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Founder  Joined: 18 Apr 2015
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x is a positive integer. [#permalink]
Expert's post 00:00

Question Stats: 58% (00:53) correct 41% (00:45) wrong based on 74 sessions

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.
[Reveal] Spoiler: OA

_________________ Intern Joined: 17 Apr 2017
Posts: 7
Followers: 0

Kudos [?]: 7  , given: 2

Re: x is a positive integer. [#permalink]
1
KUDOS
Is it 6^x and 4^(2x) ?
Founder  Joined: 18 Apr 2015
Posts: 7012
Followers: 116

Kudos [?]: 1368 , given: 6372

Re: x is a positive integer. [#permalink]
Expert's post
Here is a question to find the pattern.

no matter what 6 has exponent a positive integers the number will end up with 6

6^1 =6
6^2=36 and so forth

4^2*1=16
4^2*2=256 and so forth

C is the best
_________________ GRE Instructor Joined: 10 Apr 2015
Posts: 2021
Followers: 62

Kudos [?]: 1835  , given: 9

Re: x is a positive integer. [#permalink]
1
KUDOS
Expert's post
Carcass wrote:

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.
[Reveal] Spoiler:
C

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Brent Hanneson – Creator of greenlighttestprep.com Director Joined: 09 Nov 2018
Posts: 508
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Kudos [?]: 27 , given: 1

Re: x is a positive integer. [#permalink]
nainy05 wrote:
Is it 6^x and 4^(2x) ?

Please explain what do you think?
Intern Joined: 07 Aug 2016
Posts: 42
Followers: 0

Kudos [?]: 16 , given: 0

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..

Manager Joined: 22 Feb 2018
Posts: 163
Followers: 2

Kudos [?]: 115 , given: 22

Re: x is a positive integer. [#permalink]
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.
_________________

Manager Joined: 23 Oct 2018
Posts: 57
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Kudos [?]: 0 , given: 0

Re: x is a positive integer. [#permalink]
i didnt understand Intern Joined: 27 Jan 2019
Posts: 19
Followers: 0

Kudos [?]: 18  , given: 1

Re: x is a positive integer. [#permalink]
1
KUDOS
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. Re: x is a positive integer.   [#permalink] 13 Apr 2019, 23:44
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