Question

The figure in Panel I below is a grid of cells with four rows and four columns.
The numbers on the top and on the left represent the number of cells that are to
be shaded in that column and row, respectively. Which one of the options shown
in Panel II below represents the grid shaded correctly?

• A. (i)
• B. (ii)
• C. (iii)
• D. (iv)

Hint:

Count shaded cells per row and per column in each option and match them against the given row and column numbers; only one grid satisfies both sets of clues.

Answer 1

The Correct Option is B

Step 1: The grid has 4 rows and 4 columns. The numbers on top give, for each column, how many cells in that column must be shaded; the numbers on the left give, for each row, how many cells in that row must be shaded.

Step 2: For a shading pattern to be valid, each row must contain exactly the number of shaded cells specified by its row clue, and each column must contain exactly the number of shaded cells specified by its column clue.

Step 3: Check each candidate grid in Panel II by counting the shaded cells in every row and comparing with the row clue, then counting shaded cells in every column and comparing with the column clue.

Step 4: Options (i), (iii) and (iv) each have at least one row or one column whose shaded-cell count does not match its clue number.

Step 5: Option (ii) is the only grid where every row's shaded count matches its row clue and every column's shaded count matches its column clue simultaneously.

Final Answer: \(\boxed{\text{(ii)}}\)