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If a is an odd integer, which of the following must be an even integer
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03 Oct 2016, 22:17
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54% (01:39) correct 46% (01:46) wrong based on 254 sessions
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Re: If a is an odd integer, which of the following must be an even integer
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04 Oct 2016, 00:41
Bunuel wrote: If a is an odd integer, which of the following must be an even integer?
A. a^4−a+1 B. (a^4−a)(a+1/a) C. a^4−a^3+a^2+2a D. (a^3+a^2+a)2 E. None of the above. Let a be 1.. A. 11+1..odd B.(11)(2) = 0.. even C.11+1+2..odd D.1+1+1..odd E.None IMO option B.



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If a is an odd integer, which of the following must be an even integer
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Updated on: 04 Oct 2016, 05:44
Bunuel wrote: If a is an odd integer, which of the following must be an even integer?
A. a^4−a+1 B. (a^4−a)(a+1/a) C. a^4−a^3+a^2+2a D. (a^3+a^2+a)^2 E. None of the above. IMO B A. a^4−a+1= oddodd+odd= even+odd=odd B. (a^4−a)(a+1/a)= (oddodd)(even/odd)= even Eg: (5^45)(6/5)=even, (3^43)(4/3)=even C. a^4−a^3+a^2+2a= oddodd+odd+even= even+odd+even= odd D. (a^3+a^2+a)2= (odd+odd+odd)^2= odd E. None of the above.[/quote]



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Re: If a is an odd integer, which of the following must be an even integer
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04 Oct 2016, 03:46
Bunuel  can you pls tell if in option D the 2 in the last is for square or product. TIA



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Re: If a is an odd integer, which of the following must be an even integer
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04 Oct 2016, 05:25



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Re: If a is an odd integer, which of the following must be an even integer
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04 Oct 2016, 05:34
Vinayak Shenoy wrote: Bunuel wrote: If a is an odd integer, which of the following must be an even integer?
A. a^4−a+1 B. (a^4−a)(a+1/a) C. a^4−a^3+a^2+2a D. (a^3+a^2+a)2 E. None of the above. IMO D A. a^4−a+1= oddodd+odd= even+odd=odd B. (a^4−a)(a+1/a)= (oddodd)(even/odd)= even (even/odd) may or may not be even C. a^4−a^3+a^2+2a= oddodd+odd+even= even+odd+even= odd D. (a^3+a^2+a)2= (odd+odd+odd)* even= always even E. None of the above. [/quote] Would D be odd here? (odd+odd+odd) = odd (Odd)^even = odd For eg : 3^2, 5^2 IMO B i think



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If a is an odd integer, which of the following must be an even integer
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04 Oct 2016, 05:46
mechky wrote: Vinayak Shenoy wrote: Bunuel wrote: If a is an odd integer, which of the following must be an even integer?
A. a^4−a+1 B. (a^4−a)(a+1/a) C. a^4−a^3+a^2+2a D. (a^3+a^2+a)2 E. None of the above. IMO D A. a^4−a+1= oddodd+odd= even+odd=odd B. (a^4−a)(a+1/a)= (oddodd)(even/odd)= even (even/odd) may or may not be even C. a^4−a^3+a^2+2a= oddodd+odd+even= even+odd+even= odd D. (a^3+a^2+a)2= (odd+odd+odd)* even= always even E. None of the above. Would D be odd here? (odd+odd+odd) = odd (Odd)^even = odd For eg : 3^2, 5^2 IMO B i think[/quote] mechkyKindly note the problem did not show option D was power of 2 initially. When all other powers were mentioned as ^4, ^3 in option D it wasn't mentioned that way. Also my interpretation was wrong Corrected it now



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If a is an odd integer, which of the following must be an even integer
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20 Jan 2017, 06:11
This one is an amazing Question. I overlooked Option B. Damn.
Nevertheless here is what i would now > Firstly >Positive exponents does not affect the even/odd nature of any number Option A> a^4−a+1=> oddodd+odd=> even+odd=> odd=> Rejected. Option B>(a^4−a)(a+1/a)=> (a^31)*(a^2+a)=> (oddodd)*(odd+odd) => even*even => even=> Acceptable. OptionC>a^4−a^3+a^2+2a=> oddodd+odd+even=>even+odd=>odd=> Rejected. Option D>(a^3+a^2+a)^2=>(odd+odd+odd)^2=>(even+odd)^2=>odd^2=> odd=>Rejected. Option E>None of the above.=> Rejected.
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Re: If a is an odd integer, which of the following must be an even integer
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21 Feb 2017, 09:50
I did a substitution.
B was successful with 3 then tried 5 just to be sure and realized this holds true for all odd numbers (multiple of a)(even/a) will always be even.
Just had a question  is there anyways to know if this holds true for all cases i.e. in a scenario where a rule worked for 3 and 5 but would fail for 13..



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Re: If a is an odd integer, which of the following must be an even integer
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21 Feb 2017, 17:15
Can anyone explain how B satisfies a=3 ?? the answer should be E i believe



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Re: If a is an odd integer, which of the following must be an even integer
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21 Feb 2017, 17:52
kparik86 wrote: Can anyone explain how B satisfies a=3 ?? the answer should be E i believe Hi, Firstly lets see the equation.. \((a^4a)(a+\frac{1}{a}=(a^31)*a*\frac{a^2+1}{a}=(a^31)(a^2+1)\).. Here both a^31 and a^2+1 are even thus the answer will be even.. Let's put 3.. \((3^43)(3+\frac{1}{3}=(813)*\frac{3^2+1}{3}=(78)(10/3)=26*10=260\).. Thus EVEN
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Re: If a is an odd integer, which of the following must be an even integer
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13 Apr 2017, 00:30
Option Ba is an Odd integer. Odd: O, Even: E & Fraction: F A. a^4−a+1 = O  O + 1 = E + 1 = O B. (a^4−a)(a+1/a) = (a^4−a)(a^2 + 1)/a = (a^3  1)(a^2 + 1) = (O  1)(O + 1) = E*E = E C. a^4−a^3+a^2+2a = O  O + O + E = O D. (a^3+a^2+a)^2 = (O + O + O)^2 = (O)^2 = O E. None of the above
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Re: If a is an odd integer, which of the following must be an even integer
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18 Jul 2018, 06:13
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