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Intern  Joined: 05 May 2012
Posts: 12
When a certain integer x is divided by 5 the remainder is 2  [#permalink]

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Difficulty:   25% (medium)

Question Stats: 72% (01:26) correct 28% (01:35) wrong based on 217 sessions

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When a certain integer x is divided by 5 the remainder is 2, then each of the following could also be an integer EXCEPT.

A. x/17
B. x/11
C. x/10
D. x/6
E. x/3

Originally posted by malkov on 10 May 2012, 09:08.
Last edited by Bunuel on 20 May 2014, 08:55, edited 1 time in total.
Math Expert V
Joined: 02 Sep 2009
Posts: 58434
Re: When a certain integer [i]x[/i] is divided by 5 the  [#permalink]

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malkov wrote:
When a certain integer x is divided by 5 the remainder is 2, then each of the following could also be an integer EXCEPT.

A. x/17
B. x/11
C. x/10
D. x/6
E. x/3

What do you think?

When x is divided by 5 the remainder is 2 simply means that x is not divisible by 5, so it cannot be divisible by 10 either. Therefore x/10 is not an integer.

Hope it's clear.
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Intern  Joined: 05 May 2012
Posts: 12
Re: When a certain integer x is divided by 5 the remainder is 2  [#permalink]

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Thanks, that makes sense!
Intern  Status: K... M. G...
Joined: 22 Oct 2012
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Re: When a certain integer [i]x[/i] is divided by 5 the  [#permalink]

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Bunuel wrote:
malkov wrote:
When a certain integer x is divided by 5 the remainder is 2, then each of the following could also be an integer EXCEPT.

A. x/17
B. x/11
C. x/10
D. x/6
E. x/3

What do you think?

When x is divided by 5 the remainder is 2 simply means that x is not divisible by 5, so it cannot be divisible by 10 either. Therefore x/10 is not an integer.

Hope it's clear.

please help me to understand.. how its divisible by other option Math Expert V
Joined: 02 Sep 2009
Posts: 58434
Re: When a certain integer [i]x[/i] is divided by 5 the  [#permalink]

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breakit wrote:
Bunuel wrote:
malkov wrote:
When a certain integer x is divided by 5 the remainder is 2, then each of the following could also be an integer EXCEPT.

A. x/17
B. x/11
C. x/10
D. x/6
E. x/3

What do you think?

When x is divided by 5 the remainder is 2 simply means that x is not divisible by 5, so it cannot be divisible by 10 either. Therefore x/10 is not an integer.

Hope it's clear.

please help me to understand.. how its divisible by other option When a certain integer x is divided by 5 the remainder is 2 can be expressed as $$x=5q+2$$. Thus x can be 2, 7, 12, 17, 22, ...

If x=17, then x/17=integer.
If x=22, then x/11=integer.
If x=12, then x/6=integer and x/3=integer.

Hope it's clear.
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Re: When a certain integer x is divided by 5 the remainder is 2  [#permalink]

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Top Contributor
malkov wrote:
When a certain integer x is divided by 5 the remainder is 2, then each of the following could also be an integer EXCEPT.

A. x/17
B. x/11
C. x/10
D. x/6
E. x/3

When it comes to remainders, we have a nice rule that says:
If N divided by D leaves remainder R, then the possible values of N are R, R+D, R+2D, R+3D,. . . etc.
For example, if k divided by 5 leaves a remainder of 1, then the possible values of k are: 1, 1+5, 1+(2)(5), 1+(3)(5), 1+(4)(5), . . . etc.

When a certain integer x is divided by 5, the remainder is 2
So, the possible values of x are as follows: 2, 7, 12, 17, 22, 27, 32, . . . etc
Let's use these values to ELIMINATE answer choices

If x = 12, then x/3 is an integer. ELIMINATE D
If x = 12, then x/6 is an integer. ELIMINATE C
If x = 17, then x/17 is an integer. ELIMINATE A
If x = 22, then x/11 is an integer. ELIMINATE E

By the process of elimination, the correct answer is B

Cheers,
Brent

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Re: When a certain integer x is divided by 5 the remainder is 2  [#permalink]

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malkov wrote:
When a certain integer x is divided by 5 the remainder is 2, then each of the following could also be an integer EXCEPT.

A. x/17
B. x/11
C. x/10
D. x/6
E. x/3

let x=5q+2
because 5q has a units digit of 0 or 5,
5q+2 has a units digit of 2 or 7,
neither divisible by 10
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Re: When a certain integer x is divided by 5 the remainder is 2  [#permalink]

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malkov wrote:
When a certain integer x is divided by 5 the remainder is 2, then each of the following could also be an integer EXCEPT.

A. x/17
B. x/11
C. x/10
D. x/6
E. x/3

$$x = 5M + 2,\,\,\,M\,\,\operatorname{int} \,\,\,\,\,\,\left( * \right)$$

$$?\,\,\,:\,\,\,{\text{not}}\,\,\,{\text{integer}}$$

$$\left( {\text{A}} \right)\,\,M = 3\,\,{\text{refutes}}$$

$$\left( {\text{B}} \right)\,\,M = 4\,\,{\text{refutes}}$$

$$\left( {\text{C}} \right)\,\,\frac{x}{10} = \operatorname{int} \,\,\,\mathop \Rightarrow \limits^{ \cdot \,\,2} \,\,\,\,\frac{x}{5} = \operatorname{int} \,\,\,\, \Rightarrow \,\,\,x\,\,{\text{divisible}}\,\,{\text{by}}\,\,5\,\,\,\mathop \Rightarrow \limits^{\left( * \right)} \,\,\,\,\,{\text{impossible}}$$

We follow the notations and rationale taught in the GMATH method.

Regards,
Fabio.
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Re: When a certain integer x is divided by 5 the remainder is 2  [#permalink]

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malkov wrote:
When a certain integer x is divided by 5 the remainder is 2, then each of the following could also be an integer EXCEPT.

A. x/17
B. x/11
C. x/10
D. x/6
E. x/3

Since, when x is divisible by 5, the remainder is 2, x can be values such as:

2, 7, 12, 17, 22

So we see that x/17, x/6, x/3, and x/11 can all be integers. Thus x/10 cannot be an integer.

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If you find one of my posts helpful, please take a moment to click on the "Kudos" button. Re: When a certain integer x is divided by 5 the remainder is 2   [#permalink] 27 Jan 2019, 19:50
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