Question

The integers x and y are both positive and xy 84. The remainder when xy is divided by 84 is 36. Quantity a quantity b the remainder when y is divided by 12 4

Answer 1

Answer:

D

Step-by-step explanation:

The integers x and y are both positive, the remainder when x is divided by 12 is 7, and the remainder when y is divided by 12 is 3. Each of the following is a possible value of 2x+y EXCEPT 

A. 125 

B. 101 

C. 77 

D. 51 

E. 41

I got this right but it took me 2 minutes.

I wonder if there is a quick way to solve this question without plugging numbers to X and Y.

I wrote down like 6 numbers with remainder of 7 and 3 and found each of the numbers from the answer choices manually.

I also tried the other approach X=12Q+7, Y=12R+3 and calculated 2X+Y but couldn't understand what to do next.

thanks

The remainder when x is divided by 12 is 7:  --> .

The remainder when y is divided by 12 is 3: .

. Only D is not a multiple of 12 plus 5.