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When the positive integer x is divided by 6, the remainder is 4. Each

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When the positive integer x is divided by 6, the remainder is 4. Each  [#permalink]

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When the positive integer x is divided by 6, the remainder is 4. Each of the following could also be an integer EXCEPT


(A) \(\frac{x}{2}\)

(B) \(\frac{x}{3}\)

(C) \(\frac{x}{7}\)

(D) \(\frac{x}{11}\)

(E) \(\frac{x}{17}\)

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Re: When the positive integer x is divided by 6, the remainder is 4. Each  [#permalink]

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New post 13 Aug 2018, 04:05
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Bunuel wrote:
When the positive integer x is divided by 6, the remainder is 4. Each of the following could also be an integer EXCEPT


(A) \(\frac{x}{2}\)

(B) \(\frac{x}{3}\)

(C) \(\frac{x}{7}\)

(D) \(\frac{x}{11}\)

(E) \(\frac{x}{17}\)


x/6 leaves a remainder of 4 i.e. the number could be 4, 10, 16, 22, 28, 34, 40....
Let us check the options.
A) x/2 = Integer, if x=4,10,16...--Eliminate
B) x/3 = Not integer, HOLD
C) x/7 = Integer, if x=28 --Eliminate
D) x/11 = Integer, if x=22 --Eliminate
E) x/17 = Integer, if x=34 --Eliminate.
Answer B.
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Re: When the positive integer x is divided by 6, the remainder is 4. Each  [#permalink]

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New post 13 Aug 2018, 10:05
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Bunuel wrote:
When the positive integer x is divided by 6, the remainder is 4. Each of the following could also be an integer EXCEPT


(A) \(\frac{x}{2}\)

(B) \(\frac{x}{3}\)

(C) \(\frac{x}{7}\)

(D) \(\frac{x}{11}\)

(E) \(\frac{x}{17}\)



Note : If any number is not divisible by 3 it's not divisible by 6.

X is not divisible by 6. So, x is not divisible by 3.

The best answer is B.
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Re: When the positive integer x is divided by 6, the remainder is 4. Each  [#permalink]

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New post 13 Aug 2018, 12:03
1
Bunuel wrote:
When the positive integer x is divided by 6, the remainder is 4. Each of the following could also be an integer EXCEPT


(A) \(\frac{x}{2}\)

(B) \(\frac{x}{3}\)

(C) \(\frac{x}{7}\)

(D) \(\frac{x}{11}\)

(E) \(\frac{x}{17}\)


x/6=q+4→
x=6q+4→
x/3=2q+4/3
if q is integer, 2q+4/3 cannot be
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Re: When the positive integer x is divided by 6, the remainder is 4. Each  [#permalink]

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New post 14 Aug 2018, 06:39
Bunuel wrote:
When the positive integer x is divided by 6, the remainder is 4. Each of the following could also be an integer EXCEPT


(A) \(\frac{x}{2}\)

(B) \(\frac{x}{3}\)

(C) \(\frac{x}{7}\)

(D) \(\frac{x}{11}\)

(E) \(\frac{x}{17}\)


Possibles values of x are { 4 , 10 , 16 , 22, 28, 34......................}

(A) Possible as all the numbers are divisible by 2
(B) Not possible as none of the number is divisible by 3
(C) Possible, 28 is divisible by 7
(D) Possible , 22 is divisible by 11
(E) Possible, 34 is divisible by 7

Thus, Answer must be (B)
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Re: When the positive integer x is divided by 6, the remainder is 4. Each  [#permalink]

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New post 18 Aug 2018, 18:19
Bunuel wrote:
When the positive integer x is divided by 6, the remainder is 4. Each of the following could also be an integer EXCEPT


(A) \(\frac{x}{2}\)

(B) \(\frac{x}{3}\)

(C) \(\frac{x}{7}\)

(D) \(\frac{x}{11}\)

(E) \(\frac{x}{17}\)


Since when x is divided by 6, the remainder is 4, x can be the following:

4, 10, 16, 22, 28, 34, ...

So we see that x will never be a multiple of 3.

Answer: B
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Re: When the positive integer x is divided by 6, the remainder is 4. Each &nbs [#permalink] 18 Aug 2018, 18:19
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When the positive integer x is divided by 6, the remainder is 4. Each

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