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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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Manager
Joined: 28 May 2018
Posts: 150
Location: India
Schools: ISB '21 (A)
GMAT 1: 640 Q45 V35
GMAT 2: 670 Q45 V37
GMAT 3: 730 Q50 V40
What is the value of n? 1). The tens’ digit of 11^n is 4 2). The h  [#permalink]

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20 Mar 2019, 09:31
00:00

Difficulty:

75% (hard)

Question Stats:

38% (02:08) correct 62% (02:08) wrong based on 21 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
NUS School Moderator
Joined: 18 Jul 2018
Posts: 1024
Location: India
Concentration: Finance, Marketing
WE: Engineering (Energy and Utilities)
Re: What is the value of n? 1). The tens’ digit of 11^n is 4 2). The h  [#permalink]

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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.

Intern
Joined: 18 May 2017
Posts: 12
Re: What is the value of n? 1). The tens’ digit of 11^n is 4 2). The h  [#permalink]

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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.
Manager
Joined: 28 May 2018
Posts: 150
Location: India
Schools: ISB '21 (A)
GMAT 1: 640 Q45 V35
GMAT 2: 670 Q45 V37
GMAT 3: 730 Q50 V40
Re: What is the value of n? 1). The tens’ digit of 11^n is 4 2). The h  [#permalink]

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20 Mar 2019, 11:45
Can any of you suggest a shorter way of doing this?
Math Expert
Joined: 02 Aug 2009
Posts: 8283
What is the value of n? 1). The tens’ digit of 11^n is 4 2). The h  [#permalink]

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20 Mar 2019, 20:03
3
PriyankaPalit7 wrote:
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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