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If A is an integer, what is the value of A?

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If A is an integer, what is the value of A?  [#permalink]

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New post 22 Feb 2018, 12:21
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If A is an integer, what is the value of A?


(1) \(1,000,000 < 23^A < 10,000,000\)

(2) \(\frac{7^{A+2}−7^A}{48}=7^A\)

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Re: If A is an integer, what is the value of A?  [#permalink]

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New post 22 Feb 2018, 15:24
correct should be A but I'm sure this process worked in this case but is not that reliable for other ones so:

1) sufficient

we want to know 23^A, since 23 is a hard number to work with powers I just used 20, and so 20^5=3200000, 23^5 should higher but not higher than 10^7 ; likewise 20^4=160000 so 23^4 should no be higher than 10^6

2) not sufficient:

7A+2-7A= 7A(7^2-1) = 7^A=7^A ->> so A could number
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Re: If A is an integer, what is the value of A?  [#permalink]

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New post 24 Apr 2018, 20:07
Bunuel niks18 gmatbusters VeritasPrepKarishma chetan2u

Quote:
If A is an integer, what is the value of A?

Statement #1: 1,000,000 <\(23^A\) < 10,000,000


Can you please help me to analyze St 1?
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Re: If A is an integer, what is the value of A?  [#permalink]

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New post 24 Apr 2018, 20:21
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Statement1 : \(1,000,000<23^A<10,000,000\)

Since \(10,000,000/1,000,000 = 10\) which is less than 23, hence there can be at most only one multiple of 23 between 1,000,000 and 10,000,000

hence A is uniquely defined by this inequality.

Hence it is sufficient.

adkikani wrote:
Bunuel niks18 gmatbusters VeritasPrepKarishma chetan2u

Quote:
If A is an integer, what is the value of A?

Statement #1: 1,000,000 <\(23^A\) < 10,000,000


Can you please help me to analyze St 1?

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Re: If A is an integer, what is the value of A?  [#permalink]

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New post 12 May 2018, 05:32
I) 23^A

23 has two digits
23*23= 3 digits
(If we have 100*100 here then we get 4 digits ,but value is less than 100 so we have 3 digits)
Similarly
23*23*23=5 digits
23*23*23*23=7 digits
Sufficient
Lies within range

II) take 7^A as common
7^A(49-1)/48
=7^A
So lhs=RHs
But there can be multiple values of A so insufficient

A is ANSWER

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Re: If A is an integer, what is the value of A? &nbs [#permalink] 12 May 2018, 05:32
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