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# What is the least positive integer p such that 5^(-p) < 0.0025 ?

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Math Expert
Joined: 02 Sep 2009
Posts: 53657
What is the least positive integer p such that 5^(-p) < 0.0025 ?  [#permalink]

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23 Apr 2018, 01:10
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Difficulty:

45% (medium)

Question Stats:

57% (01:43) correct 43% (01:45) wrong based on 100 sessions

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What is the least positive integer p such that $$5^{-p} < 0.0025$$ ?

(A) 3
(B) 4
(C) 5
(D) 6
(E) 7

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Re: What is the least positive integer p such that 5^(-p) < 0.0025 ?  [#permalink]

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23 Apr 2018, 04:53
1
2
Bunuel wrote:
What is the least positive integer p such that $$5^{-p} < 0 0025$$ ?

(A) 3
(B) 4
(C) 5
(D) 6
(E) 7

Testing the options starting from A = 3

$$5^{-3}$$ = 1/(5^3) = 1/125 = 0.008 NOT the answer option A = 3

$$5^{-4}$$ = 1/(5^4) = 1/625 = 0.0016 THE the answer option B = 4

Hence option B = 4 is the answer.
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Re: What is the least positive integer p such that 5^(-p) < 0.0025 ?  [#permalink]

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23 Apr 2018, 17:55
1
1
Bunuel wrote:
What is the least positive integer p such that $$5^{-p} < 0 0025$$ ?

(A) 3
(B) 4
(C) 5
(D) 6
(E) 7

Not sure where the decimal lies, but assuming we have to find smallest p such that $$5^{-p} < 0.0025$$

$$0.0025=5^2*10^-4=5^2*2^-4*5^-4=5^-2*2^-4$$

$$5^-2 < 2^-4 < 5^-1$$

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Re: What is the least positive integer p such that 5^(-p) < 0.0025 ?  [#permalink]

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24 Apr 2018, 19:19
Bunuel wrote:
What is the least positive integer p such that $$5^{-p} < 0 0025$$ ?

(A) 3
(B) 4
(C) 5
(D) 6
(E) 7

I can't see the decimal in the ques.
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Re: What is the least positive integer p such that 5^(-p) < 0.0025 ?  [#permalink]

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25 Apr 2018, 15:02
Anki2609 wrote:
Bunuel wrote:
What is the least positive integer p such that $$5^{-p} < 0 0025$$ ?

(A) 3
(B) 4
(C) 5
(D) 6
(E) 7

I can't see the decimal in the ques.

Bunuel , would you please add a decimal point? I am fairly sure from your conventional style that the number is 0.0025 - but not positive. Thanks!

Anki2609 , in case you do not know; in order to ask the author or a specific person a question that s/he has a chance to see . . .

Type the "@" sign with the username next to it:
1) no space between symbol and username;
2) leave one space AFTER (before any punctuation, including the possessive apostrophe); and
3) don't actually use quotation marks around the "@" symbol (I must in order to outwit automatic formatting)
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Math Expert
Joined: 02 Sep 2009
Posts: 53657
Re: What is the least positive integer p such that 5^(-p) < 0.0025 ?  [#permalink]

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25 Apr 2018, 21:06
generis wrote:
Anki2609 wrote:
Bunuel wrote:
What is the least positive integer p such that $$5^{-p} < 0 0025$$ ?

(A) 3
(B) 4
(C) 5
(D) 6
(E) 7

I can't see the decimal in the ques.

Bunuel , would you please add a decimal point? I am fairly sure from your conventional style that the number is 0.0025 - but not positive. Thanks!

Anki2609 , in case you do not know; in order to ask the author or a specific person a question that s/he has a chance to see . . .

Type the "@" sign with the username next to it:
1) no space between symbol and username;
2) leave one space AFTER (before any punctuation, including the possessive apostrophe); and
3) don't actually use quotation marks around the "@" symbol (I must in order to outwit automatic formatting)

Yes, decimal point was missing. Sorry for that. Edited. Thank you.
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Re: What is the least positive integer p such that 5^(-p) < 0.0025 ?  [#permalink]

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09 May 2018, 09:18
On right side we have four digits after decimal and 5 to power -p is fraction so at least p=4 .

Since this is 5

So 1/5=0.2

0.2 to power 4 gives 0.0016

So 4 is answer in this case

Posted from my mobile device
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Re: What is the least positive integer p such that 5^(-p) < 0.0025 ?  [#permalink]

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28 Feb 2019, 07:28
Algebraic approach

$$5^{-p}<5^2*10^{-4}$$ $$\implies$$ $$5^{-p}<5^{-2}*2^{-4}$$
$$5^{2-p}<2^{-4}$$ $$\implies$$ $$16*25<5^p$$
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Re: What is the least positive integer p such that 5^(-p) < 0.0025 ?   [#permalink] 28 Feb 2019, 07:28
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