Hi M7MBA.
Let's take a look at your question.
Is a*b*c divisible by 32?
First statement
(1) a, b and c are consecutive even integers.
We can have different cases:
- a=2, b=4 and c=6.
Then a*b*c=48 which is not divisible by 32.
NO
- a=4, b=6 and c=8.
Then a*b*c=192 which is divisible by 32.
YES
Since we got two different answers, then this statement is
not sufficient.
Second statement
(2) a*c < 0
This statement just tells us that "a" and "c" have different signs. We can have the following cases:
- a=-2, b=1, c=4
Then a*b*c=-8 which is not divisible by 32.
NO
- a=4, b=-1, c=-8
Then a*b*c=32 which is divisible by 32.
YES
Again, since we got two different answers, then this statement is
not sufficient.
Both statements together
(1) a, b and c are consecutive even integers.
(2) a*c < 0
Now, we know that "a, b" and "c" are consecutive even integers and we also know that "a" and "c" have different signs. The unique case that holds these two condition s when b=0:
a=-2, b=0, c=2 or c=-2, b=0, a=2
In any case, we obtain a*b*c=0, and 0 is divisible by any number different from zero.
Therefore, in this case, a*b*c is divisible by 32 and it is the unique answer.
YES
In conclusion, using both statements is
sufficient.
The OA is the option
C.
Regards.
