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If 2^x(5^n) = t, what is the value of t? (1) x = n + 3 (2) 2^x = 32

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Bunuel
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If 2^x(5^n) = t, what is the value of t? (1) x = n + 3 (2) 2^x = 32 [#permalink] If 2^x(5^n) = t, what is the value of t? (1) x = n + 3 (2) 2^x = 32   03 Oct 2018, 03:00
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If \(2^x(5^n) = t\), what is the value of t?


(1) \(x = n + 3\)

(2) \(2^x = 32\)
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C
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Re: If 2^x(5^n) = t, what is the value of t? (1) x = n + 3 (2) 2^x = 32 [#permalink] If 2^x(5^n) = t, what is the value of t? (1) x = n + 3 (2) 2^x = 32   03 Oct 2018, 03:05
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Bunuel wrote:
If \(2^x(5^n) = t\), what is the value of t?


(1) \(x = n + 3\)

(2) \(2^x = 32\)


Question: What is the value of t?

Given: \(2^x(5^n) = t\)
To infer something about t from this expression, we need information about values of x and m

Statement 1: \(x = n + 3\)

i.e. \(2^x(5^n) = 2^{n+3}*5^n = t\)
But no information about the value of n hence
NOT SUFFICIENT

Statement 2: \(2^x = 32\)

i.e. \(2^x = 2^5\)

i.e. x = 5 but value of n is still unknown hence
NOT SUFFICIENT

Combining the two statements

\(x = 5 = n+3\)
i.e. \(n = 2\)
ie. \(t = 2^x(5^n) = 2^5*5^2\)
SUFFICIENT

Answer: Option C
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Re: If 2^x(5^n) = t, what is the value of t? (1) x = n + 3 (2) 2^x = 32 [#permalink] If 2^x(5^n) = t, what is the value of t? (1) x = n + 3 (2) 2^x = 32   03 Oct 2018, 03:06
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Statement 1:

x = n+3.
Clearly insufficient.

Statement 2:

\(2^x\) = 32

x = 5.
No info about n. Insufficient.

Combining both gives x as 5 and n as 2.

t = \(2^5\)\(5^2\)
Sufficient.

C is the answer.
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Re: If 2^x(5^n) = t, what is the value of t? (1) x = n + 3 (2) 2^x = 32 [#permalink] If 2^x(5^n) = t, what is the value of t? (1) x = n + 3 (2) 2^x = 32   03 Oct 2018, 03:13
(1) \(x = n + 3\)
This tells you how to figure out one value if you have another but no values are provided. INSUFFICIENT


(2) \(2^x = 32\)
You can solve for \(x\)
\(2^x = 32\)
\(2^x = 2^4\)
\(x = 4\)

But we still do not know \(n\) to answer for \(t\). INSUFFICIENT

TOGETHER

\(x = 4 = n + 3\) → \(n = 1\) SUFFICIENT

Answer is C.
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Re: If 2^x(5^n) = t, what is the value of t? (1) x = n + 3 (2) 2^x = 32 [#permalink] If 2^x(5^n) = t, what is the value of t? (1) x = n + 3 (2) 2^x = 32   03 Oct 2018, 03:16
MsInvBanker wrote:
(1) \(x = n + 3\)
This tells you how to figure out one value if you have another but no values are provided. INSUFFICIENT


(2) \(2^x = 32\)
You can solve for \(x\)
\(2^x = 32\)
\(2^x = 2^4\)
\(x = 4\)

But we still do not know \(n\) to answer for \(t\). INSUFFICIENT

TOGETHER

\(x = 4 = n + 3\) → \(n = 1\) SUFFICIENT

Answer is C.



Hi, Just a small correction. \(2^4\) is 16 and \(2^5\) is 32. :)
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Re: If 2^x(5^n) = t, what is the value of t? (1) x = n + 3 (2) 2^x = 32 [#permalink] If 2^x(5^n) = t, what is the value of t? (1) x = n + 3 (2) 2^x = 32   03 Oct 2018, 03:18
Afc0892 wrote:
MsInvBanker wrote:
(1) \(x = n + 3\)
This tells you how to figure out one value if you have another but no values are provided. INSUFFICIENT


(2) \(2^x = 32\)
You can solve for \(x\)
\(2^x = 32\)
\(2^x = 2^4\)
\(x = 4\)

But we still do not know \(n\) to answer for \(t\). INSUFFICIENT

TOGETHER

\(x = 4 = n + 3\) → \(n = 1\) SUFFICIENT

Answer is C.



Hi, Just a small correction. \(2^4\) is 16 and \(2^5\) is 32. :)


Thank you for correcting Afc0892
The answer remains the same though i.e. C.
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Re: If 2^x(5^n) = t, what is the value of t? (1) x = n + 3 (2) 2^x = 32 [#permalink] If 2^x(5^n) = t, what is the value of t? (1) x = n + 3 (2) 2^x = 32   07 Mar 2024, 07:55
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Re: If 2^x(5^n) = t, what is the value of t? (1) x = n + 3 (2) 2^x = 32 [#permalink]
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