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## GMAT - Data Sufficiency - Inequalities

### If n is a positive integer, is

$If \quad n\quad is\quad a\quad positive\quad integer,is\quad { \left( \frac { 1 }{ 10 } \right) }^{ n }<0.01?\\ \\ 1.\quad n\quad >\quad 2\\ \\ 2.\quad { \left( \frac { 1 }{ 10 } \right) }^{ n-1 }<\quad 0.1$

Statement 1

n > 2

since 1/10 < 1 the sign of inequality will change because (1/10)x is a decreasing function

(1/10)n < (1/10)2

(1/10)n < 0.01

sufficient

Statement 2

(1/10)n-1 < 0.1

(1/10)n * (1/10)-1 < 0.1

(1/10)n * 10 < 0.1

(1/10)n < 0.01

sufficient