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Updated on: 23 Nov 2019, 18:56
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.
Last edited by chetan2u on 23 Nov 2019, 18:56, edited 1 time in total.
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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
(A) 1
(B) 2
(C) 3
(D) 4
(E) 6
23 Nov 2019, 18:56
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CaptainLevi
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
(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
B
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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
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
