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

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

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New post 23 Apr 2018, 01:10
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A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

56% (01:43) correct 44% (01:47) wrong based on 124 sessions

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

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New post 23 Apr 2018, 04:53
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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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New post 23 Apr 2018, 17:55
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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 \(5^{-p} < 0.0025\)

\(0.0025=5^2*10^-4=5^2*2^-4*5^-4=5^-2*2^-4\)

\(5^-2 < 2^-4 < 5^-1\)

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

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

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New post 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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New post 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

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

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New post 28 Feb 2019, 07:28
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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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What is the least positive integer p such that 5^(-p) < 0.0025 ?

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