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Which of the following is equivalent to
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18 Sep 2021, 16:40
18 Sep 2021, 16:40
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Question Stats:
32% (01:47) correct
67% (02:19) wrong based on 28 sessions
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Which of the following is equivalent to:
\((2+3)(2^2+3^2)(2^4+3^4)(2^8+3^8)(2^{16}+3^{16})(2^{32}+3^{32})(2^{64}+3^{64})\)
(A) \(3^{127} + 2^{127}\)
(B) \(3^{127} + 2^{127} + 3*2^{63} + 2*3^{63}\)
(C) \(3^{128} - 2^{128}\)
(D) \(3^{128} + 3^{128}\)
(E) \(5^{127}\)
Source: 2021 AMC 10A Problems/Problem 10
\((2+3)(2^2+3^2)(2^4+3^4)(2^8+3^8)(2^{16}+3^{16})(2^{32}+3^{32})(2^{64}+3^{64})\)
(A) \(3^{127} + 2^{127}\)
(B) \(3^{127} + 2^{127} + 3*2^{63} + 2*3^{63}\)
(C) \(3^{128} - 2^{128}\)
(D) \(3^{128} + 3^{128}\)
(E) \(5^{127}\)
Source: 2021 AMC 10A Problems/Problem 10
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Which of the following is equivalent to
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19 Sep 2021, 05:43
19 Sep 2021, 05:43
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\(5*13*97\) are factors of an expression in the question below. Factoring of the expression by 5, 13 and 97 which are prime factors should help identify a correct answer.
It's known that \(3+2=5\), \(3^2+2^2=13\) and \(3^4+2^4=97\). IMO, the answer must be in the form of \(3^n-2^n\) with \(n\) defined as even number.
Answer choice C is matching \(3^n-2^n\) format, as \(3^{128} - 2^{128}\)=\((3^{64} - 2^{64})(3^{64} + 2^{64})\)=\((3^{32} - 2^{32})(3^{32} + 2^{32})(3^{64} - 2^{64})\) ... \(...(3-2)\), where the last differential value is equal to 1
Answer is C
It's known that \(3+2=5\), \(3^2+2^2=13\) and \(3^4+2^4=97\). IMO, the answer must be in the form of \(3^n-2^n\) with \(n\) defined as even number.
Answer choice C is matching \(3^n-2^n\) format, as \(3^{128} - 2^{128}\)=\((3^{64} - 2^{64})(3^{64} + 2^{64})\)=\((3^{32} - 2^{32})(3^{32} + 2^{32})(3^{64} - 2^{64})\) ... \(...(3-2)\), where the last differential value is equal to 1
Answer is C
grenico wrote:
Which of the following is equivalent to:
\((2+3)(2^2+3^2)(2^4+3^4)(2^8+3^8)(2^{16}+3^{16})(2^{32}+3^{32})(2^{64}+3^{64})\)
(A) \(3^{127} + 2^{127}\)
(B) \(3^{127} + 2^{127} + 3*2^{63} + 2*3^{63}\)
(C) \(3^{128} - 2^{128}\)
(D) \(3^{128} + 3^{128}\)
(E) \(5^{127}\)
Source: 2021 AMC 10A Problems/Problem 10
\((2+3)(2^2+3^2)(2^4+3^4)(2^8+3^8)(2^{16}+3^{16})(2^{32}+3^{32})(2^{64}+3^{64})\)
(A) \(3^{127} + 2^{127}\)
(B) \(3^{127} + 2^{127} + 3*2^{63} + 2*3^{63}\)
(C) \(3^{128} - 2^{128}\)
(D) \(3^{128} + 3^{128}\)
(E) \(5^{127}\)
Source: 2021 AMC 10A Problems/Problem 10
Re: Which of the following is equivalent to
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26 Jan 2022, 07:43
26 Jan 2022, 07:43
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