on this larger board?

A. 49
B. 81
C. 25
D. 121
E. 64

Simple steps to solve word problems:

  • Underline key information
  • Determine what they are trying to ask, and what you will need to solve it
    • Eliminate any non-essential information
  • Draw a picture, graph, or equation
    • In moments of high stress like exam taking, always work with the paper they give you to avoid careless mistakes.
  • Solve

Approach: find out how many tiles are in a row and then square that number. We are looking for a square piece, so the number of rows = the number of columns.

Make a grid where the numbers line up with each other as they do in the problem. Then, count up or down, depending on the row, until you reach the numbers that make each line continuous. Be careful, you need to make sure everything lines up, not just 2/3 rows.



14→13→12→10→ 9 → 8 → 7

So we have 7 rows. Since we are looking for a square board, we can conclude there are 7 columns as well.

(7)(7) = 49

\fcolorbox{red}{grey!30}{Therefore the answer is A, $49$.}