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Is n an integer?
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Updated on: 08 Apr 2012, 03:57
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Is n an integer? (1) 2n is an integer. (2) 3n is an integer. Please explain your answeres
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Originally posted by ts2014 on 08 Apr 2012, 03:51.
Last edited by Bunuel on 08 Apr 2012, 03:57, edited 1 time in total.
Edited the question




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Re: Is n an integer?
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08 Apr 2012, 04:01




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Re: Is n an integer?
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08 Apr 2012, 04:19
+1 C Bunuel like the shortcut for getting "n" while solving both. I was trying to use a fraction to break the question stem
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Re: Is n an integer?
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08 Apr 2012, 06:25
thanks Bunuel!!!
i was taking into the realm of LCM's but couldnt get a headway. i.e., 1 and 2 cannot deduce the fact that n is an integer.
combining both of them together 2n and 3n is an integer, it would mean that 6n would be an integer but reached a block there again as it still doesnt prove n is an integer.
ur method is short and easy. thanks!!



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Re: Is n an integer?
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28 May 2013, 08:35
Is there any other way to solve the problem except "3n  2n" approach?



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Re: Is n an integer?
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28 May 2013, 09:42



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Re: Is n an integer?
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28 May 2013, 21:17
Bunuel wrote: VadimKlimenko wrote: Is there any other way to solve the problem except "3n  2n" approach? ... a/b=2/3. Since a and b are integers, then a is a multiple of 2 ... So for any integers a and b when a/b = k/m (a>k) (fractions simplifying) a is multiple of k, and b is multiple of b, isn't it ? Delicious solution, thank you!



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Re: Is n an integer?
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28 May 2013, 23:24



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Re: Is n an integer?
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30 May 2013, 00:09
rajasami4u wrote: Bunuel wrote: VadimKlimenko wrote: Is there any other way to solve the problem except "3n  2n" approach? Yes, it is. Though the approach provided is the easiest one. From (1): 2n=a, for some integer a > n=a/2. From (2): 3n=b, for some integer b > n=b/2. a/2=b/3 > a/b=2/3. Since a and b are integers, then a is a multiple of 2 > a=2k, for some integer k > 2n=2k > n=k=integer. Sufficient. Answer: C. Hope it's clear. Hi Bunuel, Can u explain how u got C? a=2K, Why K should be integer K can also be 1/2. Please correct me. We have a/b=2/3. Since a and b are integers, then a is a multiple of 2 (or simply a must be an even number). Even number can be represented as a=2k, where k is an integer. If k=1/2, then a=2k=1=odd. Hope it's clear.
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Re: Is n an integer?
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30 May 2013, 00:11
rajasami4u wrote: Bunuel wrote: VadimKlimenko wrote: Is there any other way to solve the problem except "3n  2n" approach? Yes, it is. Though the approach provided is the easiest one. From (1): 2n=a, for some integer a > n=a/2. From (2): 3n=b, for some integer b > n=b/2. a/2=b/3 > a/b=2/3. Since a and b are integers, then a is a multiple of 2 > a=2k, for some integer k > 2n=2k > n=k=integer. Sufficient. Answer: C. Hope it's clear. Hi Bunuel, Can u explain how u got C? a=2K, Why K should be integer K can also be 1/2. Please correct me. Hi, I had the same concern, let me answer your question: We know that a/2=b/3 (if we had no info about a & b then a/2=b/3 could be anything, for example 1/3=0.333) and it gives us a/b = 2/3 (again, if no information about a & b it could be a = 1 and b = 1.5). Our key knowledge gives us that a = integer and b = integer and it means that minimum a = 2 and minimum b=3 and in general a is multiple of 2 and b is multiple of 3.



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Is n an integer?
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02 Jun 2013, 09:38
IMO the answer is C.
For statement 1, n=1/2 results in 2n = 1; not suff For statement 2, n=1/3 results in 3n =1; not suff
Considering both the statements, 3n2n=n; therefore n is an integer because the difference of two integer numbers is always integer. Suff.



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Re: Is n an integer?
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11 Aug 2017, 22:12
Bunuel wrote: Is n an integer?
(1) 2n is an integer > 2n=integer: if n=1/2 then the answer is NO but if n=1 then the answer is YES. Not sufficient. (2) 3n is an integer > 3n=integer: if n=1/3 then the answer is NO but if n=1 then the answer is YES. Not sufficient.
(1)+(2) Subtract (1) from (2): 3n2n=integerinteger > n=integer (since integerinteger=integer). Sufficient.
Answer: C.
Hope it's clear. What if the IInd statement says its 5N then also the Answer will be C ??



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Re: Is n an integer?
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12 Aug 2017, 00:31
ashwin1590 wrote: Bunuel wrote: Is n an integer?
(1) 2n is an integer > 2n=integer: if n=1/2 then the answer is NO but if n=1 then the answer is YES. Not sufficient. (2) 3n is an integer > 3n=integer: if n=1/3 then the answer is NO but if n=1 then the answer is YES. Not sufficient.
(1)+(2) Subtract (1) from (2): 3n2n=integerinteger > n=integer (since integerinteger=integer). Sufficient.
Answer: C.
Hope it's clear. What if the IInd statement says its 5N then also the Answer will be C ?? Yes. 2n = integer and 5n = integer gives 5n  2n = 3n = integer. 2n = integer and 3n = integer gives 3n  2n = n = integer. Or: 2n = integer, means 2*2n = 4n = 2*integer = integer. So, if 5n = integer, then 5n  4n = n = integer. Hope it's clear.
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Is n an integer?
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12 Aug 2017, 11:02
1) 2n is integer, 2n can be 1,2,3,4,5 which can give n as integer as well as fractions, A and D ruled out 2) 3n is integer same as above B ruled out. combining both if 2n is integer let say 2n=1 i.e. n=1/2 and 3n is integer let say 3n=1 i.e. n=1/3 then the common series will be divisible by 6 (which is LCM of 2 and 3) i.e. 0,6,12,18,......and so on including negative values as well, clearly n is integer here. Therefore Answer is C
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Re: Is n an integer?
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30 Oct 2018, 12:16
ts2014 wrote: Is n an integer?
(1) 2n is an integer. (2) 3n is an integer.
Please explain your answeres 1 may or may not be integer because of exceptions such as 1/2, 3/2 ... 2 may or may not be sufficient because of exceptions such as 1/3, 2/3... Combining, both type of exceptions are eliminated and we know that N is an integer. C is the answer.



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Re: Is n an integer?
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30 Oct 2018, 12:48
ts2014 wrote: Is n an integer?
(1) 2n is an integer. (2) 3n is an integer.
Please explain your answeres Statement 1) 2n = 1 Here n = 1/2 and no it is not an integer. 2n = 0 Here n = 0 and yes it is an integer. Insufficient. Statement 2) In a similar way to statement 1 we can have n = 1/3 and n = 0 so insufficient. Combined we know 2n = x and 3n = y n = x/2 3x/2 = y 3x = 2y Since they have no common factor we know that it must be an integer. Posted from my mobile device




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