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If x is a positive integer, which of the following CANNOT be expressed
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If x is a positive integer, which of the following CANNOT be expressed as n^2, where n is an integer? A. \(x^5\) B. \(x^2 − 1\) C. \(\sqrt{x^8}\) D. \(x^2 + 1\) E. \(\sqrt{x^5}\)
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Originally posted by emmak on 11 Feb 2013, 11:09.
Last edited by Bunuel on 09 Dec 2017, 06:39, edited 2 times in total.
Edited the question.




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Re: If x is a positive integer, which of the following CANNOT be expressed
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11 Feb 2013, 15:13
emmak wrote: If x is a positive integer, which of the following CANNOT be expressed as n^2, where n is an integer?
A. x^5 B. x^2 − 1 C. \(\sqrt{x^8}\) D. x^2 + 1 E. \(\sqrt{x^5}\) The question basically asks: if x is a positive integer, which of the following CANNOT be a perfect square. Now, if x=1, then options A, B, C and E ARE perfect squares, therefore by POE the correct answer must be D. Answer: D.
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Re: If x is a positive integer, which of the following CANNOT be expressed
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06 Mar 2014, 00:06
If we take x = 2 & calculate, we cant get the answers; seems that x has to be taken 1 to execute all the options
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Re: If x is a positive integer, which of the following CANNOT be expressed
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27 Mar 2014, 17:12
emmak wrote: If x is a positive integer, which of the following CANNOT be expressed as n^2, where n is an integer?
A. x^5 B. x^2 − 1 C. \(\sqrt{x^8}\) D. x^2 + 1 E. \(\sqrt{x^5}\) So I guess zero does count as a perfect square then Cheers J



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Re: If x is a positive integer, which of the following CANNOT be expressed
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27 Mar 2014, 21:21
PareshGmat wrote: If we take x = 2 & calculate, we cant get the answers; seems that x has to be taken 1 to execute all the options Any random value of x will not help you get the answer. Even if you do not try x = 1, you can use reasoning to solve this question. A. \(x^5\) If x is a number with an even power, such as \(x = a^4\) (a is an integer), then \(x^5 = a^{20} = n^2\) n will be \(a^{10}\), an integer here. B. \(x^2  1\) \(x^2  1 = n^2\) You need two consecutive perfect squares. Only 0 and 1 are consecutive perfect squares. Thereafter, the distance between perfect squares keeps increasing. x needs to be a positive integers so if x = 1, n = 0 (an integer) C. \(\sqrt{x^8}\) \(\sqrt{x^8} = x^4 = n^2\) n will be \(x^2\), an integer here. D. \(x^2 + 1\) x is a positive integer so it must be at least 1. After 1, there are no two consecutive integers. n cannot be an integer. E. \(\sqrt{x^5}\) If x is a number with an even power which is a multiple of 4, such as \(x = a^4\) (a is an integer), then \(\sqrt{x^5} = \sqrt{a^{20}} = a^{10} = n^2\) n will be \(a^5\), an integer here. Answer (D)
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Re: If x is a positive integer, which of the following CANNOT be expressed
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29 Mar 2014, 02:38
Even though Bunuel and karishma have answered this question, I am not able to digest any fundamental of this .... Not sure how to crack this one... as I got this question in my Veritas prep exam today...
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Re: If x is a positive integer, which of the following CANNOT be expressed
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30 Mar 2014, 19:01
Mountain14 wrote: Even though Bunuel and karishma have answered this question, I am not able to digest any fundamental of this .... Not sure how to crack this one... as I got this question in my Veritas prep exam today... Look, the question simply asks which option CANNOT be a perfect square. In the options, x is a positive integer. Can x^5 be a perfect square? Can x take some value such that x^5 is a perfect square? Say, x = 4. Then x^5 = 4^5 = 2^10 This is a perfect square. Hence for some value of x, x^5 could be a perfect square. Hence this is not our answer. How do we find a value for which x^5 will be a perfect square? Perfect squares have even powers. We have x^5 which is an odd power. To get an even power, we could select x such that it already has an even power  we selected x = 2^2. Similarly, x could be 1^2 or 3^2 or 4^2 or 5^2 or 3^4 etc Now think, can x^2  1 be a perfect square? The reasoning for all the options is given in the post above. A more intuitive approach is putting x = 1 as given by Bunuel. When x = 1, all options except option (D) results in a perfect square. So we know that all options CAN be perfect squares except (D). By elimination, answer must be (D).
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Re: If x is a positive integer, which of the following CANNOT be expressed
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30 Mar 2014, 21:18
VeritasPrepKarishma wrote: Mountain14 wrote: Even though Bunuel and karishma have answered this question, I am not able to digest any fundamental of this .... Not sure how to crack this one... as I got this question in my Veritas prep exam today... Look, the question simply asks which option CANNOT be a perfect square. In the options, x is a positive integer. Can x^5 be a perfect square? Can x take some value such that x^5 is a perfect square? Say, x = 4. Then x^5 = 4^5 = 2^10 This is a perfect square. Hence for some value of x, x^5 could be a perfect square. Hence this is not our answer. How do we find a value for which x^5 will be a perfect square? Perfect squares have even powers. We have x^5 which is an odd power. To get an even power, we could select x such that it already has an even power  we selected x = 2^2. Similarly, x could be 1^2 or 3^2 or 4^2 or 5^2 or 3^4 etc Now think, can x^2  1 be a perfect square? The reasoning for all the options is given in the post above. A more intuitive approach is putting x = 1 as given by Bunuel. When x = 1, all options except option (D) results in a perfect square. So we know that all options CAN be perfect squares except (D). By elimination, answer must be (D). So the one point where I get tripped up is the X^2  1. 0 is assumed to be a perfect square? How can I tell from the verbage of the question that what they are asking for is determining whether or not something is a perfect square or not? Thanks for the help.



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Re: If x is a positive integer, which of the following CANNOT be expressed
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30 Mar 2014, 22:59
dbiersdo wrote: VeritasPrepKarishma wrote: Mountain14 wrote: Even though Bunuel and karishma have answered this question, I am not able to digest any fundamental of this .... Not sure how to crack this one... as I got this question in my Veritas prep exam today... Look, the question simply asks which option CANNOT be a perfect square. In the options, x is a positive integer. Can x^5 be a perfect square? Can x take some value such that x^5 is a perfect square? Say, x = 4. Then x^5 = 4^5 = 2^10 This is a perfect square. Hence for some value of x, x^5 could be a perfect square. Hence this is not our answer. How do we find a value for which x^5 will be a perfect square? Perfect squares have even powers. We have x^5 which is an odd power. To get an even power, we could select x such that it already has an even power  we selected x = 2^2. Similarly, x could be 1^2 or 3^2 or 4^2 or 5^2 or 3^4 etc Now think, can x^2  1 be a perfect square? The reasoning for all the options is given in the post above. A more intuitive approach is putting x = 1 as given by Bunuel. When x = 1, all options except option (D) results in a perfect square. So we know that all options CAN be perfect squares except (D). By elimination, answer must be (D). So the one point where I get tripped up is the X^2  1. 0 is assumed to be a perfect square? How can I tell from the verbage of the question that what they are asking for is determining whether or not something is a perfect square or not? Thanks for the help. Yes, both 0 and 1 are perfect squares. "Can you express 'this' as n^2 where n is an integer?" asks us whether we can write 'this' as square of an integer. Square of an integer is a perfect square. So the question becomes "Can you express 'this' as a perfect square?" Slightly convoluted verbiage is common in GMAT.
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Re: If x is a positive integer, which of the following CANNOT be expressed
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20 Jul 2014, 01:05
Bunuel wrote: emmak wrote: If x is a positive integer, which of the following CANNOT be expressed as n^2, where n is an integer?
A. x^5 B. x^2 − 1 C. \(\sqrt{x^8}\) D. x^2 + 1 E. \(\sqrt{x^5}\) The question basically asks: if x is a positive integer, which of the following CANNOT be a perfect square. Now, if x=1, then options A, B, C and E ARE perfect squares, therefore by POE the correct answer must be D. Answer: D. Please refer to option [b] where value comes 0. Would you please clarify whether 0 is a perfect square?
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Re: If x is a positive integer, which of the following CANNOT be expressed
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20 Jul 2014, 04:16
musunna wrote: Bunuel wrote: emmak wrote: If x is a positive integer, which of the following CANNOT be expressed as n^2, where n is an integer?
A. x^5 B. x^2 − 1 C. \(\sqrt{x^8}\) D. x^2 + 1 E. \(\sqrt{x^5}\) The question basically asks: if x is a positive integer, which of the following CANNOT be a perfect square. Now, if x=1, then options A, B, C and E ARE perfect squares, therefore by POE the correct answer must be D. Answer: D. Please refer to option [b] where value comes 0. Would you please clarify whether 0 is a perfect square? Yes, 0 is a perfect square 0 = 0^2.
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Re: If x is a positive integer, which of the following CANNOT be expressed
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16 Mar 2016, 18:12
I picked B, because I thought that 2 consecutive integers multiplied do not equal a perfect square...I did not take into consideration the possibility of 0...



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Re: If x is a positive integer, which of the following CANNOT be expressed
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21 May 2016, 15:21
I think the hardest part about this question is working out what is being asked. Which of the following cannot be expressed as n^2 means which of the following cannot be perfect square when n is an integer. Subbing in 1 for x in each example brings us to answer D. 1^2 + 1 = 2, which is not the square of any integer. D is your answer! Easy



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