GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 23 May 2019, 22:07 ### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here. ### Request Expert Reply # If n > 2 where n is an integer, what is the value of n?

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

### Hide Tags

Math Expert V
Joined: 02 Sep 2009
Posts: 55275
If n > 2 where n is an integer, what is the value of n?  [#permalink]

### Show Tags 00:00

Difficulty:   95% (hard)

Question Stats: 35% (02:18) correct 65% (02:12) wrong based on 158 sessions

### HideShow timer Statistics

If n > 2 where n is an integer, what is the value of n?

(1) The ten's digit of 11^n is 4
(2) The hundred's digit of 5^n is 6

_________________
Manager  G
Joined: 19 Nov 2017
Posts: 181
Location: India
Schools: ISB
GMAT 1: 670 Q49 V32 GPA: 4
Re: If n > 2 where n is an integer, what is the value of n?  [#permalink]

### Show Tags

1
Bunuel wrote:
If n > 2 where n is an integer, what is the value of n?

(1) The ten's digit of 11^n is 4
(2) The hundred's digit of 5^n is 6

Should be E

Statement 1: The ten's digit of $$11^n$$ is 4
in 11^4 ten's digit is 4. BUT in 11^14 ten's digit is also 4.
($$11^1 = 11; 11^2 = 121; 11^3 = 1331$$... forms a pattern and will repeat)
Insufficient

Statement 2: The hundred's digit of 5^n is 6
in 5^4 hundred's digit is 6. BUT in 5^6 hundred's digit is also 6.
($$5^4 = 625; 5^6 = 15625; 5^8 = 390625$$... forms a pattern and will repeat)
Insufficient

Statement 1 and 2:
N could be 4, 14, 24... No definite answer.
Insufficient

Therefore, E.

Hope this helps.

Regards,
V
_________________
Regards,

Vaibhav

Sky is the limit. 800 is the limit.

~GMAC
VP  D
Status: Learning stage
Joined: 01 Oct 2017
Posts: 1008
WE: Supply Chain Management (Energy and Utilities)
Re: If n > 2 where n is an integer, what is the value of n?  [#permalink]

### Show Tags

Bunuel wrote:
If n > 2 where n is an integer, what is the value of n?

(1) The ten's digit of 11^n is 4
(2) The hundred's digit of 5^n is 6

St1:-
The ten's digit of $$11^n$$ is 4.
So n=4,14,24 etc
So insufficient.

St2:-
The hundred's digit of $$5^n$$ is 6.
So, n=4,6,8,10,12,14,16,18,20,24 etc
So, insufficient.

Combining, we have n=4,14 etc.

Hence, insufficient.

Ans (E)
_________________
Regards,

PKN

Rise above the storm, you will find the sunshine
Manager  S
Joined: 10 Sep 2015
Posts: 73
Location: India
Concentration: Finance, Human Resources
GMAT 1: 640 Q47 V31 GMAT 2: 660 Q47 V35 GMAT 3: 700 Q49 V36 GPA: 4
Re: If n > 2 where n is an integer, what is the value of n?  [#permalink]

### Show Tags

isnt there any other way, other than finding all the initial values for both statement, as it took a lot of time?
looking forward for OE
Director  P
Joined: 14 Dec 2017
Posts: 522
Location: India
Re: If n > 2 where n is an integer, what is the value of n?  [#permalink]

### Show Tags

1
Bunuel wrote:
If n > 2 where n is an integer, what is the value of n?

(1) The ten's digit of 11^n is 4
(2) The hundred's digit of 5^n is 6

Given n is an integer & n > 2

Question: n = ?

Statement 1: Tens digit of 11^n is 4

The tens digits of 11^ n will be 4 if units digit of n is 4.

But we don't know whether n is a single digit number or 2 digits or more.

Statement 1 is Not Sufficient.

Additional Tip: In general last two digits of any power of a number ending in 1 are found by multiplying the units digit of the power by the tens digit of the number for the tens place & units place is always 1.

e.g. 11^12 has last two digits as 21

41^23 has last two digits as 21

241^2234 has last two digits as 61

Statement 2: The hundreds digit of 5^n is 6

We have 5^3 = 125
5^4 = 625, hence n could be 4
5^5 = 3125
5^6 = 15625, hence n could be 6

we can see the pattern here that hundreds digit is either 1 or 6, for subsequent powers.

Hence n = 4, 6, 8,...

Statement 2 is Not Sufficient.

In general, for n>=3, hundreds digit for 5^n will be 1 if n is odd & it will be 6 if n is even.

Combining 1 & 2,

We don't get any new information. Since n can still be a single digit or a two digit or more number.

Combining is not sufficient.

Answer E.

Thanks,
GyM
_________________
Director  G
Joined: 20 Feb 2015
Posts: 795
Concentration: Strategy, General Management
Re: If n > 2 where n is an integer, what is the value of n?  [#permalink]

### Show Tags

Bunuel wrote:
If n > 2 where n is an integer, what is the value of n?

(1) The ten's digit of 11^n is 4
(2) The hundred's digit of 5^n is 6

1.Tens digit of 11^n is 4
since n > 2
let n be 3 , then 11^3=1331
let n be 4, then 11^4,last two digits =41 - Tens digit in this case is 4
let n be 5 , then 11^5,last two digits = 51
There seems to be a pattern such that the value of n and the tens digit is same
based on above n can be 4 or 44 or probably 444 who knows.
insufficient.

2.hundred's digit of 5^n is 6
will start off with n=4 , 5^4 is 625
625*25 last three digits =625
so n =4 or n=6 or n=8
insufficient

combining both n=4 or n=44 insufficient

Therefore E
Manager  B
Joined: 31 Jan 2012
Posts: 70
Re: If n > 2 where n is an integer, what is the value of n?  [#permalink]

### Show Tags

It's E. Wow Bunuel your still here. I am retaking my GMAT since it has been 5 years. Hopefully I can score 750ish this time. 50 points increase should be okay, I hope.
Retired Moderator P
Joined: 22 Aug 2013
Posts: 1443
Location: India
Re: If n > 2 where n is an integer, what is the value of n?  [#permalink]

### Show Tags

1
asthagupta wrote:
isnt there any other way, other than finding all the initial values for both statement, as it took a lot of time?
looking forward for OE

I think there is another approach possible to this question. For every base and exponent of the form a^n, where a and n are positive integers, there always exists a certain cyclicity in powers for units digit, tens digit, hundreds digit etc.

Eg, consider 2^n. For various values of 'n', 2^n will take various values of last digit (units digit) but at a certain point it will start getting repeated. 2^1, 2^2, 2^3, 2^4 end in 2, 4, 8, 6 respectively. After that, it starts getting repeated - so 2^5, 2^6, 2^7, 2^8 also end in 2, 4, 6, 8 respectively.

Similarly 11^n will take various values of tens digit depending on the value of n. So 11^1, 11^2, 11^3, 11^4, 11^5, 11^6, 11^7, 11^8, 11^9, 11^10 respectively take the last two digits as 11, 21, 31, 41, 51, 61, 71, 81, 91, 01. After that it starts getting repeated. So 11^11, 11^12, 11^13.... also end in 11, 21, 31.. respectively.

Similarly 5^n, once it starts getting into 3 digits, will take its hundreds place digit as 1 and 6 only. 5^3 = 125, 5^4 = 625, 5^5 = 3125... and so on.

So, the approach is as follows:
Knowing the fact that units or tens or hundreds digit for a^n will start repeating after a certain fixed value of power 'n' (depending on the value of base 'a' also), we can never uniquely determine a single value for which the tens place digit will be 4 or for which the hundreds place digit will be 6. We are sure to get various values for which the same tens digit and hundreds digit will occur.

Since there is no unique value, answer has to be straight E.
Manager  S
Joined: 05 Oct 2017
Posts: 79
Location: India
Concentration: Finance, International Business
Schools: ISB '21, IIMA , IIMB
GPA: 4
WE: Analyst (Energy and Utilities)
Re: If n > 2 where n is an integer, what is the value of n?  [#permalink]

### Show Tags

From statement 1 - It can be observed that whenever we multiply a number with 11 the ten's place digit gets added to the unit's place digit to form the ten's place digit of the resulting product. From these observation last 2 digits of the following can be written as:
11^3 =121*11= ..31,
11^4= ...31*11 = ..41
11^5= ..41*11 = ..51
11^6 =...51*11 = ..61
11^7=...61*11=..71
11^8=...71*11 = ..81
11^9= ...81*11= ..91
11^10= ..91*11= ..01
11^11= ..01*11= ..11
11^12 = ..11*11= ...21
11^13= ...21*11= ..31
So the ten's digit number starts to repeat.So a particular value of n for which ten's place digit will be 6 cannot be determined. Hence 1) Not sufficient.

From statement 2- Similary 5^3 = 25*5=125, 5^4=625 5^5 = 3025

Last three digits are 025 if we keep on multiplying the hundred's digit will keep giving value of 6 for n= 4,7,10,13..so on.Hence statement 2) insufficient. Re: If n > 2 where n is an integer, what is the value of n?   [#permalink] 12 Sep 2018, 13:34
Display posts from previous: Sort by

# If n > 2 where n is an integer, what is the value of n?

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.

#### MBA Resources  