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What is the remainder when 3^50 is divided by 4?  [#permalink]

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Difficulty:   5% (low)

Question Stats: 79% (00:56) correct 21% (01:05) wrong based on 106 sessions

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What is the remainder when $$3^5^0$$ is divided by 4?

A. 0 B. 1 C. 2 D. 3 E. -1

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What is the remainder when 3^50 is divided by 4?  [#permalink]

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Rewrite $$3^{50}$$ as $$(3^{2})^{25} = 9^{25}$$.

$$9^{25} = (8+1)^{25}$$. Now $$8^{25}$$ will always be divisible by 4 and leaves remainder 0. $$1^{25}$$ = 1 and leaves remainder 1.

Originally posted by koenh on 06 Dec 2016, 02:26.
Last edited by koenh on 06 Dec 2016, 08:45, edited 2 times in total.
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Re: What is the remainder when 3^50 is divided by 4?  [#permalink]

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MathRevolution wrote:
What is the remainder when $$3^5^0$$ is divided by 4?

A. 0 B. 1 C. 2 D. 3 E. -1

$$3^{50} = 9^{25}$$

$$\frac{9}{4}$$ = Remainder 1

So, $$9^{25}$$ , will have remainer as 1

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Math Revolution GMAT Instructor V
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Re: What is the remainder when 3^50 is divided by 4?  [#permalink]

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==> The units digit of $$3^n$$ is the repetition of $$3-->9-->7--->1-->3-->9-->7-->1$$, so you get $$50=4*12+2$$.
Thus, from $$3^5^0=3^4^*^1^2^+^2$$ --> $$~3^2=~9$$, the units digit becomes 9, and if you divide it by 4, from $$9=4*2+1$$, the remainder becomes 1.
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Re: What is the remainder when 3^50 is divided by 4?  [#permalink]

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hat is the remainder when 3^50 is divided by 4?

A. 0 B. 1 C. 2 D. 3 E. -1

unit digit of powers of 3 follows a pattern of 4 (3,9,7,1)
So we divide 50/4=2 remainder which means power of 2 will be there
3 power 2= 9

Option B (1)
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Re: What is the remainder when 3^50 is divided by 4?  [#permalink]

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MathRevolution wrote:
What is the remainder when $$3^5^0$$ is divided by 4?

A. 0 B. 1 C. 2 D. 3 E. -1

Since 3 = 4 - 1, we can think 3 as “-1” when it’s divided by 4. Therefore, the remainder when 3^50 is divided by 4 is same as the remainder when (-1)^50 is divided by 4. So the remainder is (-1)^50 = 1.

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GMAT 1: 600 Q46 V27 Re: What is the remainder when 3^50 is divided by 4?  [#permalink]

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MathRevolution wrote:
What is the remainder when $$3^5^0$$ is divided by 4?

A. 0 B. 1 C. 2 D. 3 E. -1

You should use negative remainders. (If you're comfortable)

3/4 gives remainder of -1.

$$(-1)^50$$ is 1 since it is raised to an even power.

Hence B
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You are missing on great learning if you don't know what this is: Project SC Butler Re: What is the remainder when 3^50 is divided by 4?   [#permalink] 01 Dec 2019, 10:39
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