What is the remainder when

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

One approach is to rewrite 47 and 49.

We get: (47)(49) = (48 - 1)(48 + 1)
= 48^2 - 1

Notice that 48^2 divided by 8 leaves remainder 0 (since 48 is a multiple of 8)
So, 48^2 - 1 divided by 8 leaves remainder 7

Cheers,
Brent

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