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# One inch represents 20 miles on Map K and one inch represents 30 miles

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Re: One inch represents 20 miles on Map K and one inch represents 30 miles [#permalink]
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One square inch represents 20*20 square miles on Map K
3 square inch represents 3*20*20 square miles on Map K

One square inch represents 30*30 square miles on Map L
3 square inch represents 3*30*30 square miles on Map L

Difference in the area = 3*(30*30 -20*20) = 1500 square miles

gmatt1476 wrote:
One inch represents 20 miles on Map K and one inch represents 30 miles on Map L. An area of 3 square inches represents how many more square miles on Map L than on Map K ?

A. 30
B. 400
C. 500
D. 900
E. 1,500

PS41450.02
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Re: One inch represents 20 miles on Map K and one inch represents 30 miles [#permalink]
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1 inch in k = 20 miles
1 square inch = 400 miles
3 square inch = 1200 miles ----(1)

1 inch in L = 30 miles
1 square inch = 900 miles
3 square inch = 2700 miles ----(2)

2700-1200=1500
IOC should be E

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One inch represents 20 miles on Map K and one inch represents 30 miles [#permalink]
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gmatt1476 wrote:
One inch represents 20 miles on Map K and one inch represents 30 miles on Map L. An area of 3 square inches represents how many more square miles on Map L than on Map K ?

A. 30
B. 400
C. 500
D. 900
E. 1,500

PS41450.02

$$1 in= 20 miles$$ (On map K)
$$1 in= 30 miles$$ (On Map L)

3 $$in^{2}$$= 3*$$(20miles)^{2}$$= 1200 $$ml^{2}$$ (On Map K)
3 $$in^{2}= 3*(30miles)^{2}$$= 2700 $$ml^{2}$$ (On Map L)
--> 2700 $$ml^{2}$$ - 1200 $$ml^{2}$$= 1500 $$ml^{2}$$

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Re: One inch represents 20 miles on Map K and one inch represents 30 miles [#permalink]
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gmatt1476 wrote:
One inch represents 20 miles on Map K and one inch represents 30 miles on Map L. An area of 3 square inches represents how many more square miles on Map L than on Map K ?

A. 30
B. 400
C. 500
D. 900
E. 1,500

PS41450.02

map K ; 1 inch ; 20 miles so 1 inch ^2 = 400 miles^2 and
map L ; 1 inch ; 30 miles so 1 inch ^2 = 900 miles^2
so for 3 square inches we get ; 3 * ( 900-400) ; 3 * 500 ; 1500 miles ^2
OPTION E
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Re: One inch represents 20 miles on Map K and one inch represents 30 miles [#permalink]
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gmatt1476 wrote:
One inch represents 20 miles on Map K and one inch represents 30 miles on Map L. An area of 3 square inches represents how many more square miles on Map L than on Map K ?

A. 30
B. 400
C. 500
D. 900
E. 1,500

PS41450.02

On Map K, since 1 inch = 20 miles, 1 in^2 = 400 mi^2 and 3 in^2 = 1200 mi^2.

On Map L, since 1 inch = 30 miles, 1 in^2 = 900 mi^2 and 3 in^2 = 2700 mi^2.

Thus, the difference is 2700 - 1200 = 1500 mi^2.

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Re: One inch represents 20 miles on Map K and one inch represents 30 miles [#permalink]
gmatt1476 wrote:
One inch represents 20 miles on Map K and one inch represents 30 miles on Map L. An area of 3 square inches represents how many more square miles on Map L than on Map K ?

A. 30
B. 400
C. 500
D. 900
E. 1,500

PS41450.02

3sq inch => side =(sqrt(3))
K = (sqrt(3)*20)^2; L = (sqrt(3)*30)^2
L-K = 2700-1200 = 1500
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Re: One inch represents 20 miles on Map K and one inch represents 30 miles [#permalink]
gmatt1476 wrote:
One inch represents 20 miles on Map K and one inch represents 30 miles on Map L. An area of 3 square inches represents how many more square miles on Map L than on Map K ?

