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Is A divisible by 3? (1) A+1 is a prime number (2) A-1 is a

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Is A divisible by 3? (1) A+1 is a prime number (2) A-1 is a [#permalink]

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New post 25 Nov 2010, 15:36
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Question Stats:

59% (01:27) correct 41% (00:58) wrong based on 66 sessions

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Is A divisible by 3?

(1) A+1 is a prime number
(2) A-1 is a prime number

[Reveal] Spoiler:
My solution:
(1) A+1 is a prime number
if A=1, A+1 =2 which is prime, but A is not divisble by 3,
whereas if A=6, A+1 =7 which is prime, A is divisible by 3
Hence (1) is Not Sifficient

(2) A-1 is prime
is A= 6, A-1 = 5 which is prime, A is divisible by 3
but if A=8, A-1=7 which is prime, A is not divisible by 3

(1)+(2) the numbers A-1,A,A+1 are consequtive numbers such that A-1 & A+1 are prime numbers.

Such pairs are
3,4,5----A=4, not divisible by 3
11,12,13-----A=12, divisible by 3
17,18,19-----A=18, divisible by 3

Hence Answer is E

Is this solution correct?

Thanks
NAD
[Reveal] Spoiler: OA

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Re: Is A divisible by 3? (1) A+1 is a prime number (2) A-1 is a [#permalink]

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New post 26 Nov 2010, 04:25
nades09 wrote:
Is A divisible by 3?

(1) A+1 is a prime number
(2) A-1 is a prime number

My solution:
(1) A+1 is a prime number
if A=1, A+1 =2 which is prime, but A is not divisble by 3,
whereas if A=6, A+1 =7 which is prime, A is divisible by 3
Hence (1) is Not Sifficient

(2) A-1 is prime
is A= 6, A-1 = 5 which is prime, A is divisible by 3
but if A=8, A-1=7 which is prime, A is not divisible by 3

(1)+(2) the numbers A-1,A,A+1 are consequtive numbers such that A-1 & A+1 are prime numbers.

Such pairs are
3,4,5----A=4, not divisible by 3
11,12,13-----A=12, divisible by 3
17,18,19-----A=18, divisible by 3

Hence Answer is E

Is this solution correct?

Thanks
NAD


Prime numbers proerty:
Exept 2, all the other prime #s are ODD...

qtn: is A=3K, for any integer K.

stmnt 1: A+1 is a prime number

case1-a: A+1 not = 2 but some other prime #
then A+1, prime , is an ODD # ==> A is an EVEN that may be divisible by 3. e.g 12

case1-b: A+1= 2, prime #
then A = 1 , not divisible by 3 but due to case 1a we can not answer the qtn:
hence stmnt 1 NOT SUFF

stmnt 2: A-1 is a prime number

case2-a: A-1 not = 2 but some other prime #
then A-1, prime , is an ODD # ==> A is an EVEN that may be divisible by 3. e.g 12

case2-b: A-1= 2, prime #
then A = 3 , and divisible by 3 but due to case 2-a we can not answer the qtn:
hence stmnt 2 NOT SUFF

1&2 together will eliminate case1-b and case2-b (as both A-1 and A+1 can not be = 2) and retain case1-a and case2-a that say that A is an EVEN but nothing else abt A
hence 1&2 together NOT SUFF.

answer "E"

Regards,
Murali.
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Re: Is A divisible by 3? (1) A+1 is a prime number (2) A-1 is a [#permalink]

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New post 28 Nov 2010, 07:41
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This post received
KUDOS
nades09 wrote:
Is A divisible by 3?

(1) A+1 is a prime number
(2) A-1 is a prime number

My solution:
(1) A+1 is a prime number
if A=1, A+1 =2 which is prime, but A is not divisble by 3,
whereas if A=6, A+1 =7 which is prime, A is divisible by 3
Hence (1) is Not Sifficient

(2) A-1 is prime
is A= 6, A-1 = 5 which is prime, A is divisible by 3
but if A=8, A-1=7 which is prime, A is not divisible by 3

(1)+(2) the numbers A-1,A,A+1 are consequtive numbers such that A-1 & A+1 are prime numbers.

Such pairs are
3,4,5----A=4, not divisible by 3
11,12,13-----A=12, divisible by 3
17,18,19-----A=18, divisible by 3

Hence Answer is E

Is this solution correct?

Thanks
NAD


Possible values of A using S1: 1,2,4,6,10,12..... NOT SUFFICIENT
Possible values of A using S2: 3,4,6,8,12......... NOT SUFFICIENT

Common values in both the lists: 4,6,12...........NOT SUFFICIENT

Answer: E
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Vaibhav

PS: Correct me if I am wrong.

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Re: Is A divisible by 3? (1) A+1 is a prime number (2) A-1 is a [#permalink]

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New post 30 Nov 2010, 23:16
(1) A=1 & A=6 ... insufficient
(2) A=3 & A=14 ... insufficient

(1+2) A+1 & A-1 is a prime number ... A=4 & A=12 ... insufficient

Answer is (e)
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Kudos [?]: 1256 [0], given: 25

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Re: Is A divisible by 3? (1) A+1 is a prime number (2) A-1 is a [#permalink]

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New post 01 Dec 2010, 19:04
NAD[/quote]

Possible values of A using S1: 1,2,4,6,10,12..... NOT SUFFICIENT
Possible values of A using S2: 3,4,6,8,12......... NOT SUFFICIENT

Common values in both the lists: 4,6,12...........NOT SUFFICIENT

Answer: E[/quote]

Nice simple solution.....

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Is A divisible by 3? (1) A+1 is a prime number (2) A-1 is a [#permalink]

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New post 27 Nov 2017, 13:24
Answer E

Statement 1and 2 are clearly insuff on their own.

A-1, A, A+1 are consecutive integers, given than A-1, A+1 are primes -> A-1 odd, A+1 odd, so A must be even.

if A-1 is prime number other than 3, then A is divisible by 3 for sure.(since one of three consecutive integers will be divisible by 3, and A-1 and A+1 are prime numbers not divisible by prime number 3, so A must be divisible by 3).
if A-1 =3, then A is NOT divisible by 3.

Not Sufficient -> Answer (E)

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Is A divisible by 3? (1) A+1 is a prime number (2) A-1 is a   [#permalink] 27 Nov 2017, 13:24
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