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If n is a positive integer greater than 2, n=?

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Manager
Joined: 20 Jun 2012
Posts: 85
Location: United States
Concentration: Finance, Operations
GMAT 1: 710 Q51 V25
If n is a positive integer greater than 2, n=?  [#permalink]

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25 Jun 2013, 01:26
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95% (hard)

Question Stats:

46% (02:19) correct 54% (02:02) wrong based on 152 sessions

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If n is a positive integer greater than 2, n=?

(1) The tens' digit of 11^n is 4.
(2) The hundreds' digit of 5^n is 6.

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Re: If n is a positive integer greater than 2, n=?  [#permalink]

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25 Jun 2013, 03:32
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stunn3r wrote:
If n is a positive integer greater than 2, n=?

(1) The tens' digit of 11^n is 4.
(2) The hundreds' digit of 5^n is 6.

The units digit of $$11^n$$ for any positive integer (n) is always 1. Also, the tens digit of $$11^n$$, follows a cyclic order, and assumes all the values from 0-9.

$$11^1 = 11$$
$$11^2 = X21$$
$$11^3 = XX31$$
$$11^4 = XXX41$$ and so on

The tens and units digit for $$5^n$$, is always 25, for$$n\geq2$$. The hundreds digit keeps switching between 1 for n = odd OR as 6 for n = even

From F.S 1, we would have the tens digit as 4 for n = 4, and then again for n = (4+10) = 14. Insufficient.

From F. S 2, we would have the hundreds digit as 6 for n = 4,6,8 and so on. Insufficient.

Even after combing both fact statements, n could be n = 4 or n = 14. Insufficient.

E.
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Re: If n is a positive integer greater than 2, n=?  [#permalink]

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27 Sep 2014, 05:38
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stunn3r wrote:
If n is a positive integer greater than 2, n=?

(1) The tens' digit of 11^n is 4.
(2) The hundreds' digit of 5^n is 6.

E.

1) 11^1 = 11
11^2 = 121
11^3 = 1331
11^4 = 14641
.
.
.
11^10 mod 100 = 01
(taking mod 100 or remainder by 100 as that gives the ten's digit)
after this the cycle repeats
11^14 will also have ten's digit as 4.
11^n will have ten's digit as 4 for n = 4,14,24,...
So, insufficient.

2) 5^4 = 625
5^14 mod 1000 = 625
so here also n would be 4,14,...

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Re: If n is a positive integer greater than 2, n=?  [#permalink]

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02 Apr 2018, 08:10
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Re: If n is a positive integer greater than 2, n=? &nbs [#permalink] 02 Apr 2018, 08:10
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