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If a and b are positive integers, which of the following can
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11 Jun 2013, 02:34
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If a and b are positive integers, which of the following cannot be odd? A. (2+4a)/(4+4b) B. (4a)/(b) C. a/b D. (4+a)/(2+4b) E. (4+a)/(1+4b) P.S: Bunuel/VeritasPrepKarishma guys I would request you to provide an explanation on this question.Is there any generic approach for this kind of questions?
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Re: If a and b are positive integers, which of the following can
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11 Jun 2013, 06:08




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Re: If a and b are positive integers, which of the following can
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11 Jun 2013, 02:48
In my view, Best approach to such type of questions is to prove that the constraint is possible. Let's see how it works 1 is odd integer & a, b can take any positive integer value. So if we can prove that any fraction can yield 1, we can reject that choice A. (2+4a)/(4+4b)  Under any condition this can't be odd. Answer B. (4a)/(b) = 4.1/4 = 1 = Odd C. a/b = 4/4 = Odd D.(4+a)/(2+4b) = (4+2)/(2+4.1) = 1 = Odd E.(4+a)/(1+4b) = (4+1)/(1+4.1) = 1 = Odd Hope this helps.
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Re: If a and b are positive integers, which of the following can
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11 Jun 2013, 03:16
fameatop wrote: In my view, Best approach to such type of questions is to prove that the constraint is possible. Let's see how it works 1 is odd integer & a, b can take any positive integer value. So if we can prove that any fraction can yield 1, we can reject that choice
A. (2+4a)/(4+4b)  Under any condition this can't be odd. Answer B. (4a)/(b) = 4.1/4 = 1 = Odd C. a/b = 4/4 = Odd D.(4+a)/(2+4b) = (4+2)/(2+4.1) = 1 = Odd E.(4+a)/(1+4b) = (4+1)/(1+4.1) = 1 = Odd
Hope this helps. Hi fameatop, Other than plugin, how one can be sure that A is the answer...? and plugin takes time in this type of questions i guess...Your thoughts please!
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Re: If a and b are positive integers, which of the following can
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11 Jun 2013, 03:30
fameatop wrote: In my view, Best approach to such type of questions is to prove that the constraint is possible. Let's see how it works 1 is odd integer & a, b can take any positive integer value. So if we can prove that any fraction can yield 1, we can reject that choice A. (2+4a)/(4+4b)  Under any condition this can't be odd. Answer B. (4a)/(b) = 4.1/4 = 1 = Odd C. a/b = 4/4 = Odd D.(4+a)/(2+4b) = (4+2)/(2+4.1) = 1 = Odd E.(4+a)/(1+4b) = (4+1)/(1+4.1) = 1 = Odd Hope this helps. Like Flametop has mentioned, I'd like to rephrase the question in a form that 'which of the following can yeild integers'. The expressions are such that one of them under no circumstances can yeild an integer. If one of them always stays a fraction, it can neither be considered odd or even. Choice 1 can be reduced to \((1 + 2a)/2*(1+b).\)Now for all values of a, the nuemerator will be odd, but the denominator is even (product of 2 and (1+b) which can be even or odd). Hence, the nuemerator and the denom are odd and even respectively, and do not depend on the values of a and b. Hence it will always be a fraction. For the rest of the choices, the value of the expression can be reduced to an integer for some values of a and b. Hence, according to me, the trick is to find the expression whose value is independent of the underlying variables and yeilds a constant value for all cases as above, where the value is a fraction no matter what. Hope it helps! Regards, A
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Re: If a and b are positive integers, which of the following can
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11 Jun 2013, 06:33
arpanpatnaik wrote: fameatop wrote: In my view, Best approach to such type of questions is to prove that the constraint is possible. Let's see how it works 1 is odd integer & a, b can take any positive integer value. So if we can prove that any fraction can yield 1, we can reject that choice A. (2+4a)/(4+4b)  Under any condition this can't be odd. Answer B. (4a)/(b) = 4.1/4 = 1 = Odd C. a/b = 4/4 = Odd D.(4+a)/(2+4b) = (4+2)/(2+4.1) = 1 = Odd E.(4+a)/(1+4b) = (4+1)/(1+4.1) = 1 = Odd Hope this helps. Like Flametop has mentioned, I'd like to rephrase the question in a form that 'which of the following can yeild integers'. The expressions are such that one of them under no circumstances can yeild an integer. If one of them always stays a fraction, it can neither be considered odd or even. Choice 1 can be reduced to \((1 + 2a)/2*(1+b).\)Now for all values of a, the nuemerator will be odd, but the denominator is even (product of 2 and (1+b) which can be even or odd). Hence, the nuemerator and the denom are odd and even respectively, and do not depend on the values of a and b. Hence it will always be a fraction. For the rest of the choices, the value of the expression can be reduced to an integer for some values of a and b. Hence, according to me, the trick is to find the expression whose value is independent of the underlying variables and yeilds a constant value for all cases as above, where the value is a fraction no matter what. Hope it helps! Regards, A Thank you arpanpatnaik I like this strategy....was looking for something generic like this!
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Re: If a and b are positive integers, which of the following can
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14 Sep 2018, 17:44
bagdbmba wrote: If a and b are positive integers, which of the following cannot be odd?
A. (2+4a)/(4+4b) B. (4a)/(b) C. a/b D. (4+a)/(2+4b) E. (4+a)/(1+4b) In answer choice A, notice that 2 + 4a = 2(1 + 2a) and 4 + 4b = 4(1 + b). So (2+4a)/(4+4b) 2(1+2a)/[4(1+b)] (1+2a)/[2(1+b)] We see that (1 + 2a) is an odd number and 2(1 + b) is an even number, regardless what a and b are, so the quotient can’t be an odd number since it’s not even an integer. Answer: A
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Re: If a and b are positive integers, which of the following can
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