## two strings have equal length. One of the strings is shaped, with no overlap, into a circle. The other string is shaped,

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### two strings have equal length. One of the strings is shaped, with no overlap, into a circle. The other string is shaped,

by BTGmoderatorLU » Wed Jan 12, 2022 5:46 pm

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Source: GMAT Prep

Two strings have equal length. One of the strings is shaped, with no overlap, into a circle. The other string is shaped, with no overlap, into a square. What is the ratio of the area of the region enclosed by the circle to the area of the region enclosed by the square?

A. $$1 : 2$$
B. $$\pi : 2$$
C. $$1 : 1$$
D. $$4 : \pi$$
E. The ratio depends on the length of the two strings

The OA is D

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### Re: two strings have equal length. One of the strings is shaped, with no overlap, into a circle. The other string is sha

by gmatter2012 » Mon Jan 17, 2022 7:59 am
BTGmoderatorLU wrote:
Wed Jan 12, 2022 5:46 pm
Source: GMAT Prep

Two strings have equal length. One of the strings is shaped, with no overlap, into a circle. The other string is shaped, with no overlap, into a square. What is the ratio of the area of the region enclosed by the circle to the area of the region enclosed by the square?

A. $$1 : 2$$
B. $$\pi : 2$$
C. $$1 : 1$$
D. $$4 : \pi$$
E. The ratio depends on the length of the two strings

The OA is D
ans should be \4 \pi :1 \ rather than 4 : \ pi

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Posts: 126
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### Re: two strings have equal length. One of the strings is shaped, with no overlap, into a circle. The other string is sha

by gmatter2012 » Mon Jan 17, 2022 8:02 am
BTGmoderatorLU wrote:
Wed Jan 12, 2022 5:46 pm
Source: GMAT Prep

Two strings have equal length. One of the strings is shaped, with no overlap, into a circle. The other string is shaped, with no overlap, into a square. What is the ratio of the area of the region enclosed by the circle to the area of the region enclosed by the square?

A. $$1 : 2$$
B. $$\pi : 2$$
C. $$1 : 1$$
D. $$4 : \pi$$
E. The ratio depends on the length of the two strings

The OA is D
ans should be $$4 \pi :1$$ rather than $$4 : \pi$$

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### Re: two strings have equal length. One of the strings is shaped, with no overlap, into a circle. The other string is sha

by regor60 » Mon Jan 17, 2022 12:52 pm
gmatter2012 wrote:
Mon Jan 17, 2022 8:02 am
BTGmoderatorLU wrote:
Wed Jan 12, 2022 5:46 pm
Source: GMAT Prep

Two strings have equal length. One of the strings is shaped, with no overlap, into a circle. The other string is shaped, with no overlap, into a square. What is the ratio of the area of the region enclosed by the circle to the area of the region enclosed by the square?

A. $$1 : 2$$
B. $$\pi : 2$$
C. $$1 : 1$$
D. $$4 : \pi$$
E. The ratio depends on the length of the two strings

The OA is D
ans should be $$4 \pi :1$$ rather than $$4 : \pi$$
L= length of strings

Circumference of circle=L=2piR
R=L/2pi.

Area of circle: piR^2= pi*L^2/4pi^2
= L^2/4pi

Each side of square= L/4

Area of square: L^2/16

Ratio of area of circle to area of square means:
Area of circle/Area of square

= (L^2/4pi)/(L^2/16)
= (L^2/4pi)*(16/L^2)
=4/pi which is 4:pi D

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