Last visit was: 19 Jul 2024, 21:54 It is currently 19 Jul 2024, 21:54

Close

GRE Prep 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 GRE 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.

Close

Request Expert Reply

Confirm Cancel
Verbal Expert
Joined: 18 Apr 2015
Posts: 29125
Own Kudos [?]: 34154 [4]
Given Kudos: 25516
Send PM
avatar
Intern
Intern
Joined: 17 Apr 2017
Posts: 7
Own Kudos [?]: 13 [0]
Given Kudos: 0
Send PM
Verbal Expert
Joined: 18 Apr 2015
Posts: 29125
Own Kudos [?]: 34154 [0]
Given Kudos: 25516
Send PM
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Own Kudos [?]: 11874 [2]
Given Kudos: 136
Send PM
x is a positive integer. [#permalink]
1
1
Bookmarks
Carcass wrote:

This question is part of GREPrepClub - The Questions Vault Project



x is a positive integer.


Quantity A
Quantity B
The units digit of \(6^x\)
The units digit of \(4^{2x}\)


A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.


Quantity A: The units digit of 6^x
Quantity B: The units digit of 4^(2x)

Notice that (4^2)^x = 4^(2x), so let's replace Quantity B with its equivalent to get:
Quantity A: The units digit of 6^x
Quantity B: The units digit of (4^2)^x

Evaluate 4^2 to get:
Quantity A: The units digit of 6^x
Quantity B: The units digit of 16^x

Since all positive powers of 6 and 16 will have units digit 6, we can conclude that the two quantities will always be equal.
Answer:
Show: ::
C


RELATED VIDEO
avatar
Director
Director
Joined: 09 Nov 2018
Posts: 505
Own Kudos [?]: 131 [0]
Given Kudos: 0
Send PM
Re: x is a positive integer. [#permalink]
nainy05 wrote:
Is it 6^x and 4^(2x) ?


Please explain what do you think?
avatar
Manager
Manager
Joined: 07 Aug 2016
Posts: 59
Own Kudos [?]: 67 [0]
Given Kudos: 0
GRE 1: Q166 V156
Send PM
Re: x is a positive integer. [#permalink]
A units digit of 6 raised to any positive integer is 6.

6^1 = 6
6^2 = 36

16^2 = 256 etc..

C is the answer
avatar
Manager
Manager
Joined: 22 Feb 2018
Posts: 163
Own Kudos [?]: 212 [0]
Given Kudos: 0
Send PM
Re: x is a positive integer. [#permalink]
Answer: C
By units digits it means the last right digit,
We assume x is 1,2,3,….., n as it is said that it’s a positive integer

x = 1 A = 6^1 = 6 B=4^2*1=(16)
x = 2 A = 6^2 = 36 B=4^2*2= (16)^2
x = 1 A = 6^3 = 216 B=4^2*3= (16)^3
.
.
.
x = n A = 6^n B=4^2*n= (16)^n

So they both end in 6. And the answer is C.

Because both 6 and 16 end in 6, when they have any positive integer power, they will end with 6, definitely this rule is not true for all other numbers. For instance 2 in different powers might end in 2,4,8.
avatar
Manager
Manager
Joined: 23 Oct 2018
Posts: 57
Own Kudos [?]: 0 [0]
Given Kudos: 0
Send PM
Re: x is a positive integer. [#permalink]
i didnt understand
avatar
Intern
Intern
Joined: 27 Jan 2019
Posts: 29
Own Kudos [?]: 53 [0]
Given Kudos: 0
Send PM
Re: x is a positive integer. [#permalink]
1
Whenever 4 is raised to an positive even power the units digit will always be 6. So the two quantities are equal. Watch out for zero. It is also an even integer but not positive.
avatar
Intern
Intern
Joined: 24 Oct 2020
Posts: 15
Own Kudos [?]: 16 [0]
Given Kudos: 0
Send PM
Re: x is a positive integer. [#permalink]
Whatever the exponent was for 6 its unit digits is always going to be 6.

test out yourself: -

6^1 = 6

6^2 = 36

6^3 = 36*6 = ...6
etc...

As for 4 it is going to alternate between 4 and 6.

4^1 = 4

4^2 = 16

4^3 = ..4

4^4 = ..6

4^5 = ..4
etc..

notice for 4 when the exponent is odd it ends with 4, when its even it ends with 6.

Quantity A is always going to end in 6. Quantity B is 4^[(2)(x)] --> even exponent all the time because of the 2 multiplied by the x (odd x even = even)

Therefore Quantity B is always going to end in 6 too.
Moderator
Moderator
Joined: 02 Jan 2020
Status:GRE Quant Tutor
Posts: 1091
Own Kudos [?]: 904 [1]
Given Kudos: 9
Location: India
Concentration: General Management
Schools: XLRI Jamshedpur, India - Class of 2014
GMAT 1: 700 Q51 V31
GPA: 2.8
WE:Engineering (Computer Software)
Send PM
x is a positive integer. [#permalink]
1
Quantity A : The units digit of \(6^x\)

To find the units digit of power of 6 we need to check the cyclicity in the units digit of powers of 6

\(6^1\) units’ digit is 6 [ 6 ]
\(6^2\) units’ digit is 3 [ 36 ]
\(6^3\) units’ digit is 3 [ 216 ]

=> Units digit of any positive integer power of 6 is 6
=> The units digit of \(6^x\) = 6 (as x is a positive integer)

Quantity B : The units digit of \(4^{2x}\)

To find the units digit of power of 4 we need to check the cyclicity in the units digit of powers of 4

\(4^1\) units’ digit is 4 [ 4 ]
\(4^2\) units’ digit is 6 [ 16 ]
\(4^3\) units’ digit is 4 [ 64 ]
\(4^4\) units’ digit is 6 [ 256 ]

=> Units digit of any positive odd integer power of 4 is 4
=> Units digit of any positive even integer power of 4 is 6
=> The units digit of \(4^2x\) = 6 (as 2x is a positive even integer)

Clearly, Quantity A(6) = Quantity B(6)

So, Answer will be C!
Hope it helps!

Watch the following video (from 2:48 mins) to learn how to find cyclicity of 3 and other numbers
Intern
Intern
Joined: 20 Aug 2022
Posts: 4
Own Kudos [?]: 0 [0]
Given Kudos: 65
Send PM
Re: x is a positive integer. [#permalink]
Why can't I raise it to the power of 0 (it is a positive integer). Am I missing something here?
Verbal Expert
Joined: 18 Apr 2015
Posts: 29125
Own Kudos [?]: 34154 [0]
Given Kudos: 25516
Send PM
x is a positive integer. [#permalink]
Expert Reply
AP001 wrote:
Why can't I raise it to the power of 0 (it is a positive integer). Am I missing something here?


ZERO:
1. 0 is an integer.
2. 0 is an even integer. An even number is an integer that is "evenly divisible" by 2, i.e., divisible by 2 without a remainder and as zero is evenly divisible by 2 then it must be even.
3. 0 is neither positive nor negative integer (the only one of this kind).
4. 0 is divisible by EVERY integer except 0 itself.

I suggest you brush your fundamentals Integers properties

https://gre.myprepclub.com/forum/gre-qu ... tml#p51913
Prep Club for GRE Bot
[#permalink]
Moderators:
GRE Instructor
49 posts
GRE Forum Moderator
26 posts
Moderator
1091 posts
GRE Instructor
218 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne