vaivish wrote:There are six cards numbered from 1 to 6 in a box. With replacement, a card is taken out from the box three times. If the sum of the three cards is 12, is the card numbered 5 taken out at least for once?
(1) All the cards taken out cannot be divisible by 3.
(2) Two of the cards had been taken out.


Oa is C[spoiler][/spoiler]

1. Cannot be divisible by 3 ---> excludes 3 & 6, leaving 1, 2, 4, 5

With given information, it can be (4,4,4) or (5,5,2) therefore NOT SUFFICIENT.

2. two cards had been taken out.
Options: (3,3,6) or (5,5,2) therefore NOT SUFFICIENT.

3. Combined. looking at both options, it can't be 4,4,4 because only two identical cards had been taken out and 3,3,6 is divible by 3. Therefore, only option left is 5,5,2 which is SUFFICIENT.

Answer C.

kshin78 wrote:

vaivish wrote:There are six cards numbered from 1 to 6 in a box. With replacement, a card is taken out from the box three times. If the sum of the three cards is 12, is the card numbered 5 taken out at least for once?
(1) All the cards taken out cannot be divisible by 3.
(2) Two of the cards had been taken out.


Oa is C[spoiler][/spoiler]

1. Cannot be divisible by 3 ---> excludes 3 & 6, leaving 1, 2, 4, 5

With given information, it can be (4,4,4) or (5,5,2) therefore NOT SUFFICIENT.

2. two cards had been taken out.
Options: (3,3,6) or (5,5,2) therefore NOT SUFFICIENT.

3. Combined. looking at both options, it can't be 4,4,4 because only two identical cards had been taken out and 3,3,6 is divible by 3. Therefore, only option left is 5,5,2 which is SUFFICIENT.

Answer C.

I have a doubt in your explanation:
why don't we include (4,4,4) in st 2. it just says that two cards had been taken out it doesn't say which two cards had been taken out or whether two identical cards had been taken out.