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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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Intern
Joined: 18 Feb 2010
Posts: 24
Is A divisible by 3? (1) A+1 is a prime number (2) A-1 is a  [#permalink]

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25 Nov 2010, 15:36
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Difficulty:

45% (medium)

Question Stats:

61% (01:32) correct 39% (01:32) wrong based on 74 sessions

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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

Is this solution correct?

Thanks
Manager
Joined: 30 Aug 2010
Posts: 88
Location: Bangalore, India
Re: Is A divisible by 3? (1) A+1 is a prime number (2) A-1 is a  [#permalink]

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26 Nov 2010, 04:25
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

Is this solution correct?

Thanks

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.

Regards,
Murali.
kudos?
Manager
Status: I rest, I rust.
Joined: 04 Oct 2010
Posts: 102
Schools: ISB - Co 2013
WE 1: IT Professional since 2006
Re: Is A divisible by 3? (1) A+1 is a prime number (2) A-1 is a  [#permalink]

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28 Nov 2010, 07:41
1
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

Is this solution correct?

Thanks

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

_________________

Respect,
Vaibhav

PS: Correct me if I am wrong.

Retired Moderator
Joined: 02 Sep 2010
Posts: 769
Location: London
Re: Is A divisible by 3? (1) A+1 is a prime number (2) A-1 is a  [#permalink]

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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

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Manager
Joined: 04 May 2009
Posts: 53
Location: Astoria, NYC
Re: Is A divisible by 3? (1) A+1 is a prime number (2) A-1 is a  [#permalink]

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01 Dec 2010, 19:04

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

Nice simple solution.....
Senior Manager
Joined: 02 Apr 2014
Posts: 472
GMAT 1: 700 Q50 V34
Is A divisible by 3? (1) A+1 is a prime number (2) A-1 is a  [#permalink]

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27 Nov 2017, 13:24

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.

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