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If A is an integer, what is the value of A?
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22 Feb 2018, 13:21
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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?
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22 Feb 2018, 16:24
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+27A= 7A(7^21) = 7^A=7^A >> so A could number _________ _________ 48 48



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Re: If A is an integer, what is the value of A?
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24 Apr 2018, 21:07
Bunuel niks18 gmatbusters VeritasPrepKarishma chetan2uQuote: 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?
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24 Apr 2018, 21:21
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 chetan2uQuote: 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?
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12 May 2018, 06:32
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(491)/48 =7^A So lhs=RHs But there can be multiple values of A so insufficient A is ANSWER Give kudos if it helps Posted from my mobile device
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