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A rectangle the length of which is 8 inches and the width of which is

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MartyTargetTestPrep
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A rectangle the length of which is 8 inches and the width of which is [#permalink] New post   Updated on: 03 Jun 2016, 06:15
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A rectangle the length of which is 8 inches and the width of which is 6 inches is made up 48 1 inch by 1 inch squares. Through how many of the squares does a diagonal of the rectangle pass?

(A) 6

(B) 8

(C) 10

(D) 12

(E) 16


Source: Marty Murray
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Originally posted by MartyTargetTestPrep on 03 Jun 2016, 05:44.
Last edited by MartyTargetTestPrep on 03 Jun 2016, 06:15, edited 1 time in total.
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chetan2u
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Re: A rectangle the length of which is 8 inches and the width of which is [#permalink] New post   03 Jun 2016, 06:02
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MartyMurray wrote:
A rectangle the length of which is 8 inches and the width of which is 6 inches is made up 48 one inch by one inch squares. Through how many of the squares does a diagonal of the rectangle pass?

(A) 6

(B) 8

(C) 10

(D) 12

(E) 16


Source: Marty Murray


Hi,

I have done this earlier in a different format..
there is a pattern involved in it..

two case-


1)If the two sides are co-prime, SUM of sides -1..
2)and if not co-prime , Sum of sides - HCF of sides..

the difference is related to the diagonal passing through a vertex of squares at some place..

here 6 and 8 are NOT co-primes, so ans \(= 6+8-HCF(6,8) = 14-2 =12\)
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rohit8865
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Re: A rectangle the length of which is 8 inches and the width of which is [#permalink] New post   25 Jun 2016, 12:59
chetan2u wrote:
MartyMurray wrote:
A rectangle the length of which is 8 inches and the width of which is 6 inches is made up 48 one inch by one inch squares. Through how many of the squares does a diagonal of the rectangle pass?

(A) 6

(B) 8

(C) 10

(D) 12

(E) 16


Source: Marty Murray


Hi,

I have done this earlier in a different format..
there is a pattern involved in it..

two case-


1)If the two sides are co-prime, SUM of sides -1..
2)and if not co-prime , Sum of sides - HCF of sides..

the difference is related to the diagonal passing through a vertex of squares at some place..

here 6 and 8 are NOT co-primes, so ans \(= 6+8-HCF(6,8) = 14-2 =12\)
D

Hi chetan

Can u please elaborate the highlighted a little for me
or any link explaining the same..

thanks
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Aviralft9
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Re: A rectangle the length of which is 8 inches and the width of which is [#permalink] New post   19 Jan 2020, 06:53
This can be solved by a little bit of geometry,
Consider ABCD as the rectangle. The length of the diagonal will 10 units.
Required ans 10 + 2(corners) = 12.
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ravigupta2912
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Re: A rectangle the length of which is 8 inches and the width of which is [#permalink] New post   19 Jan 2020, 07:15
Aviralft9 wrote:
This can be solved by a little bit of geometry,
Consider ABCD as the rectangle. The length of the diagonal will 10 units.
Required ans 10 + 2(corners) = 12.


Can you explain how will the diag. pass through the 2 additional tiles in the corner? I'm unable to get that bit.

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Re: A rectangle the length of which is 8 inches and the width of which is [#permalink] New post   25 Jan 2020, 22:30
Aviralft9 wrote:
This can be solved by a little bit of geometry,
Consider ABCD as the rectangle. The length of the diagonal will 10 units.
Required ans 10 + 2(corners) = 12.


That logic makes no sense, it just happens to be correct.
If i take a 4x4 square or 2x2 square the number of 1x1 squares the diagonal goes through are 4 and 2, respectively.
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cjk52793
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Re: A rectangle the length of which is 8 inches and the width of which is [#permalink] New post   25 Jan 2020, 23:08
I drew a rough sketch. The slope of the line using point slope formula will give you 3/4=m. When X=1, Y=3/4, when X=2, Y= 1.5. A line going from the origin through those two points will go through 3 squares. So every 2 increases in X equals 3 squares it passes through.

=8/2=4 and 4*3=12.

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Re: A rectangle the length of which is 8 inches and the width of which is [#permalink]
25 Jan 2020, 23:08
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