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If x is a positive integer, what is the remainder when x is divided by [#permalink]
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30 Jan 2018, 06:59
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Re: If x is a positive integer, what is the remainder when x is divided by [#permalink]
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30 Jan 2018, 07:12
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St1: (1)^odd = 1 > x^2 = odd > x = odd odd/2 > Rem = 1 Sufficient
St2: n^x = n^(2x  1) If n = 1; x can be odd or even. Not sufficient
Answer: A



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Re: If x is a positive integer, what is the remainder when x is divided by [#permalink]
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30 Jan 2018, 08:39
Vyshak wrote: St1: (1)^odd = 1 > x^2 = odd > x = odd odd/2 > Rem = 1 Sufficient
St2: n^x = n^(2x  1) If n = 1; x can be odd or even. Not sufficient
Answer: A I think its D .. Statemnt 1 is right as u said. But in st.2 As base are same so we can equalise expo. x= 2x1 x=1 So sufficient... Answer is D.. Correct me if i am wrong... Sent from my BNDAL10 using GMAT Club Forum mobile app



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Re: If x is a positive integer, what is the remainder when x is divided by [#permalink]
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30 Jan 2018, 11:06
viv007 wrote: Vyshak wrote: St1: (1)^odd = 1 > x^2 = odd > x = odd odd/2 > Rem = 1 Sufficient
St2: n^x = n^(2x  1) If n = 1; x can be odd or even. Not sufficient
Answer: A I think its D .. Statemnt 1 is right as u said. But in st.2 As base are same so we can equalise expo. x= 2x1 x=1 So sufficient... Answer is D.. Correct me if i am wrong... Sent from my BNDAL10 using GMAT Club Forum mobile appHi I think we cannot always equate the exponents if we dont know anything about the base. What if n = 1. (1)^3 is same as (1)^5, but that doesn't mean 3 is equal to 5



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Re: If x is a positive integer, what is the remainder when x is divided by [#permalink]
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05 Feb 2018, 12:40
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Bunuel wrote: Fresh GMAT Club Tests' Question If x is a positive integer, what is the remainder when x is divided by 2? (1) \((1)^{(x^2)} = 1\) (2) \(n^x = n^{(2x  1)}\) I think the answer must be D. Statement 1, for (−1)^(x^2)=−1, x^2 must be an odd number and odd number when divided by 2 always give a remainder 1. Hence sufficient. Statement 2, considering n=1, (1)^x = (1)^(2x1) only when both the exponents are either odd or even. When x is even, 2x1 cannot be even. Therefore x is odd and the remainder again is 1. Hence sufficient. Correct me if I am wrong.



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Re: If x is a positive integer, what is the remainder when x is divided by [#permalink]
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06 Feb 2018, 21:20
I think ur right coz when I take X=2 then 2x1 comes to be odd. When I take X as odd 2x1 is odd. So second option is correct too Ans Is D
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Re: If x is a positive integer, what is the remainder when x is divided by [#permalink]
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06 Feb 2018, 21:53
OFFICIAL SOLUTION:If x is a positive integer, what is the remainder when x is divided by 2?(1) \((1)^{(x^2)} = 1\). This implies that x^2 is odd (if it were even, then (1)^even = 1). x^2 = odd, on the other hand means that x is odd (since given that x is an integer). Any odd number divided by 2 gives the remainder of 1. Sufficient. (2) \(n^x = n^{(2x  1)}\). Be careful not to fall into the trap. Remember we can automatically equate the exponents of equal bases when that base does not equal 0, 1 or 1: \(1^x = 1^y\), for any values of x and y (they are not necessarily equal); \((1)^x = (1)^y\), for any even values of x and y (they are not necessarily equal); \(0^x = 0^y\), for any nonzero x and y (they are not necessarily equal). Thus, for \(n^x = n^{(2x  1)}\), we could equate the exponents if we knew that n is not 0, 1 or 1. In this case we'd have: x = 2x  1, which would give x = 1. But if n is 0, 1 or 1, then we cannot equate the exponents. For example, if n = 1, then x can be even as well as odd. Not sufficient. Answer: A.
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Re: If x is a positive integer, what is the remainder when x is divided by [#permalink]
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06 Feb 2018, 23:09
Thanks for the explanation. Understand the key take away here is that exponents can be equated only when base is not equal to 0, 1 or 1. Sent from my ONEPLUS A3003 using GMAT Club Forum mobile app



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Re: If x is a positive integer, what is the remainder when x is divided by [#permalink]
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07 Feb 2018, 10:52
Bunuel wrote: OFFICIAL SOLUTION:
If x is a positive integer, what is the remainder when x is divided by 2?
(1) \((1)^{(x^2)} = 1\).
This implies that x^2 is odd (if it were even, then (1)^even = 1). x^2 = odd, on the other hand means that x is odd (since given that x is an integer). Any odd number divided by 2 gives the remainder of 1. Sufficient.
(2) \(n^x = n^{(2x  1)}\).
Be careful not to fall into the trap. Remember we can automatically equate the exponents of equal bases when that base does not equal 0, 1 or 1:
\(1^x = 1^y\), for any values of x and y (they are not necessarily equal); \((1)^x = (1)^y\), for any even values of x and y (they are not necessarily equal); \(0^x = 0^y\), for any nonzero x and y (they are not necessarily equal).
Thus, for \(n^x = n^{(2x  1)}\), we could equate the exponents if we knew that n is not 0, 1 or 1. In this case we'd have: x = 2x  1, which would give x = 1. But if n is 0, 1 or 1, then we cannot equate the exponents. For example, if n = 1, then x can be even as well as odd. Not sufficient.
Answer: A. Thank you "BUNUEL"...for nice expalination... Sent from my BNDAL10 using GMAT Club Forum mobile app




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