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05 Sep 2019, 03:41
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If a is an even integer and b is an odd integer, then \(\frac{a^3b^2}{8}\)?
A. Always even
B. Always odd
C. Always a fraction
D. Could be a fraction
E. Always an integer
A. Always even
B. Always odd
C. Always a fraction
D. Could be a fraction
E. Always an integer
05 Sep 2019, 10:10
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Before we solve this problem we should note the following properties:
(Odd Number) * (Odd Number) = (Odd Number)
(Even Number) * (Even Number) = (Even Number)
(Odd Number) * (Even Number) = (Even Number)
(Even Number) / (Even Number) = (Even Number)
as per the given: a is an even integer and b is an odd integer:
a^3= (Even Number) * (Even Number) * (Even Number)= (Even Number)
and b^2= (Odd Number) * (Odd Number) = (Odd Number)
(a^3)(b^2)= (Odd Number) * (Even Number) = (Even Number) and 8 is an even number so (a^3)(b^2)/8= Always even(here the question stem did not specify if integer or not so we can assume it can be both)
the correct answer is A.
(Odd Number) * (Odd Number) = (Odd Number)
(Even Number) * (Even Number) = (Even Number)
(Odd Number) * (Even Number) = (Even Number)
(Even Number) / (Even Number) = (Even Number)
as per the given: a is an even integer and b is an odd integer:
a^3= (Even Number) * (Even Number) * (Even Number)= (Even Number)
and b^2= (Odd Number) * (Odd Number) = (Odd Number)
(a^3)(b^2)= (Odd Number) * (Even Number) = (Even Number) and 8 is an even number so (a^3)(b^2)/8= Always even(here the question stem did not specify if integer or not so we can assume it can be both)
the correct answer is A.
05 Sep 2019, 23:49
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a^3b^2/8 (a is even and b is odd)
Since, a = 2n hence a^3 will be divisible by 8. But, n may be even or may be odd integer while b^2 is always odd.
So we can't comment whether the expression is even or odd. The expression can't be a fraction since a^3 is always divisible by 8.
So the expression is an integer.
Since, a = 2n hence a^3 will be divisible by 8. But, n may be even or may be odd integer while b^2 is always odd.
So we can't comment whether the expression is even or odd. The expression can't be a fraction since a^3 is always divisible by 8.
So the expression is an integer.
