A chocolate bar is marked into 2 rows of 4 equal pieces. How many rectangles of any size, squares counted, do its lines form? The figure is a rectangle divided into a grid of 2 rows and 4 columns of equal squares.

A chocolate bar is marked into 2 rows of 4 equal…

A chocolate bar is marked into 2 rows of 4 equal pieces.

MediumOriginal question

A chocolate bar is marked into 2 rows of 4 equal pieces. How many rectangles of any size, squares counted, do its lines form?

30Correct answerYour answer31Correct answerYour answer32Correct answerYour answer33Correct answerYour answer

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CorrectNot quiteAnswer A

Correct answer: A

A rectangle is fixed by choosing 2 of the 5 vertical lines and 2 of the 3 horizontal lines.
Vertical pairs: $\binom{5}{2} = 10$ . Horizontal pairs: $\binom{3}{2} = 3$ .
Rectangles $= 10 \times 3 = 30$ .

Worth noting

Counting only the small squares, or only the squares, misses the long thin rectangles. The line-pair method counts every rectangle exactly once.

Ten questions from Non-verbal Reasoning, at your own pace.

Ten questions from Non-verbal Reasoning, at your own pace.