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# When positive integer x is divided by 6, the remainder is 1. Which of

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When positive integer x is divided by 6, the remainder is 1. Which of  [#permalink]

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14 Feb 2016, 03:25
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When positive integer x is divided by 6, the remainder is 1. Which of the following must be true?

I. x is a prime number
II. x is odd
III. x is divisible by 7

A. I only
B. II only
C. III only
D. I and II only
E. II and III only

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Re: When positive integer x is divided by 6, the remainder is 1. Which of  [#permalink]

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15 Feb 2016, 16:15
Bunuel wrote:
When positive integer x is divided by 6, the remainder is 1. Which of the following must be true?

I. x is a prime number
II. x is odd
III. x is divisible by 7

A. I only
B. II only
C. III only
D. I and II only
E. II and III only

X=6q+1

Examine II) put q=0,1,2,3....... we have x=1,7,13,...25 so x must be odd

Examine III) 14/6 has reminder 2 & 49/7 has reminder 1 so not always true

Examine I) X= 7 true but while 2 is prime, it does not give reminder 1

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When positive integer x is divided by 6, the remainder is 1. Which of  [#permalink]

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15 Feb 2016, 19:19
I would also go with B.
X=6q+1

i)
if x=7,then remainder is 1.
if x=11,then remainder is 5
So,X can or cannot be prime.

ii)
X=6q(even)+1
i.e. x will always be odd .
You can plug in values.

iii)
X-1=6q
for 7,it is true that it will be divisible by 7
for 13,it X-1 will be a multiple of 6 but is not divisible by 7.

Ans:-B

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Re: When positive integer x is divided by 6, the remainder is 1. Which of  [#permalink]

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17 Feb 2016, 22:31
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Hi All,

When dealing with these types of questions, you MUST restrict your 'examples' to ones that fit the description given in the prompt. Here, we're told that X is a positive integer and that when X is divided by 6, the remainder is 1. We're asked which of the following MUST be true.

Using the information in the prompt, we can list out the first several numbers that fit the given description:

1, 7, 13, 19, 25

X CANNOT be any other value between 1 and 25 (for example, it can't be 2 or 11 because neither of those values fit what we were told about X). From here, we can quickly eliminate Roman Numerals:

I. X is a prime number.

Sometimes X is prime, sometimes X is NOT prime.
This is NOT always true.

II. X is odd

This certainly appears true.

III. X is divisible by 7

Sometimes X is divisible by 7, sometimes X is NOT divisible by 7.

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Re: When positive integer x is divided by 6, the remainder is 1. Which of  [#permalink]

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18 Feb 2016, 08:22
Positive integer x is divided by 6, the remainder is 1.

So, the number "X" will be of the form (6y+1).

Now,

I. x is a prime number:

True for No such as 7 (6x1+1), 13 (6x2+1),19 (6x3+1)

False for No such as 25 (6x4+1), as 25 is not a prime number (divisible by 5,1,25)

II. x is odd

True, as all the number of the form (6y+1) will be odd.

III. x is divisible by 7

True for No such as 7 (6x1+1)

False for No such as 13 (6x2+1),19 (6x3+1), 25 (6x4+1)

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Re: When positive integer x is divided by 6, the remainder is 1. Which of  [#permalink]

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08 Jul 2018, 12:12
Bunuel wrote:
When positive integer x is divided by 6, the remainder is 1. Which of the following must be true?

I. x is a prime number
II. x is odd
III. x is divisible by 7

A. I only
B. II only
C. III only
D. I and II only
E. II and III only

I. If x = 25 and it is divided by 6, the remainder is 1, however, x is not a Prime number.
II. x = 6q + 1 ; 6q will always be an Even number and when 1 is added to it it will always result in an ODD number.
III. Similarly If x = 13 and it is divided by 6, the remainder is 1, however, x is not divisible by 7.

Thus, Answer must be (B) II.
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Re: When positive integer x is divided by 6, the remainder is 1. Which of   [#permalink] 08 Jul 2018, 12:12
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