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What is the value of n? 1). The tens’ digit of 11^n is 4 2). The h

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What is the value of n? 1). The tens’ digit of 11^n is 4 2). The h  [#permalink]

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New post 20 Mar 2019, 09:31
00:00
A
B
C
D
E

Difficulty:

  75% (hard)

Question Stats:

38% (01:50) correct 63% (02:11) wrong based on 16 sessions

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What is the value of \(n\)?

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

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Re: What is the value of n? 1). The tens’ digit of 11^n is 4 2). The h  [#permalink]

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New post 20 Mar 2019, 10:10
From S1:

\(11^n\)'s tens digit is 4.
\(11^1 = 11\)
\(11^2 = 121\)
\(11^3 = 1331\)
\(11^4 = 14641\)
.
.
.
\(11^{14} = .....241\)
Here, n has two different values.
Hence S1 is Insufficient.

From S2:

\(5^n\)'s hundreds digit is 6.
\(5^4 = 625\)
\(5^8 = ...645.\)
Here also n has two different values.
Hence S2 is Insufficient.

Combining also is insufficient.

E is the answer.
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Re: What is the value of n? 1). The tens’ digit of 11^n is 4 2). The h  [#permalink]

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New post 20 Mar 2019, 11:26
from I, the tenth digit of 11^n can never be 4, so not A, neither D.
From II, for n=4, 6... (and more), the hundredth digit will be 6, so not B
combining, 11^n x 5^n will have a units digit of 5 but no other information is available, so not C.
Answer is E.
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Re: What is the value of n? 1). The tens’ digit of 11^n is 4 2). The h  [#permalink]

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New post 20 Mar 2019, 11:45
Bunuel, VeritasKarishma, chetan2u, amanvermagmat, gmatbusters
Can any of you suggest a shorter way of doing this?
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What is the value of n? 1). The tens’ digit of 11^n is 4 2). The h  [#permalink]

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New post 20 Mar 2019, 20:03
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PriyankaPalit7 wrote:
Bunuel, VeritasKarishma, chetan2u, amanvermagmat, gmatbusters
Can any of you suggest a shorter way of doing this?



Quote:
What is the value of \(n\)?

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


Hi, the biggest give away is that it is not mentioned that n is integer.

If n is not an integer, there will always be a value of n for every integer..
for example \(11^n\) = 40, \(11^n=41\) or 141, 148 and so on, there will be a value of n, may be in decimals that will fit .
So, infinite values of n possible..
If i look for an integer value, \(5^4=625\) and \(11^4=14641\), so n=4 is a value..... but \(n=4.0000000001\) is another value
Thus insufficient

E
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What is the value of n? 1). The tens’ digit of 11^n is 4 2). The h   [#permalink] 20 Mar 2019, 20:03
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What is the value of n? 1). The tens’ digit of 11^n is 4 2). The h

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