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x is a positive integer.

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x is a positive integer. [#permalink] New post 26 Jun 2017, 01:54
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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

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Re: x is a positive integer. [#permalink] New post 26 Jun 2017, 05:27
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Is it 6^x and 4^(2x) ?
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Re: x is a positive integer. [#permalink] New post 27 Jun 2017, 02:10
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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
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Re: x is a positive integer. [#permalink] New post 27 Jun 2017, 10:27
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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.
Answer:
[Reveal] Spoiler:
C


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Re: x is a positive integer. [#permalink] New post 13 Nov 2018, 19:49
nainy05 wrote:
Is it 6^x and 4^(2x) ?


Please explain what do you think?
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Re: x is a positive integer. [#permalink] New post 19 Nov 2018, 16:11
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
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Re: x is a positive integer. [#permalink] New post 26 Nov 2018, 19:28
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.
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Re: x is a positive integer. [#permalink] New post 27 Nov 2018, 02:17
i didnt understand
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Re: x is a positive integer. [#permalink] New post 13 Apr 2019, 23:44
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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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x is a positive integer.

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