Product and Remainder

abhirup1711 wrote:For the positive integers q,r s and t, the remainder when q is divided by r is 7 and when s is divided by t, the remainder is 3. All of the following are possible values for the product rt EXCEPT
32
38
44
53
63

Is there supposed to be more that 1 correct answer?

The solution relies on an important property that says . . .
When N is divided by D, 0 < remainder < D
In other words, the remainder can never be greater than the divisor (the number we are dividing by).
For example, if N is divided by 7, then 0 < remainder < 7 (the remainder cannot be greater than 6)

the remainder when q is divided by r is 7
By the above rule, we can conclude that r must be greater than 7

when s is divided by t, the remainder is 3
By the above rule, we can conclude that t must be greater than 3

So, if r must be greater than 7, and t must be greater than 3, which of the following are possible values for the product rt?

A) 32
This works when r = 8 and t = 4
ELIMINATE A

B) 38
If r must be greater than 7, and t must be greater than 3, then rt cannot equal 38
Note: there are only 2 ways to get a product of 38: (1)(38) or (2)(19)
So, the answer could be B

C) 44
This works when r = 11 and t = 4
ELIMINATE C

D) 53
If r must be greater than 7, and t must be greater than 3, then rt cannot equal 53
Note: there is only 1 way to get a product of 53: (1)(53)
So, the answer could be D

E) 63
This works when r = 9 and t = 7
ELIMINATE E

So the correct answers are B and D
Cheers,
Brent

abhirup1711 wrote:Sorry Brent, the option is 52 and not 53

Ahhh.

So, we get:
D) 52
This works when r = 13 and t = 4
ELIMINATE D

Answer = B

Cheers,
Brent