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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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Joined: 02 Sep 2009
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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]

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03 Oct 2018, 02:00
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90% (01:01) correct 10% (01:04) wrong based on 78 sessions

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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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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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03 Oct 2018, 02:05
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

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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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03 Oct 2018, 02:06
1
Statement 1:

x = n+3.
Clearly insufficient.

Statement 2:

$$2^x$$ = 32

x = 5.

Combining both gives x as 5 and n as 2.

t = $$2^5$$$$5^2$$
Sufficient.

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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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03 Oct 2018, 02:13
(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

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Director
Joined: 18 Jul 2018
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Location: India
Concentration: Finance, Marketing
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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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03 Oct 2018, 02:16
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

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]

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03 Oct 2018, 02:18
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

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] 03 Oct 2018, 02:18
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