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Hello Gmat_mission.Gmat_mission wrote:$$Is\ \ \ 10^m<5,000?$$ $$(1)\ \ \ 10^{m+1}>9,000$$ $$(2)\ \ \ \ 10^{m-1}=10^m-900$$ [spoiler]OA=B[/spoiler].
Could someone explain how to solve this DS question to me? Thanks for your help.
We can rewrite this expression and find the possible values for m. $$10^{m+1}>9000\ \ \ \Rightarrow\ \ \ 10^m\cdot10>9000\ \ \ \Rightarrow\ \ 10^m>900\ \ \ \Rightarrow\ \ m\ge3.$$$$(1)\ \ \ 10^{m+1}>9,000$$
Again, we can solve the inequality for m as follows: $$10^{m-1}=10^m-900\ \ \Rightarrow\ \ 10^m\cdot10^{-1}-10^m=-900\ \ \Rightarrow\ \ 10^m\left(\frac{1}{10}-1\right)=-900\ \ \ \Rightarrow\ 10^m\left(-\frac{9}{10}\right)=-900$$ $$10^m=1000\ <5000.\ \ \ YES.$$ Therefore, this statement is SUFFICIENT.$$(2)\ \ \ \ 10^{m-1}=10^m-900$$
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Statement One Alone:Gmat_mission wrote:$$Is\ \ \ 10^m<5,000?$$ $$(1)\ \ \ 10^{m+1}>9,000$$ $$(2)\ \ \ \ 10^{m-1}=10^m-900$$ [spoiler]OA=B[/spoiler].
