BTGModeratorVI wrote: ↑

Wed Dec 16, 2020 12:34 pm

For the positive integers q, r, s, and t, the remainder when q is divided by r is 7 and the remainder when s is divided by t is 3. All of the following are possible values for the product rt EXCEPT

A. 32
B. 38
C. 44
D. 52
E. 63

Answer: B
Source: Kaplan

USEFUL PROPERTY:
When positive integer N is divided by positive integer D, the remainder R is such that 0 ≤ R < D
For example, if we divide some positive integer by 7, the remainder will be 6, 5, 4, 3, 2, 1, or 0
Conversely, if I know that, when k is divided by w, the remainder is 5, then I know that w must be greater than 5

The remainder when q is divided by r is 7
This tells us that r is greater than 7

s is divided by t is 3
This tells us that t is greater than 3

Now check the answer choices...

A) 32
Is it POSSIBLE for rt to equal 32?
Yes, if r = 8 and t = 4, then rt = 32
ELIMINATE A

B) 38
Is it POSSIBLE for rt to equal 38?
NO.
There are only two ways to write 38 as the product of POSITIVE INTEGERS:
i) (2)(19) = 38
ii) (1)(38) = 38
If r is greater than 7 and t is greater than 3, there's no way that one of the values (r or t) can equal 1 or 2.

Answer: B