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Is the product of a, b and c divisible by 3?

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Is the product of a, b and c divisible by 3? [#permalink]

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New post 02 Dec 2017, 04:28
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Is the product of a, b and c divisible by 3?

(1) a + b + c is divisible by 3.
(2) a - b = b - c
[Reveal] Spoiler: OA

_________________

Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

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Re: Is the product of a, b and c divisible by 3? [#permalink]

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New post 02 Dec 2017, 05:27
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I feel it's either one. Option 2 is AP. eg: 5,6,7. Or 11,13,15. If you take any 3 numbers in AP one of them should be a multiple of 3.

Option 1: divisible by 3. Take any set of examples. Even this satisfies

Hence each statement alone



Please correct me if wrong

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Re: Is the product of a, b and c divisible by 3? [#permalink]

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New post 02 Dec 2017, 05:38
VijayRocky wrote:
I feel it's either one. Option 2 is AP. eg: 5,6,7. Or 11,13,15. If you take any 3 numbers in AP one of them should be a multiple of 3.

Option 1: divisible by 3. Take any set of examples. Even this satisfies

Hence each statement alone



Please correct me if wrong

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Can't a,b,c be same ?
In that case, 1+1+1 is divisible by 3 but not its product and 3+3+3 is divisible by 3 and its product too.

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Is the product of a, b and c divisible by 3? [#permalink]

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New post 02 Dec 2017, 06:03
chetan2u wrote:
Is the product of a, b and c divisible by 3?

(1) a + b + c is divisible by 3.
(2) a - b = b - c


Hi chetan2u

I think for clarity, the question must mention that a, b, c are integers and/or different, otherwise it becomes very easy to eliminate both the options.

Statement 1: if we assume a=b=c=2, then a+b+c=6, divisible by 3 but a*b*c=8 not divisible by 3, but if a=b=c=3, then abc will be divisible by 3

again if a=1.1 b=2 and c=2.9, then a+b+c=6, divisible by 3 but a*b*c clearly not divisible by 3

and if a=2, b=5 & c=8, then a+b+c=15, divisible by 3 but a*b*c=80, not divisible by 3

Hence Insufficient

statement 2:implies that a, b & c is an AP series, so if a=2, b=5 & c=8, then abc=80 not divisible by 3

but if a=2, b=4 & c=6, then abc=48, divisible by 3. Insufficient

Combining 1 & 2, again if we have a=b=c=3 or a=2, b=4 & c=6, then abc is divisible by 3

but if a=2, b=5 & c=8, then abc is not divisible by 3.

Insufficient

Option E

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Is the product of a, b and c divisible by 3? [#permalink]

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New post 02 Dec 2017, 06:49
niks18 wrote:
chetan2u wrote:
Is the product of a, b and c divisible by 3?

(1) a + b + c is divisible by 3.
(2) a - b = b - c


Hi chetan2u

I think for clarity, the question must mention that a, b, c are integers and/or different

Statement 1: if we assume a=b=c=2, then a+b+c=6, divisible by 3 but a*b*c=8 not divisible by 3, but if a=b=c=3, then abc will be divisible by 3

again if a=1.1 b=2 and c=2.9, then a+b+c=6, divisible by 3 but a*b*c clearly not divisible by 3

and if a=2, b=5 & c=8, then a+b+c=15, divisible by 3 but a*b*c=80, not divisible by 3

Hence Insufficient

statement 2:implies that a, b & c is an AP series, so if a=2, b=5 & c=8, then abc=80 not divisible by 3

but if a=2, b=4 & c=6, then abc=48, divisible by 3. Insufficient

Combining 1 & 2, again if we have a=b=c=3 or a=2, b=4 & c=6, then abc is divisible by 3

but if a=2, b=5 & c=8, then abc is not divisible by 3.

Insufficient

Option E


I agree with niks18. 2) a+c=2b is valid for three consecutive numbers 1,2,3.....3,4,5 as well as APs such as 4,7,10... 5,8,11 etc.

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Re: Is the product of a, b and c divisible by 3? [#permalink]

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New post 02 Dec 2017, 07:10
alokgupta1009 wrote:
VijayRocky wrote:
I feel it's either one. Option 2 is AP. eg: 5,6,7. Or 11,13,15. If you take any 3 numbers in AP one of them should be a multiple of 3.

Option 1: divisible by 3. Take any set of examples. Even this satisfies

Hence each statement alone



Please correct me if wrong

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Can't a,b,c be same ?
In that case, 1+1+1 is divisible by 3 but not its product and 3+3+3 is divisible by 3 and its product too.

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As some others have mentioned here, I guess the question also has a point that a,b and c are distinct numbers

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Re: Is the product of a, b and c divisible by 3? [#permalink]

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New post 02 Dec 2017, 09:10
niks18 wrote:
chetan2u wrote:
Is the product of a, b and c divisible by 3?

(1) a + b + c is divisible by 3.
(2) a - b = b - c


Hi chetan2u

I think for clarity, the question must mention that a, b, c are integers and/or different, otherwise it becomes very easy to eliminate both the options.

Statement 1: if we assume a=b=c=2, then a+b+c=6, divisible by 3 but a*b*c=8 not divisible by 3, but if a=b=c=3, then abc will be divisible by 3

again if a=1.1 b=2 and c=2.9, then a+b+c=6, divisible by 3 but a*b*c clearly not divisible by 3

and if a=2, b=5 & c=8, then a+b+c=15, divisible by 3 but a*b*c=80, not divisible by 3

Hence Insufficient

statement 2:implies that a, b & c is an AP series, so if a=2, b=5 & c=8, then abc=80 not divisible by 3

but if a=2, b=4 & c=6, then abc=48, divisible by 3. Insufficient

Combining 1 & 2, again if we have a=b=c=3 or a=2, b=4 & c=6, then abc is divisible by 3

but if a=2, b=5 & c=8, then abc is not divisible by 3.

Insufficient

Option E


Hi..
The Question is 600-700 level, so it doesn't have too deep a secret involved in it.
Very many will go wrong by not differentiating between integers and non integers and few answers on top do point towards that and ofcourse the OA is accordingly written.
_________________

Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

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Re: Is the product of a, b and c divisible by 3? [#permalink]

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New post 02 Dec 2017, 10:26
I am considering a , b and c as integers .
is product of abc divisible by 3 ..for this to happen among a,b and c at least one should be 3 or should have a factor 3 .

Now check

statement 1 : a+b+c is divisible by 3 ... a=1 b=1 c=1 a+b+c =3 is divisible by 3 but abc=1 not divisible by 3

or a=4 b =16 c=10 abc not divisible by 3

so statement 1 is insufficient .

Statement 2 : 2b =a+c
i.e terms are in AP ..lets consider terms are a-d , a and a+d ...Sum is 3a which is always divisible by 3 i.e statement 1 always hold correct for sum of 3 terms which are in AP.
now check if a(a-d)(a+d) are divisible by 3 or not
i.e a=10 d=3 abc=10* 7*13 ...means insufficient ..

we already proved statement 2 auto validates statement 1 so both statements together also are not sufficient ..


Hence , answer is E .

Please respond if you feel otherwise

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Re: Is the product of a, b and c divisible by 3? [#permalink]

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New post 02 Dec 2017, 11:00
chetan2u wrote:
Is the product of a, b and c divisible by 3?

(1) a + b + c is divisible by 3.
(2) a - b = b - c

Hi @Chetan2u,

I think both the options will be insufficient when a,b,c is a non-integer.

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Re: Is the product of a, b and c divisible by 3?   [#permalink] 02 Dec 2017, 11:00
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