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powers

by finance » Tue Jul 05, 2011 12:34 am
x is a positive number. If 9^x + 9^(x+1) + 9^(x+2) + 9^(x+3) + 9^(x+4) + 9^(x+5) = y, is y divisible by 5?
1) 5 is a factor of x.
2) x is an integer.

OA after some posts. Please explain your answers. Thank you!
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Source: — Data Sufficiency |
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by kmittal82 » Tue Jul 05, 2011 1:14 am
Hmm, interesting, I'm sure there ought to be a better way of doing this than what I am about to propose

first, this equation can be progressively broken down:

9^x[ 1 + 9 + 9^2 + 9^3 + 9^4 + 9^5 ]

= 9^x [ 10 + 9^2(10) + 9^4(10)]
= 9^x [10 + 810 + 810(9^2)]
y = 9^x [66430]

Now, considering the given statements:

(1) Sufficient
(2) Sufficient

Thus, (D).

This took me about 90seconds to solve, so I'm sure there should be an easier way to do this
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by finance » Tue Jul 05, 2011 1:23 am
Hi!

Well, you do not need to make calculations...start from the fact that" 9 ^(odd number) will give you a result whose units digit is 9 and 9^even, gives a number ending in 1"

Does it help?
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