At least 1 solution

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sanaa.rizwan: Senior | Next Rank: 100 Posts; Posts: 69; Joined: Wed Aug 08, 2012 9:00 amFollowed by: 1 member

by sanaa.rizwan » Tue May 14, 2013 12:12 pm

Each of the following equations has at least one solution EXCEPT

a. -2^n = (-2)^-n
b. 2^-n = (-2)^n
c. 2^n = (-2)^-n
d. (-2)^n = -2^n
e. (-2)^-n = -2^-n

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Source: Beat The GMAT — Problem Solving | Tue May 14, 2013 12:12 pm

srcc25anu: Master | Next Rank: 500 Posts; Posts: 423; Joined: Fri Jun 11, 2010 7:59 amFollowed by: 2 members; Location: Seattle, WA; Thanked: 86 times

by srcc25anu » Tue May 14, 2013 12:50 pm

Lets pick numbers 1 and 0

A. LHS -(2)^0 = -1 RHS (-2)^-n = 1/1 = 1 (No SOLUTION)
B. LHS 2^(-n) = 2^0 = 1 RHS (-2)^n = (-2)^0 = 1 VALID SOLUTION
C. LHS 2^n = 2^0 = 1 RHS (-2)^-n = (-2)^0 = 1 VALID SOLUTION
D. LHS (-2)^n = (-2)^1 = -2 RHS -2^n = -2^1 = -2 VALID SOLUTION
E. LHS (-2)^-n = (-2)^-1 = -(1/2) RHS -2^-n = -(2^-1) = -(1/2) VALID SOLUTION

Hence Only A does not have any valid solution.
Ans A

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