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If 5^(k + 1) = 2,000, what is the value of 5^k + 1?

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If 5^(k + 1) = 2,000, what is the value of 5^k + 1?  [#permalink]

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New post 26 Aug 2018, 05:31
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A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

82% (01:13) correct 18% (01:15) wrong based on 28 sessions

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Re: If 5^(k + 1) = 2,000, what is the value of 5^k + 1?  [#permalink]

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New post 26 Aug 2018, 05:36
B?
\(5^k\).5 = \(2^4\).\(5^3\)

\(5^k\)= \(2^4\).\(5^2\) = 16 * 25 = 400

\(5^k\) + 1 = 400 + 1 = 401
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Re: If 5^(k + 1) = 2,000, what is the value of 5^k + 1?  [#permalink]

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New post 26 Aug 2018, 06:48
Bunuel wrote:
If \(5^{k + 1} = 2,000\), what is the value of \(5^k + 1\)?

(A) 399
(B) 401
(C) 1,996
(D) 2,000
(E) 2,001


\(5^k*5 = 2^4*5^3\)

So, \(5^k = 2^4*5^2\)

Or, \(5^k = 400\)

So, \(5^k + 1 = 401\) , Answer must be (B)
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Re: If 5^(k + 1) = 2,000, what is the value of 5^k + 1?  [#permalink]

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New post 26 Aug 2018, 09:43
Bunuel wrote:
If \(5^{k + 1} = 2,000\), what is the value of \(5^k + 1\)?

(A) 399
(B) 401
(C) 1,996
(D) 2,000
(E) 2,001



\(5^{k+1} = 2000\)
\(5^{k+1} = 2^45^3\)
\(5^k5 = 5^32^4\)
\(5^k = 5^22^4\)

\(5^2 = 25\)
\(2^4 = 16\)

25*16 = 400

\(5^k = 400\)

\(5^k\) + 1 = 401.

The best answer is B.
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Re: If 5^(k + 1) = 2,000, what is the value of 5^k + 1?  [#permalink]

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New post 26 Aug 2018, 10:53
Bunuel wrote:
If \(5^{k + 1} = 2,000\), what is the value of \(5^k + 1\)?

(A) 399
(B) 401
(C) 1,996
(D) 2,000
(E) 2,001
Answer is B
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Re: If 5^(k + 1) = 2,000, what is the value of 5^k + 1?  [#permalink]

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New post 26 Aug 2018, 21:56
Bunuel wrote:
If \(5^{k + 1} = 2,000\), what is the value of \(5^k + 1\)?

(A) 399
(B) 401
(C) 1,996
(D) 2,000
(E) 2,001



\(5^{k + 1} = 2,000\),

5^k . 5 = 2000,
5^k = 400

Therefore, 5^k + 1 = 400 + 1 = 401.

Hence answer is B.
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Re: If 5^(k + 1) = 2,000, what is the value of 5^k + 1? &nbs [#permalink] 26 Aug 2018, 21:56
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