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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.

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

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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 ..