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Intern  B
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Is x is an integer, what is the remainder when x is divided by 5?  [#permalink]

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1
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Difficulty:   95% (hard)

Question Stats: 50% (02:15) correct 50% (02:28) wrong based on 132 sessions

### HideShow timer Statistics Is x is an integer, what is the remainder when x is divided by 5?

(1) x^2 has a remainder of 4 when divided by 5
(2) x^3 has a remainder of 2 when divided by 5

The official answer is B but i think it is C.

Originally posted by ravidparikh92 on 02 Oct 2016, 01:09.
Last edited by Bunuel on 02 Oct 2016, 01:14, edited 1 time in total.
Renamed the topic and edited the question.
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Re: Is x is an integer, what is the remainder when x is divided by 5?  [#permalink]

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ravidparikh92 wrote:
Is x is an integer, what is the remainder when x is divided by 5?

(1) x^2 has a remainder of 4 when divided by 5
(2) x^3 has a remainder of 2 when divided by 5

The official answer is B but i think it is C.

Statement 2 : $$x^3$$ has a remainder of 2 when divided by 5.

Now, the above equation will be satisfied when x = 3 , 8 , 13 and so on. Try putting the values, you will get to know.
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Re: Is x is an integer, what is the remainder when x is divided by 5?  [#permalink]

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8^3 is 512 which also gives a remainder of 2 when divided by 5. Thus statement 2 as 2 options as answers (3 and 8)
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Re: Is x is an integer, what is the remainder when x is divided by 5?  [#permalink]

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ravidparikh92
I think you are forgetting the question: x/5 = r?
 x^3 / 5 = r(2) => x = cuberoot(5*k + 2)
(i) k = 5 => x = cuberoot(27) => x = 3 & 3/5 = r(3) &
(ii) k =102 => x = cuberoot(512) => x = 8 & 8/5 = r(3).
Thus in both cases remainder is 3. Hence B sufficient.

Hope this helps.
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Is x is an integer, what is the remainder when x is divided by 5?  [#permalink]

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ravidparikh92 wrote:
Is x is an integer, what is the remainder when x is divided by 5?

(1) x^2 has a remainder of 4 when divided by 5
(2) x^3 has a remainder of 2 when divided by 5

The official answer is B but i think it is C.

FROM STATEMENT - I ( NOT POSSIBLE )

If $$x = 3$$ , $$x^2 = 9$$

$$\frac{x^2}{5}$$= remainder 4 ; thus $$\frac{x}{5}$$ will have remainder 3

If $$x = 7$$ , $$x^2 = 49$$

$$\frac{x^2}{5}$$= remainder 4 ; thus $$\frac{x}{5}$$ will have remainder 2

Thus no unique value can be obtained from statement I about the value of x

FROM STATEMENT - II (POSSIBLE)

If $$x = 3$$ $$\frac{x^3}{5}$$ will have remainder 2

And $$\frac{x}{5}$$ will have remainder as 3

If $$x = 8$$ $$\frac{x^3}{5}$$ will have remainder 2

And $$\frac{x}{5}$$ will have remainder as 3

We get a unique solution for statement II , each time remainder will be 3

Hence, Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked, answer will be (B)

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Re: Is x is an integer, what is the remainder when x is divided by 5?  [#permalink]

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_________________ Re: Is x is an integer, what is the remainder when x is divided by 5?   [#permalink] 27 Feb 2018, 11:13
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