A square countertop has a square tile inlay in the center, leaving an untiled strip of uniform width around the tile. If the ratio of the tiled area to the untiled area is 25 to 39, which of the following could be the width, in inches, of the strip?
I. 1
II. 3
III. 4
A) I only
B) II only
C) I and II only
D) I and III only
E) I, II and III
Could you please also tell me what level is this question? (700+; 650 etc)
thanks
Andrew
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Square countertop
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IMO its 3 . whats the OA?
ratio of the square tile inside to the total area of the larger tile will be -
25x / ( 25+39)x = 25x / 64x
x prefarably should be a perfect square number
1. let x be 4 ------- then the sides will be 10 and 16 ---- width will be 3
2.let x be 9 -----------sides will be 15 and 24 ---- width will be 3 again
METHOD 2 ----
sqrt 64x = 2( widht of the strip ) + sqrt 25x
solving this we get --
9x =4 (width ) ^2
wher e width is 3
ratio of the square tile inside to the total area of the larger tile will be -
25x / ( 25+39)x = 25x / 64x
x prefarably should be a perfect square number
1. let x be 4 ------- then the sides will be 10 and 16 ---- width will be 3
2.let x be 9 -----------sides will be 15 and 24 ---- width will be 3 again
METHOD 2 ----
sqrt 64x = 2( widht of the strip ) + sqrt 25x
solving this we get --
9x =4 (width ) ^2
wher e width is 3
I am lost 
I think all are possible.
There is no point which says width of squares (countertop and tile) has to be integer.
If these are non integers I can get any legth.
ratio as 2009wish found
25x : 64x
x = 4
width = 3
x = 4/9
width = 1
here ratio will be
100/9 : 256/9
so sides will be
10/3 and 16/3
so width = 1
similarly x=8/3 will give width as 4.
Whats the OA?
I am with E
btw, this is one of the most difficult Q I have seen.
I almost gave up
I think all are possible.
There is no point which says width of squares (countertop and tile) has to be integer.
If these are non integers I can get any legth.
ratio as 2009wish found
25x : 64x
x = 4
width = 3
x = 4/9
width = 1
here ratio will be
100/9 : 256/9
so sides will be
10/3 and 16/3
so width = 1
similarly x=8/3 will give width as 4.
Whats the OA?
I am with E
btw, this is one of the most difficult Q I have seen.
I almost gave up
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Ian Stewart
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I suppose a reasonable question, when reading the above, would be "why would any of the values be impossible?" Really, the width of the strip is just telling you how big the diagram is; if the question can be answered at all, then the width could have any positive value -- just scale the diagram appropriately. No calculations are actually required.acorra wrote:A square countertop has a square tile inlay in the center, leaving an untiled strip of uniform width around the tile. If the ratio of the tiled area to the untiled area is 25 to 39, which of the following could be the width, in inches, of the strip?
I. 1
II. 3
III. 4
A) I only
B) II only
C) I and II only
D) I and III only
E) I, II and III
Could you please also tell me what level is this question? (700+; 650 etc)
thanks
Andrew
To illustrate:
We have a smaller square inside a larger square. If the ratio of the area of the smaller square to the area of the strip is 25 to 39, that means the area of the smaller square is 25/64 of the area of the large square. So, the smaller square could be 5x5, and the larger square could be 8x8, leaving a strip of width (8-5)/2 = 3/2 = 1.5 inches. What happens if we double all of the dimensions? We get a 10x10 square inside a 16x16 square; the ratio is then 10*10/16*16 = (2*5)(2*5)/(2*8)(2*8) = 25/64 (the 2's cancel), and the width of the strip has doubled. Similarly, you can make the strip any width you like by scaling the dimensions appropriately.
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gmat009
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Can someone plz. help me in this question. I am not getting width=3 when x=4.
The way I am doing this is:-
Let x be the side of smaller square . If w is width around tile, then side of larger square is x+2w
Therefore
(x^2)/((x+2w)^2) = 25/64
(x)/(x+2w)=5/8
w=3x/10
If x=1,3,4 then I am getting different width of 3/10, 9/10, 6/5.
Can someone plz. help me where I am going wrong...
The way I am doing this is:-
Let x be the side of smaller square . If w is width around tile, then side of larger square is x+2w
Therefore
(x^2)/((x+2w)^2) = 25/64
(x)/(x+2w)=5/8
w=3x/10
If x=1,3,4 then I am getting different width of 3/10, 9/10, 6/5.
Can someone plz. help me where I am going wrong...
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logitech
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Well the question is actually an EASY tough question, like a skinny fat people. ( People who have excess body fat but not really HEAVY )acorra wrote:A square countertop has a square tile inlay in the center, leaving an untiled strip of uniform width around the tile. If the ratio of the tiled area to the untiled area is 25 to 39, which of the following could be the width, in inches, of the strip?
I. 1
II. 3
III. 4
A) I only
B) II only
C) I and II only
D) I and III only
E) I, II and III
Could you please also tell me what level is this question? (700+; 650 etc)
thanks
Andrew
I attached a picture showing what the problem is talking about
And we can see that X/Y = bla bla and Width is bla bla but whatever the width ration we can multiply it by a NUMBER and make it: 1, 4, 128, 212718 , and so on..
And so EVERYTHING could be the answer. And remember when we are talking about RATIOS ..we have a freedom to define any number we want as long as it is proportional.
So I would say E as in EVEREST 8)
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logitech
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X does NOT need to be an integer! :!:gmat009 wrote:Can someone plz. help me in this question. I am not getting width=3 when x=4.
The way I am doing this is:-
Let x be the side of smaller square . If w is width around tile, then side of larger square is x+2w
Therefore
(x^2)/((x+2w)^2) = 25/64
(x)/(x+2w)=5/8
w=3x/10
If x=1,3,4 then I am getting different width of 3/10, 9/10, 6/5.
Can someone plz. help me where I am going wrong...
LGTCH
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"DON'T LET ANYONE STEAL YOUR DREAM!"
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"DON'T LET ANYONE STEAL YOUR DREAM!"
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gmat009
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I understand that X doesnot need to be an integer but my question is how is everyone getting width=3 when x=4.logitech wrote:
X does NOT need to be an integer! :!:
I am getting width=6/5 when x=4
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logitech
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gmat009 wrote:I understand that X doesnot need to be an integer but my question is how is everyone getting width=3 when x=4.logitech wrote:
X does NOT need to be an integer! :!:
I am getting width=6/5 when x=4
Because your X and their X are NOT the same
Your X refers to the length of the one side of inner SQUARE
Their X is the variable in 25x/64x
Got it ?
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santosh_surathkal
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gmat009 wrote:Can someone plz. help me in this question. I am not getting width=3 when x=4.
The way I am doing this is:-
Let x be the side of smaller square . If w is width around tile, then side of larger square is x+2w
Therefore
(x^2)/((x+2w)^2) = 25/64
(x)/(x+2w)=5/8
w=3x/10
If x=1,3,4 then I am getting different width of 3/10, 9/10, 6/5.
Can someone plz. help me where I am going wrong...
This can be only multiplier of 3 ... because whatever you do with 5 and 8 the width is always the multiplier of 1.5.
@Ian Stewart could you check your calculation once again????
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