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If x and y are positive integers and r is the remainder when 3^(4x+2)

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Bunuel
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If x and y are positive integers and r is the remainder when 3^(4x+2) [#permalink] New post   05 Oct 2020, 07:45
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If x and y are positive integers and r is the remainder when \(3^{4x + 2}+y\) is divided by 10, what is the value of r?

(1) x = 25

(2) y = 1
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GowriPrakash
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Re: If x and y are positive integers and r is the remainder when 3^(4x+2) [#permalink] New post   05 Oct 2020, 08:04
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Bunuel wrote:
If x and y are positive integers and r is the remainder when \(3^{4x + 2}\) is divided by 10, what is the value of r?

(1) x = 25

(2) y = 1



Is the equation \(3^{4x + 2}\) right ? Because there is no y in it.
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Re: If x and y are positive integers and r is the remainder when 3^(4x+2) [#permalink] New post   05 Oct 2020, 08:27
GowriPrakash wrote:
Bunuel wrote:
If x and y are positive integers and r is the remainder when \(3^{4x + 2}\) is divided by 10, what is the value of r?

(1) x = 25

(2) y = 1



Is the equation \(3^{4x + 2}\) right ? Because there is no y in it.


Agreed...if that is truly the equation then A. If you know x=25 then you would be able to figure out the value of 3^(4x+2) and solve for the remainder r.
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Re: If x and y are positive integers and r is the remainder when 3^(4x+2) [#permalink] New post   05 Oct 2020, 08:30
If x and y are positive integers and r is the remainder when 34x+234x+2 is divided by 10, what is the value of r?

(1) x = 25

(2) y = 1

Bunuel kindly recheck the question as with given stem you don't need either S1 or S2 to answer the question.There is something wrong with the original question part.
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Re: If x and y are positive integers and r is the remainder when 3^(4x+2) [#permalink] New post   05 Oct 2020, 09:03
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Bunuel wrote:
If x and y are positive integers and r is the remainder when \(3^{4x + 2}+y\) is divided by 10, what is the value of r?

(1) x = 25

(2) y = 1


Fixed the question. It's - If x and y are positive integers and r is the remainder when \(3^{4x + 2}+y\) is divided by 10, what is the value of r?
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Re: If x and y are positive integers and r is the remainder when 3^(4x+2) [#permalink] New post   05 Oct 2020, 09:39
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Bunuel wrote:
If x and y are positive integers and r is the remainder when \(3^{4x + 2}+y\) is divided by 10, what is the value of r?

(1) x = 25

(2) y = 1


cyclicity of 3 ; 3,9,7,1
given \(3^{4x + 2}+y\) is divided by 10 remainder r is left determine its value
#1
x=25
we see that \(3^{4x + 2}+y\) the value of 3^4x+2 would always give unit digit as 9 ; so its value of y which is important to know unit digit of expression ; insufficient
#2
y=1
we see that the unit digit is 0 ; hence r is 0
sufficient
option B
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Re: If x and y are positive integers and r is the remainder when 3^(4x+2) [#permalink] New post   05 Oct 2020, 09:39
Asked: If x and y are positive integers and r is the remainder when \(3^{4x + 2}+y\) is divided by 10, what is the value of r?

(1) x = 25
3^{102} + y mod 10 = (9+y)mod10
NOT SUFFICIENT

(2) y = 1
9*3^{4x} + y mod 10 = (9+y)mod10 = 10mod10 = 0
SUFFICIENT

IMO B
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Re: If x and y are positive integers and r is the remainder when 3^(4x+2) [#permalink] New post   28 Oct 2020, 04:44
Cyclicity of 3: 3, 9, 7, 1

If x and y are positive integers and r is the remainder when \(3^{4x + 2}+y\) is divided by 10, what is the value of r?

(1) x = 25

We don't know the value of y; insufficient.

(2) y = 1

We can determine that 4x + 2 is 2 more than a multiple of 4; thus, 3^{4x+2} has a units digit of 9 and y = 1.

9 + 1 = 10.
10/10 = remainder 0.

Statement 2 is sufficient. Answer is B.
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Re: If x and y are positive integers and r is the remainder when 3^(4x+2) [#permalink] New post   09 Mar 2024, 05:06
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Re: If x and y are positive integers and r is the remainder when 3^(4x+2) [#permalink]
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