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

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

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New post 25 Jun 2013, 01:26
2
6
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A
B
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D
E

Difficulty:

  95% (hard)

Question Stats:

44% (02:16) correct 56% (02:05) wrong based on 191 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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New post 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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New post 27 Sep 2014, 05:38
1
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,...

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

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New post 10 Dec 2018, 05:14
Trap Question alert !!!

One should consider all the case and follow the pattern for both the statement

Option E is right choice
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Re: If n is a positive integer greater than 2, n=?   [#permalink] 10 Dec 2018, 05:14
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