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x is a positive integer.

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

52% (00:58) correct 47% (00:54) wrong based on 38 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]  26 Jun 2017, 05:27
1
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Is it 6^x and 4^(2x) ?
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Re: x is a positive integer. [#permalink]  27 Jun 2017, 02:10
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
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Re: x is a positive integer. [#permalink]  27 Jun 2017, 10:27
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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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Re: x is a positive integer. [#permalink]  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]  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..

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Re: x is a positive integer. [#permalink]  26 Nov 2018, 19:28
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]  27 Nov 2018, 02:17
i didnt understand
Re: x is a positive integer.   [#permalink] 27 Nov 2018, 02:17
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