If a, b, and c are each positive integers greater than 1 is the produc

Question

If a, b, and c are each positive integers greater than 1 is the product abc divisible by 6?

(1) The product ab is even
(2) The product bc is divisible by 3

Bunuel · Accepted Answer

If a, b, and c are each positive integers greater than 1 is the product abc divisible by 6?

(1) The product ab is even. No info about c. Not sufficient.

(2) The product bc is divisible by 3. No info about a. Not sufficient.

(1)+(2) abc is divisible by 2 from (1) and by 3 from (2), hence it's divisible by 2*3=6. Sufficient.

Answer: C.

AbhiJ · Answer

Stmt 1 : The product ab is even, so either a or b must be a multiple of 2. However we can have a , b , c such that none of them is a multiple of 3. For eg 4, 8, 16.
Else we can have one of them a multiple of 3 : 4, 6, 16
The answer can be both Yes & No

Not sufficient.

Stmt 2 : The product bc is divisible by 3, so either c or b must be a multiple of 3. However we can have a , b , c such that none of them is a multiple of 2. For eg 3, 9, 27
Else we can have one of them a multiple of 2 : 3, 6, 18

The answer can be both Yes & No
Not sufficient.

Combining 1 & 2 either a or b must be a multiple of 2 and either b or c is a multiple of 3. So in a , b, c we must have a multiple of 2 and one multiple of 3. Hence sufficient.

ueh55406 · Answer

1>  a*b  = an even integer
 abc =even integer*(c)= an even integer. but are all even integers divisible by 6? nope. Not suff.

2>The product bc is divisible by 3.

bc is a multiple of 3 (let's denote bc=3q, q=1,2,3,4..)

thus,  abc= 3q*a  = any multiple of 3.

but are all multiples of 3 divisible by 6? nope.eg  3*1=3  which is not divisible by 6. but  3*2=6 , which is divisible by 6. Not suff.

1+2 together. and Bunuel has already given the theory about what we can infer if a product is divisible by 2 and 3 then it MUST be divisible by 6 as well. Sufficient.

Dongfeng · Answer

for (1) : ab is even --> not sufficient
(2) --> also not sufficient

consider both (1) and (2)
ab is divisible by 2 so ab = 2 * ...
bc is divisible by 3 so bc = 3 * ...
this means that abc should be 6 * ... as it should have a component of 2 and 3

If a, b, and c are each positive integers greater than 1 is the produc

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GMAT Data Sufficiency (DS) Questions

If a, b, and c are each positive integers greater than 1 is the produc

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