Problem 11 · 2021 Math Kangaroo
Medium
Arithmetic & Operations
division
A rectangular chocolate bar is made of equal squares. Neil breaks off two complete strips of squares and eats the 12 squares he obtains. Later, Jack breaks off one complete strip of squares from the same bar and eats the 9 squares he obtains. How many squares of chocolate are left in the bar?
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Answer: D — 45
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Hint 1 of 2
Neil's two equal strips total 12, so a strip in that direction holds 6 — that fixes one side of the bar.
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Hint 2 of 2
Jack's strip runs the other way; remember Neil already removed two rows before Jack broke his strip.
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Approach: recover the bar's dimensions from the strip sizes
- Neil's two equal strips give 12 squares, so each strip holds 6: one side of the bar is 6.
- Jack's strip runs the other way and holds 9, but Neil had already removed 2 squares from that direction, so the full bar was 6 by (9+2) = 11, i.e. 66 squares.
- Eaten in all: 12 + 9 = 21 squares.
- Left: 66 − 21 = 45, so the answer is D.
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