Problem 3 · 2024 Math Kangaroo
Easy
Geometry & Measurement
grid-countingarea
The rectangle on the right has 4 rows and 7 columns, so it is made of 28 white squares. Ira paints 2 whole rows and 1 whole column. How many squares are still white?
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Answer: C — 12
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Hint 1 of 3
Instead of counting the painted squares, count the ones that stay white.
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Hint 2 of 3
A square stays white only if its row was not painted AND its column was not painted.
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Hint 3 of 3
How many rows are left unpainted, and how many columns?
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Approach: count the white squares directly using the leftover rows and columns
- A square stays white only when both its row and its column are unpainted.
- Ira paints 2 of the 4 rows, so 2 rows stay white; she paints 1 of the 7 columns, so 6 columns stay white.
- The white squares fill those 2 leftover rows across those 6 leftover columns: 2 × 6 = 12.
- So 12 (C) squares are still white.
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