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

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Math Expert
Joined: 02 Sep 2009
Posts: 47219
If m is an integer, is 7^m > 1000?  [#permalink]

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12 Sep 2017, 23:39
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Difficulty:

25% (medium)

Question Stats:

79% (01:33) correct 21% (01:21) wrong based on 72 sessions

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

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

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

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Joined: 31 Jan 2017
Posts: 48
Re: If m is an integer, is 7^m > 1000?  [#permalink]

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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..
Ans A
Director
Joined: 18 Aug 2016
Posts: 631
Concentration: Strategy, Technology
GMAT 1: 630 Q47 V29
GMAT 2: 740 Q51 V38
Re: If m is an integer, is 7^m > 1000?  [#permalink]

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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

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