x is an integer and x raised to any odd integer is greater than zero; is w - z greater than 5 times the quantity 7\(^(x-1)\) - \(5^x\)?
1) z < 25 and w =\(7^x\)
2) x = 4
A for me. And it took me 4 min to solve this Information from the question stem:
x raised to any odd integer is greater than zero ----> it implies that x>0 because x raised to even power will always greater than zero. (understanding this took most of time...after I came to this, it was easy. GMAT really is all about tricks
Statement 1: z <25, lets assume z = 24 (this way we will minimize the value of w-z and if even after minimizing w-z > 5(7^(x-1) - 5^x), we will get our answer)
Let x=1, w-z = 7-24 = -17
5(7^(x-1) - 5^x) = 5(1-5) = -20. YES
Let x = 3, w-z = 343 - 24 = 319
5(7^(x-1) - 5^x) = 5(49 - 125) = a negative value. Again YES
Similarly you can prove for any value of x.
Hence SUFFICIENTA small tip: you don't need to calculate the values, you can clearly see that as the value of x increases, w-z will increase exponentially and 5(7^(x-1) - 5^x) will keep on decreasing.
Statement 2: clearly its NOT SUFFICIENT. We don't have any information about w and z.
Hope this helps.
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