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Which of the following is equal to 8
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02 Feb 2020, 12:52
02 Feb 2020, 12:52
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Question Stats:
90% (00:26) correct
10% (00:36) wrong based on 10 sessions
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Which of the following is equal to \(8^2^4\)?
Indicate all possible values.
[A] \(2^9^6\)
[B] \(4^3^6\)
[C] \(12^1^2\)
[D] \(16^1^8\)
[E] \(24^8\)
[F] \(32^1^5\)
Indicate all possible values.
[A] \(2^9^6\)
[B] \(4^3^6\)
[C] \(12^1^2\)
[D] \(16^1^8\)
[E] \(24^8\)
[F] \(32^1^5\)
Re: Which of the following is equal to 8
[#permalink]
02 Feb 2020, 19:56
02 Feb 2020, 19:56
\(8^{24} = (2^{3})^{24} = 2^{72}\)
Looking at the options, option A can be eliminated.
Option C and E can be eliminated as well as they require a power of 3.
now, \(8 = 2 \times 2 \times 2\)
\(8^{24} = (2^{2})^{24} \times 2^{24}\)
\((2^{2})^{24} \times 2^{24} = 4^{24} \times (2^{2})^{12} = 4^{24} \times 4^{12} = 4^{36}\)
\(4^{2} = 16\)
\(4^{36} = (4^{2})^{18} = 16^{18}\)
\(2^{5} = 32\)
32 is the fifth power of 2 and we can see that there is no multiple of 5 in the exponents so it will not be possible to get 32 with simple manipulations as shown above. Hence E is also eliminated.
OA, B,D
Looking at the options, option A can be eliminated.
Option C and E can be eliminated as well as they require a power of 3.
now, \(8 = 2 \times 2 \times 2\)
\(8^{24} = (2^{2})^{24} \times 2^{24}\)
\((2^{2})^{24} \times 2^{24} = 4^{24} \times (2^{2})^{12} = 4^{24} \times 4^{12} = 4^{36}\)
\(4^{2} = 16\)
\(4^{36} = (4^{2})^{18} = 16^{18}\)
\(2^{5} = 32\)
32 is the fifth power of 2 and we can see that there is no multiple of 5 in the exponents so it will not be possible to get 32 with simple manipulations as shown above. Hence E is also eliminated.
OA, B,D
huda wrote:
Which of the following is equal to \(8^2^4\)?
Indicate all possible values.
[A] \(2^9^6\)
[B] \(4^3^6\)
[C] \(12^1^2\)
[D] \(16^1^8\)
[E] \(24^8\)
[F] \(32^1^5\)
Indicate all possible values.
[A] \(2^9^6\)
[B] \(4^3^6\)
[C] \(12^1^2\)
[D] \(16^1^8\)
[E] \(24^8\)
[F] \(32^1^5\)
gmatclubot
Re: Which of the following is equal to 8 [#permalink]
02 Feb 2020, 19:56
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