A. 30
B. 400
C. 500
D. 900
E. 1,500

PS41450.02

Ans E , imo

---------------------------K--------------------------------L------------
1 inch ------------------20 miles---------------------30 miles-----

1 square inch-----------400 sq miles-------------------900 sq miles-----

3 SQ inch--------------1200 sq miles---------------2700 sq miles

So difference = 2700 - 1200 = 1500 sq miles .
Ans : E
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Re: One inch represents 20 miles on Map K and one inch represents 30 miles [#permalink]
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Top Contributor
SOLUTION:

A NEW OG 2021 QUESTION

On Map K, 1 inch = 20 miles =>1 square inch = 400 mile square

On Map L 1 inch = 30 miles

3 square inches on Map K = 3* 400 =1200 square miles

3 square inches on Map L = 3 * 900 = 2700 square miles

The difference = 2700 - 1200 =1500 square miles (OPTION E)

Hope this helps
Devmitra Sen(Math)
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Re: One inch represents 20 miles on Map K and one inch represents 30 miles [#permalink]
gmatt1476 wrote:
One inch represents 20 miles on Map K and one inch represents 30 miles on Map L. An area of 3 square inches represents how many more square miles on Map L than on Map K ?

A. 30
B. 400
C. 500
D. 900
E. 1,500

PS41450.02

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Re: One inch represents 20 miles on Map K and one inch represents 30 miles [#permalink]
If an area is 3 square inches that means the side is SQRT(3) which is roughly 1.7.

1.7 inches in map L is 1.7*30 = 51. 51^2 = 2601
1.7 inches in map K is 1.7*20 = 34. 34^2 = 1156
subtract these two and the closest number is 1500.

Smarter way would be (sqrt(3)*30)^2 - (sqrt(3)*20)^2 = 2700 - 1200 = 1500.
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Re: One inch represents 20 miles on Map K and one inch represents 30 miles [#permalink]
SameerGupta2001 wrote:
Map K,
1inch=20 miles
1 sq.inch=400 sq. miles
3 sq.inch=1200 sq. miles

Map L,
1inch=30 miles
1 sq.inch=900 sq. miles
3 sq.inch=2700 sq. miles

Therfore, the difference is 1500 sq.miles(E)

This is the easiest method to work with.
Although I did something different.

3 square inches means one side is square root of 3 which equals 1.7. 1.7 of 20 squared is the area of of the smaller square. 34^2.

Now again, 1.7 times 30 equals 51. 51^2.

51^2 - 34^2 equals 1455. Closest is 1455.

Lengthy, but still not sure whether it is a valid approach.
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Re: One inch represents 20 miles on Map K and one inch represents 30 miles [#permalink]
Bunuel
Hi, kindly help me understand.

One inch represents 20 miles on Map K and one inch represents 30 miles on Map L. An area of 3 square inches represents how many more square miles on Map L than on Map K ?

if 1inch is 20 miles then 3inch is 60 miles on map K. then 3 sq inches is 60^2 right?
answer should be 90^2 - 60^2.
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Re: One inch represents 20 miles on Map K and one inch represents 30 miles [#permalink]
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Akioharu wrote:
Bunuel
Hi, kindly help me understand.

One inch represents 20 miles on Map K and one inch represents 30 miles on Map L. An area of 3 square inches represents how many more square miles on Map L than on Map K ?

if 1inch is 20 miles then 3inch is 60 miles on map K. then 3 sq inches is 60^2 right?
answer should be 90^2 - 60^2.

If 1 inch = 20 miles, then 3 inches = 60 miles. However, 3 inches^2 is not the same as 3 inches; one is a measure of an area and the other is a measure of length.

If 1 inch = 20 miles, then 1 inch^2 = 20 miles * 20 miles = 400 mile^2.
Re: One inch represents 20 miles on Map K and one inch represents 30 miles [#permalink]
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