One inch represents 20 miles on Map K and one inch represents 30 miles : Problem Solving (PS)

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

02 May 2020, 17:09

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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.

Answer: E

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

20 Apr 2020, 12:46

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Answer should be 1500
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

Posted from my mobile device

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

20 Apr 2020, 12:51

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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 \(ml^{2}\)

Answer (E).

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

12 Feb 2021, 03:24

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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]

20 Apr 2020, 12:42

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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]

21 Apr 2020, 11:26

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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]

21 Apr 2020, 00:12

why does the OG 2021 have so many of these kinds of questions :s

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

03 May 2020, 08:14

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]

09 Jun 2020, 19:23

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]

25 May 2021, 07:17

Expert Reply

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]

05 Dec 2021, 22:05

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]

01 Nov 2022, 21:47

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]

08 Nov 2023, 22:55

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

08 Nov 2023, 22:55

GMAT Problem Solving (PS) Questions

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