Vamshi8411
Is A multiple of 6?
(1) A = B(B+4)(B-4)
(2) B-4 is a multiple of 3.
For A to be a multiple of 6, A must be divisible by both 2 and 3.
I believe the concept of having the product as it is in statement 1 is the following:
If B is an integer, the 3 factors would be three terms separated by a common difference of +4.
Accordingly , since we have three evenly spaced integers, there will always be exactly ONE multiple of 3 no matter the integer value of B.
(The ONE EXCEPTION being if the common difference is +3 and each integer is NOT a multiple of 3)
So if we know that B is an integer, the question becomes
“is A even?”
Statement 1: is A a multiple of 6?
Even if we knew whether or not B were an integer (and we don’t have any information either way):
Case 1:
If B = ODD ——- we would have a product of three odd integers (one of them a multiple of 3).
In such a case, A would not be divisible by 2 , even thought it would be divisible by 3.
Not a multiple of 6.
Case 2: if B = EVEN —— then we would have three even factors, one of which must be a multiple of 3.
Yes: is a multiple of 6.
S1 not sufficient.
S2: no information is given regarding A.
S1 & S2 Together:
S2: (B - 4) = 3q ——- where q = any integer
Thus, we know that B must be an integer.
However, we already know from statement 1 that if B is an integer, the product of 3 evenly spaced integers will always include exactly one multiple of 3.
We still don’t know whether A is EVEN.
Case 1 and case 2 still hold.
*E*
Posted from my mobile device