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anooo31
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If t is a positive integer and 3*10^t > 15,000, what is t? Updated on: 06 May 2018, 01:58
Originally posted by anooo31 on 06 May 2018, 01:07.
Last edited by anooo31 on 06 May 2018, 01:58, edited 3 times in total.
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

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55% (hard)

Question Stats:

63% (02:01) correct 37% (02:09) wrong based on 226 sessions

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If t is a positive integer and \(3*10^{t} > 15,000\), what is t?


(1) \(10^t < 20,000\)

(2) \(5 * 10^t < 600,000\)
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A
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If t is a positive integer and 3*10^t > 15,000, what is t? 06 May 2018, 01:21
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anooo31
If t is a positive integer and \(3*10^{t} > 15,000\), what is t?


(1) \(10^t < 20,000\)

(2) \(5 * 10^t < 600,000\)


Show Spoiler
Struggling to see if the answer is B or D. Spoiler: Don't have OA yet

\(3*10^{t} > 15,000\)

i.e. \(10^{t} > 5,000\)

i.e. \(10^{t-3} > 5\)

i.e. t-3 > 0

i.e. t > 3

Question : t = ?

Statement 1: \(10^t < 20,000\)

i.e. \(10^{t-4} < 2\)

i.e. t - 4 < 1

i.e. t < 5

i.e. 3 < t < 5

i.e. t = 4

SUFFICIENT

Statement 2: \(5 * 10^t < 600,000\)

i.e. \(10^t < 120,000\)

i.e. \(10^{t-5} < 1.2\)

i.e. t-5 <1
i.e. t < 6

i.e. t may be 4 or 5 hence

NOT SUFFICIENT

Answer: Option A
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If t is a positive integer and 3*10^t > 15,000, what is t? 06 May 2018, 01:22
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If t is a positive integer and \(3*10^{t} > 15,000\), what is t?

\(3*10^{t} > 15,000\);

\(10^{t} > 5,000\);

Since t is a positive integer, then t > 3. It can be: 4, 5, 6, 7, ...


(1) \(10^t < 20,000\). From this t can be 4, 3, 2, or 1. Thus, t = 4. Sufficient.

(2) \(5 * 10^t < 600,000\) --> \(10^t < 120,000\). From this t can be 5, 4, 3, 2, or 1. Thus, t = 4 or t = 5. Not sufficient.


Answer: A.
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If t is a positive integer and 3*10^t > 15,000, what is t? 06 May 2018, 02:14
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From the question stem we know that t can be an integer greater than 3
Now let's consider (1)- t can be an integer from 1 to 4
Therefore, we can conclude that t=4; (1) is sufficient

Considering (2)- t can be an integer from 1 to 5
Thus we have two possible values of t, 4 & 5; (2) is not sufficient

Therefore, the answer is A
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If t is a positive integer and 3*10^t > 15,000, what is t? 07 May 2018, 12:17
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anooo31
If t is a positive integer and \(3*10^{t} > 15,000\), what is t?


(1) \(10^t < 20,000\)

(2) \(5 * 10^t < 600,000\)


I) here we get t=1,2,3,4
But only t=4 satisfy 3*10^t>15000
Sufficient

II) here t=1,2,3,4,5
But t=4 and 5 satisfy
3*10^t>15000
Insufficient

So A is answer

Posted from my mobile device
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If t is a positive integer and 3*10^t > 15,000, what is t? 31 Jul 2019, 14:36
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Bunuel
If t is a positive integer and \(3*10^{t} > 15,000\), what is t?

\(3*10^{t} > 15,000\);

\(10^{t} > 5,000\);

Since t is a positive integer, then t > 3. It can be: 4, 5, 6, 7, ...


(1) \(10^t < 20,000\). From this t can be 4, 3, 2, or 1. Thus, t = 4. Sufficient.

(2) \(5 * 10^t < 600,000\) --> \(10^t < 120,000\). From this t can be 5, 4, 3, 2, or 1. Thus, t = 4 or t = 5. Not sufficient.


Answer: A.

For B, how did you get 5? \(5*10^t<600,000\) on diving both sides by 5 is \(10^t<120,000\)
so 120,000 can be written as 12 X 10000 = 12 X 10^4

Can you point the error I am making?

Thanks in advance!
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If t is a positive integer and 3*10^t > 15,000, what is t? 16 Jun 2025, 09:03
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