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# Is the integer p divisible by 6 ?

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Math Expert
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Is the integer p divisible by 6 ?  [#permalink]

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29 Oct 2019, 21:48
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35% (medium)

Question Stats:

75% (01:35) correct 25% (01:26) wrong based on 85 sessions

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Is the integer p divisible by 6 ?

(1) p + 3 is divisible by 3

(2) p - 3 is an odd number

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Re: Is the integer p divisible by 6 ?  [#permalink]

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29 Oct 2019, 22:34
1
Is the integer p divisible by 6 ?

So, p should be divisible by 2 and 3 both.

(1) p + 3 is divisible by 3
Since p+3 is divisible by 3, p will also be divisible by 3. But we cannot say anything about divisibility by 2.
9+3....no, but 6+3..yes.

(2) p - 3 is an odd number
we can say that p is even, so divisible by 2. But nothing about divisibility by 3..
6-3..yes, but 8-3..no

Combined..
p is divisible by both 2 and 3
Suff
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Re: Is the integer p divisible by 6 ?  [#permalink]

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30 Oct 2019, 01:21
Is the integer p divisible by 6 ?

for p to be divisible by 6 it must be divisible by 2 and 3

(1) p + 3 is divisible by 3

p+ 3= 3q

p=3(q-1)

therefore p is divisible by 3

we don't know whether p is divisible by 2

A is insufficient

(2) p - 3 is an odd number

therefore p is any even integer

p=10 not divisible by 6
p=6 divisible by 6

no unique answer; B is insufficient

Both A and B together

P is divisible by 3 since P is an even integer divisible by 3

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Re: Is the integer p divisible by 6 ?  [#permalink]

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30 Oct 2019, 02:16
Bunuel wrote:
Is the integer p divisible by 6 ?

(1) p + 3 is divisible by 3

(2) p - 3 is an odd number

#1
p + 3 is divisible by 3
p;3 we get no
and p;6 we get yes
#2
p-3 is oddd
so p has to be even
p;6,12 ; yes
p=4,8; no
from 1 &2
p has to be even and divisible by 3 p+3
possibilities of p= 6, 12,18
IMO C ; sufficient
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Re: Is the integer p divisible by 6 ?  [#permalink]

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12 Nov 2019, 22:20
Bunuel wrote:
Is the integer p divisible by 6 ?

(1) p + 3 is divisible by 3

(2) p - 3 is an odd number

Bunuel It is probably a redundant question for you but I will ask anyway.

Do we consider negative numbers to be odd and even?

For this question, I considered p as 0 and concluded that 0-3=-3 is an odd number. Probably I am just confused. Please clarify.

Thank you!
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Re: Is the integer p divisible by 6 ?  [#permalink]

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13 Nov 2019, 00:09
TheNightKing wrote:
Bunuel wrote:
Is the integer p divisible by 6 ?

(1) p + 3 is divisible by 3

(2) p - 3 is an odd number

Bunuel It is probably a redundant question for you but I will ask anyway.

Do we consider negative numbers to be odd and even?

For this question, I considered p as 0 and concluded that 0-3=-3 is an odd number. Probably I am just confused. Please clarify.

Thank you!

An even number is an integer which is divisible by 2 without a remainder, so ..., -4, -2, 0, 2, 4, 6, ... are all even numbers.
An odd number is an integer which is NOT divisible by 2 without a remainder, so ..., -3, -1, 1, 3, 5, 7, ... are all odd numbers.
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Re: Is the integer p divisible by 6 ?  [#permalink]

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13 Nov 2019, 00:25
Bunuel wrote:
Is the integer p divisible by 6 ?

(1) p + 3 is divisible by 3

(2) p - 3 is an odd number

From 1
P=3(Q-1)
Not sufficient
From 2)
P-3=2n+1
P=2(n+2)
Not sufficient
From 1 and 2
P is multiple of both 2 and 3
P is a multiple of 6
Sufficient
C:)
Re: Is the integer p divisible by 6 ?   [#permalink] 13 Nov 2019, 00:25
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