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01 Jul 2023, 01:47
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A
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If x and y are integers such that \(x^3 = 750 * y^2\), then what is the least possible value of \(x*y\)?
A. \(-180\)
B. \(-6\)
C. \(0\)
D. \(36\)
E. \(180\)
A. \(-180\)
B. \(-6\)
C. \(0\)
D. \(36\)
E. \(180\)
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01 Jul 2023, 02:26
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rohitgm
x is a product of 750 and \(y^2\). As \(y^2\) is non-negative, x has to be non-negative. However, we do not have any restriction on y. y can be a negative integer.
\(x^3 = 5^3 * 3 * 2 * y^2\)
As x and y is an integer, \(y^2 = 36\). Therefore \(y = \pm6\)
x = 5 * 3 * 2
Minimum value of x* y = 5 * 3 * 2 * -6 = -180
Option A
General Discussion
01 Jul 2023, 08:32
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750 = 5^3 * 3*2
x^3 = 5^3 * 3*2 * y^2
y has to be 3*2 ( 6) but since we are looking for least possible value of x*y and that RHS is +ve so LHS value of x has to be +ve as well , but y can be (-6)
x = 5*3*2 ; 30
y = -6 ;
30*-6 ; -180
option A
x^3 = 5^3 * 3*2 * y^2
y has to be 3*2 ( 6) but since we are looking for least possible value of x*y and that RHS is +ve so LHS value of x has to be +ve as well , but y can be (-6)
x = 5*3*2 ; 30
y = -6 ;
30*-6 ; -180
option A
rohitgm
