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If m is an integer, is 7^m > 1000?

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Kudos [?]: 132643 [0], given: 12326

If m is an integer, is 7^m > 1000? [#permalink]

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New post 12 Sep 2017, 23:39
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Kudos [?]: 132643 [0], given: 12326

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Re: If m is an integer, is 7^m > 1000? [#permalink]

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New post 13 Sep 2017, 00:14
After resolving the question stem the question basically ask is m>3 where m is an integer means m=4,5,6...any integer value >3

S1: On solving we get 7^m=1020.8 as it >1000 but m being an integer the least possible value for 7^m to be >1000 is 2048 where m being an integer so suff...
S2: On solving we get 7^m>142.85 m could be 3 so no m could be 4 yes
insuff..
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Re: If m is an integer, is 7^m > 1000? [#permalink]

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New post 14 Sep 2017, 04:58
Bunuel wrote:
If m is an integer, is \(7^m > 1000\)?


(1) \(7^{(m-2)} = 7^m - 1000\)

(2) \(7^{(m + 1)} > 1000\)


question: is (7^m-1000)>0

(1) tells us 7^m/7^2 = 7^m - 1000

for any integer value LHS will remain + i.e. greater than 0..hence sufficient

(2) 7^m - 1000/7 >0

7^m - ~142 > 0
for m = 3, 7^m-1000 is negative
for m = 4, 7^m-1000 is positive

Hence not sufficient

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Kudos [?]: 161 [0], given: 134

Re: If m is an integer, is 7^m > 1000?   [#permalink] 14 Sep 2017, 04:58
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If m is an integer, is 7^m > 1000?

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