guerrero wrote:What is the remainder when (47)(49) is divided by 8?
(A)1
(B)3
(C)4
(D)5
(E)7
is there a rule or property to tackle such questions ?
OA E
We can also use some modular arithmetic here, but that's a little outside the GMAT domain.
The rule goes something like this.
If M divided by D leaves remainder p, and N divided by D leaves remainder q, then the remainder when MN is divided by D = the remainder when pq is divided by D.
We know that 47 divided by 8 leaves remainder
7.
Also 49 divided by 8 leaves remainder
1.
So, (47)(49) divided by 8 leaves remainder
(7)(1) =
7
NOTE: If the product of the remainders had been greater than 8, we'd have to find the remainder when that product is divided by 8.
For example, 11 divided by 8 leaves remainder
3.
Also 15 divided by 8 leaves remainder
7.
So, the remainder when (11)(15) is divided by 8 is equal to the remainder when
(3)(7) is divided by 8. Since the remainder is 5 when 21 is divided by 8, the remainder will be 5 when (11)(15) is divided by 8
Cheers,
Brebt
