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If a, b, and c are integers and a*b^2/c is a positive even [#permalink]
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26 Sep 2010, 13:04
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If a, b, and c are integers and a*b^2/c is a positive even integer, which of the following must be true? I. ab is even II. ab > 0 III. c is even A. I only B. II only C. I and II D. I and III E. I, II, and III
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Re: ab^2/c is even? [#permalink]
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26 Sep 2010, 13:43
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Orange08 wrote: If a , b, and c are integers and \(a*b^2/c\)is a positive even integer, which of the following must be true?
I. ab is even II. ab > 0 III. c is even
I only II only I and II I and III I, II, and III Given: \(\frac{a*b^2}{c}=even>0\) > \(ab^2=c*even=even\) > either \(a\) is even or \(b\) or both. I. \(ab\) is even > according to the above this must be true; II. \(ab>0\) > not necessarily true, \(b\) could be positive as well as negative (for example \(a=1\), \(c=1\) and \(b=2\)); III. \(c\) is even > not necessarily true, see above example. Answer: A (I only).
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Re: ab^2/c is even? [#permalink]
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28 Sep 2010, 07:22
Two ways this can happen: 1 Even/ Even= Even or 2 Even/Odd= Even So Ab MUST be even, with either A or B being even, Ab does not have to be positive, as B could be negative and once it is raised to 2 it becomes positive again, and of course, C could be Odd or Even as described above.
I only.letter A



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Re: If a, b, and c are integers and a*b^2/c is a positive even [#permalink]
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Re: If a, b, and c are integers and a*b^2/c is a positive even [#permalink]
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Re: If a, b, and c are integers and a*b^2/c is a positive even [#permalink]
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Re: If a, b, and c are integers and a*b^2/c is a positive even [#permalink]
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Re: If a, b, and c are integers and a*b^2/c is a positive even [#permalink]
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18 Apr 2017, 02:27
Option A(a*(b^2))/c = Positive Even integer. Odd: O, Even: E & fraction: F. i.e., a,b,c are Even or b is even, a & c are Odd or a is Even, b & c are odd. I. ab is even : True II. ab > 0 : May or May NOT be True. no information about b's value. III. c is even : May or May not be True
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Re: If a, b, and c are integers and a*b^2/c is a positive even [#permalink]
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20 Apr 2017, 16:43
Orange08 wrote: If a, b, and c are integers and a*b^2/c is a positive even integer, which of the following must be true?
I. ab is even II. ab > 0 III. c is even
A. I only B. II only C. I and II D. I and III E. I, II, and III We are given that (a*b^2)/c is a positive even integer. Therefore, a*b^2 must be even. (If a*b^2 is odd, (a*b^2)/c can’t ever be even.) Now recall that the product of an even number and any integer is even, so either a or b, or both, must be even. Thus we see that ab must be an even integer. However, ab DOES NOT have to be greater than zero, since a could be 2 and b could be 1. Finally, we see that c does not have to be even, since a could be 2, b could be 1, and c = 1. Thus, only Roman numeral I must be true. Answer: A
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