When a certain integer x is divided by 5 the remainder is 2

Question

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

Bunuel · Answer

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.

Answer: C.

Hope it's clear.

malkov · Answer

Thanks, that makes sense!

CleanSlate · Answer

please help me to understand.. how its divisible by other option :?:

Bunuel · Answer

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.

BrentGMATPrepNow · Answer

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

RELATED VIDEO
 https://www.youtube.com/watch?v=XCxgIR042tE

gracie · Answer

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
C

fskilnik · Answer

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

?\,\,\,:\,\,\,{	ext{not}}\,\,\,{	ext{integer}}

\left( {	ext{A}} ight)\,\,M = 3\,\,{	ext{refutes}}

\left( {	ext{B}} ight)\,\,M = 4\,\,{	ext{refutes}}

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

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

Regards, 
Fabio.

ScottTargetTestPrep · Answer

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.

Answer: C

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When a certain integer x is divided by 5 the remainder is 2

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When a certain integer x is divided by 5 the remainder is 2

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