THE CIRCLE

marmar29 wrote:hi all

an archery target has 3 concentric regions. the daimeter of the regions are in the ratio 1:2:3
find the ratio of thier areas
there s a drawing of a circle inside it another 2 smaller

waiting yr active answer
manar

IMO

1/4 : 1 : 9/4

let the diameter be x,2x,3x so radius = x/2, x, 3x/2

ratio of area of a circle is proportional to Sq. of radius

hence ratio = 1/4 : 1 : 9/4

thnks for help !
but the answer gvn is 1:3:5 !
how does it come !

atulmangal wrote:

marmar29 wrote:hi all

an archery target has 3 concentric regions. the daimeter of the regions are in the ratio 1:2:3
find the ratio of thier areas
there s a drawing of a circle inside it another 2 smaller

waiting yr active answer
manar

IMO

1/4 : 1 : 9/4
let the diameter be x,2x,3x so radius = x/2, x, 3x/2

ratio of area of a circle is proportional to Sq. of radius

hence ratio = 1/4 : 1 : 9/4

the principle is sound: for similar shapes, the area ratio the square of the linear ratio.

So if the diameter ratio is 1:2:3 (which means that the radius ratio is the same 1:2:3, since dividing the ratio by 2 does not change the ratio), the area of the circles with these radii would be 1:4:9.

the error lies in that the question is asking for the ratio of the areas of the concentric regions, not the circle: in other words, the area of each "ring" around the the previous circles.

inner circle has area of 1
middle ring has area of 4-1 =3 (area of middle "ring" is area of middle circle - area of inner circle)
Outer ring has area 9-4=5 (area of outer circle - area of middle circle).

marmar29 wrote:thnks for help !
but the answer gvn is 1:3:5 !
how does it come !

I don't think this is the correct answer...if u take some values for diameter

Let say, 2,4 and 6 now these values full fill the condition as they are in the ratio 1:2:3

radius = 1,2,3 hence ratio of areas = 1:4:9...this is same as my answer(if u multiply my answer from 4 u get the same)

What's the source???

Geva@MasterGMAT wrote:

atulmangal wrote:

marmar29 wrote:hi all

an archery target has 3 concentric regions. the daimeter of the regions are in the ratio 1:2:3
find the ratio of thier areas
there s a drawing of a circle inside it another 2 smaller

waiting yr active answer
manar

IMO

1/4 : 1 : 9/4
let the diameter be x,2x,3x so radius = x/2, x, 3x/2

ratio of area of a circle is proportional to Sq. of radius

hence ratio = 1/4 : 1 : 9/4

the principle is sound: for similar shapes, the area ratio the square of the linear ratio.

So if the diameter ratio is 1:2:3 (which means that the radius ratio is the same 1:2:3, since dividing the ratio by 2 does not change the ratio), the area of the circles with these radii would be 1:4:9.

the error lies in that the question is asking for the ratio of the areas of the concentric regions, not the circle: in other words, the area of each "ring" around the the previous circles.

inner circle has area of 1
middle ring has area of 4-1 =3 (area of middle "ring" is area of middle circle - area of inner circle)
Outer ring has area 9-4=5 (area of outer circle - area of middle circle).

@Geva

I got your point but please suggest...

can we expect that in GMAT, we get the diagram plus the clarity what exactly the question in asking us to find out??? IMO, In the posted question its not clear what to find out...what do u think???

atulmangal wrote:

Geva@MasterGMAT wrote:

atulmangal wrote:

marmar29 wrote:hi all

an archery target has 3 concentric regions. the daimeter of the regions are in the ratio 1:2:3
find the ratio of thier areas
there s a drawing of a circle inside it another 2 smaller

waiting yr active answer
manar

IMO

1/4 : 1 : 9/4
let the diameter be x,2x,3x so radius = x/2, x, 3x/2

ratio of area of a circle is proportional to Sq. of radius

hence ratio = 1/4 : 1 : 9/4

the principle is sound: for similar shapes, the area ratio the square of the linear ratio.

So if the diameter ratio is 1:2:3 (which means that the radius ratio is the same 1:2:3, since dividing the ratio by 2 does not change the ratio), the area of the circles with these radii would be 1:4:9.

the error lies in that the question is asking for the ratio of the areas of the concentric regions, not the circle: in other words, the area of each "ring" around the the previous circles.

inner circle has area of 1
middle ring has area of 4-1 =3 (area of middle "ring" is area of middle circle - area of inner circle)
Outer ring has area 9-4=5 (area of outer circle - area of middle circle).

@Geva

I got your point but please suggest...

can we expect that in GMAT, we get the diagram plus the clarity what exactly the question in asking us to find out??? IMO, In the posted question its not clear what to find out...what do u think???

I agree that a GMAT question needs to be indisputable and less ambiguous - meaning that it needs to explicitly state what is the shape of the region it requires the area of - a ring or a circle.

But the above notwithstanding, it is clear that whoever wrote teh question had exctly this sort of confusion in mind - i.e. the question will definitely incluce 1:4:9 as a trap answer choice for those who fail to stop for a second and ascertain exactly what are the area covered - full circles, or "rings".