different positive integers a,b,c are divisible by 7

[outreach]

How many of the three different positive integers a,b,c are divisible by 7
1. product of a,b,c is divisible by 3 but only c is divisible by 21
2. each of the positive integers is divisible by 3 but only c is divisible by 21


OAB

[kstv]

1. product of a b c is divisible by 3 and c is divisible by 21 so c can be expressed as 21x where x is any integer.
a*b*c = ab(7*3 x ) this is divisible by 3 without any restriction to the values a and b can take. Insuff.

2. a= 3y b = 3z c = 21z x, y and z are any integers
here a and b can be any multiple of 3 except 7 as only c is divisible by 21
i.e y can be 1 2 3 4 5 6 _ 8 9 (8 values) and z (7 values as it cannot be same as y)

Is that Suff ?

My answer was E but OA is B

[Fiver]

Choose B.

St1] product of a,b,c is divisible by 3 but only c is divisible by 21
E.g a=1 , b=3,c=21 :Only c is divisible by 7.
a=7, b=7, c=21 : All are divisible by 7.
a=1, b=7, c=21 : b& c are divisible by 7.

St2] each of the positive integers is divisible by 3 but only c is divisible by 21
Since 21 = 7*3, any integer multiple of 3 & 7 must be divisible by 21 also.
Hence according to st2] a & b have 3 as a factor but not 7.
So only c is divisible by 7.