Completion of an Incomplete Pattern

In this type of questions an incomplete figure is given in which a part, generally a quarter, is left blank.  The problem figure is followed by four choice figures.  Out of these choice figures, the candidate is required to choose the one which best fits into the blank space so as to complete the original pattern.

You should complete the pattern in such a way that the figure appears balanced and not haphazard.  In other words, the figure should appear symmetrical.  Obviously, then, you should choose an answer choice that symmetrically fits into the empty box. 

The first thing that should be done for this is to recognize the axis of symmetry.  You should find out the line about which the figure would be symmetrical, if completed.  This is not a difficult job and a cursory glance at the figure would be sufficient for you to detect the axis of symmetry.  Once you have found out the axis of symmetry you can draw the image of the figures on one side of the axis, taking this axis as a mirror, to find out the pattern of the other side.

Rules for solving by the method of symmetry

  1. X, Y, A, B: The given figure consists of four quarters.  The blank quarter with the question mark will be called the X-quarter; the corner diagonally opposite to it will be called the Y-quarter while the other two will be called A- and B-quarters respectively.  For example, in the incomplete patternbelow the various quarters have been marked as shown:
  2. Middle-line and Main diagonal: The two lines dividing the larger square into four quarters will be called middle-lines while the diagonal joining the X and Y quarters will be called the main diagonal.  The following figure illustrates the point:
  3. Rule I: If the figure of Y quarter is symmetrically placed about any one of the other figures (say A) about one of the middle lines then this middle line is the axis of symmetry.  In this case the reflection of B about the axis of symmetry should come in place of X.


    Rule II: If A and B are symmetrically placed about the diagonal while Y is not symmetrical with either of them, then the diagonal is the axis of symmetry.  In this case, the reflection of Y about the other diagonal should come in place of X.