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

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Math Expert
Joined: 02 Sep 2009
Posts: 51185
When the positive integer x is divided by 6, the remainder is 4. Each  [#permalink]

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13 Aug 2018, 03:53
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35% (medium)

Question Stats:

64% (01:27) correct 36% (01:28) wrong based on 102 sessions

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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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13 Aug 2018, 04:05
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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 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.
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Re: When the positive integer x is divided by 6, the remainder is 4. Each  [#permalink]

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13 Aug 2018, 10:05
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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) $$\frac{x}{17}$$

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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Joined: 07 Dec 2014
Posts: 1128
Re: When the positive integer x is divided by 6, the remainder is 4. Each  [#permalink]

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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
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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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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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.

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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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