ISEE Upper Level Quantitative : How to find circumference

Study concepts, example questions & explanations for ISEE Upper Level Quantitative

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Example Questions

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Example Question #21 : Radius


In the above figure, .

Which is the greater quantity?

(a) The sum of the circumferences of the inner and outer circles

(b) The sum of the circumferences of the second-largest and third-largest circles

Possible Answers:

(a) and (b) are equal

It is impossible to determine which is greater from the information given

(b) is the greater quantity

(a) is the greater quantity

Correct answer:

(a) and (b) are equal


For the sake of simplicity, we will assume that ; this reasoning is independent of the actual length.

The four concentric circles have radii 1, 2, 3, and 4, respectively, and their circumferences can be found by multiplying these radii by .

The inner and outer circles have circumferences  and , respectively; the sum of these circumferences is . The other two circles have circumferences   and ; the sum of these circumferences is .

The two sums are therefore equal.


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