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The area of a rectangle is 675 sq.cm. If both the length

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The area of a rectangle is 675 sq.cm. If both the length  [#permalink]

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New post Updated on: 23 Nov 2019, 18:56
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The area of a rectangle is 675 sq.cm. If both the length and the breadth (in cm) of the rectangle are integers, how many such rectangles are there, for which at least one of the dimensions is not a multiple of 3 and at least one of the dimensions is not a multiple of 5?

(A) 1
(B) 2
(C) 3
(D) 4
(E) 6

Originally posted by CaptainLevi on 23 Nov 2019, 14:41.
Last edited by chetan2u on 23 Nov 2019, 18:56, edited 1 time in total.
Formatted the choices
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The area of a rectangle is 675 sq.cm. If both the length  [#permalink]

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New post 23 Nov 2019, 18:56
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CaptainLevi wrote:
The area of a rectangle is 675 sq.cm. If both the length and the breadth (in cm) of the rectangle are integers, how many such rectangles are there, for which at least one of the dimensions is not a multiple of 3 and at least one of the dimensions is not a multiple of 5?

(A) 1
(B) 2
(C) 6
(D) 4


675=3^3*5^2=27*25

The dimensions fulfilling the criteria of at least one not being multiple of 3 and at least one not being multiple of 5..
1) (27*25)*1=675 by 1
2) 27*25, that is 27 by 25

Only two

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Re: The area of a rectangle is 675 sq.cm. If both the length  [#permalink]

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New post 24 Nov 2019, 00:34
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The area of a rectangle is 675 sq.cm. If both the length and the breadth (in cm) of the rectangle are integers, how many such rectangles are there, for which at least one of the dimensions is not a multiple of 3 "and" at least one of the dimensions is not a multiple of 5?

Since it is AND both conditions have to satisfy-- this is possible only when L * B is multiple of 5 * multiple of 3 i.e. 5^2 * 3^3......So only 2 Triangles are possible ... L*B --- 5^2*3^3 or 3^3 *5^2

Option - b
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Re: The area of a rectangle is 675 sq.cm. If both the length  [#permalink]

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New post 24 Nov 2019, 00:45
zs2 wrote:
The area of a rectangle is 675 sq.cm. If both the length and the breadth (in cm) of the rectangle are integers, how many such rectangles are there, for which at least one of the dimensions is not a multiple of 3 "and" at least one of the dimensions is not a multiple of 5?

Since it is AND both conditions have to satisfy-- this is possible only when L * B is multiple of 5 * multiple of 3 i.e. 5^2 * 3^3......So only 2 Triangles are possible ... L*B --- 5^2*3^3 or 3^3 *5^2

Option - b


Both 3^3 by 5^2 and 5^2 by 3^3 are SAME triangle in GMAT. Generally the greater side is length.
The second case will be 675 by 1, and here too 675 by 1 and 1 by 675 are SAME.
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Re: The area of a rectangle is 675 sq.cm. If both the length  [#permalink]

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New post 24 Nov 2019, 00:49
chetan2u wrote:
zs2 wrote:
The area of a rectangle is 675 sq.cm. If both the length and the breadth (in cm) of the rectangle are integers, how many such rectangles are there, for which at least one of the dimensions is not a multiple of 3 "and" at least one of the dimensions is not a multiple of 5?

Since it is AND both conditions have to satisfy-- this is possible only when L * B is multiple of 5 * multiple of 3 i.e. 5^2 * 3^3......So only 2 Triangles are possible ... L*B --- 5^2*3^3 or 3^3 *5^2

Option - b


Both 3^3 by 5^2 and 5^2 by 3^3 are SAME triangle in GMAT. Generally the greater side is length.
The second case will be 675 by 1, and here too 675 by 1 and 1 by 675 are SAME.



Right , got it. L*B is same as B*L
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Re: The area of a rectangle is 675 sq.cm. If both the length  [#permalink]

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New post 01 Dec 2019, 05:44
I feel that the question is inappropriately worded and is ambiguous.

how many such rectangles are there, for which at least one of the dimensions is not a multiple of 3 and at least one of the dimensions is not a multiple of 5

We can also comprehend this as 2 separate cases

Case 1: where the rectangle has at least 1 side which is not a multiple of 3

(5*135),(25*27),(1*675)

Case 2: where the rectangle has at least 1 side which is not a multiple of 5

(3*225),(9*75) and (25*27),(1*675) are common

So my take would be 5
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Re: The area of a rectangle is 675 sq.cm. If both the length  [#permalink]

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New post 01 Dec 2019, 07:17
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dips1122 wrote:
I feel that the question is inappropriately worded and is ambiguous.

how many such rectangles are there, for which at least one of the dimensions is not a multiple of 3 and at least one of the dimensions is not a multiple of 5

We can also comprehend this as 2 separate cases

Case 1: where the rectangle has at least 1 side which is not a multiple of 3

(5*135),(25*27),(1*675)

Case 2: where the rectangle has at least 1 side which is not a multiple of 5

(3*225),(9*75) and (25*27),(1*675) are common

So my take would be 5



The wordings are ok.
If it were say at least.... OR at least...., then your solution could be OK
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Re: The area of a rectangle is 675 sq.cm. If both the length   [#permalink] 01 Dec 2019, 07:17
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