GWD27-3

Q3:

If x and y
are positive integers and 1 + x + y + xy = 15, what is the
value of x + y?

A.  
3

B.  
5

C.  
6

D.  
8

E.   
9

Answer:

x+y+xy=14

x+y =14-xy

Now, check for the options:

A. x+y=3, then xy = 3, 14-3=11 NOT equal to x+y.

B. x+y=5, then xy=6, 14-6=8 NOT equal to x+y.

C.x+y=6, then xy=8 (4*2), 14-8=6 YES equal to x+y.

D. x+y =8, then xy=8 (4*2), 14-8=6 NOT equal to x+y.

E. x+y =9, then xy =20, 14-20 =-6 NOT eqaul to x+y.

Answer is C.

I don't understand for some parts

A. x+y=3, then xy = 3, 14-3=11 NOT equal to x+y.

how do you get xy =3 when x+y = 3, by equation x+y=14-xy, would xy = 14-3 = 13?

B. x+y=5, then xy=6, 14-6=8 NOT equal to x+y

same here, how to get xy =6, if x+y =5,

C.x+y=6, then xy=8 (4*2), 14-8=6 YES equal to x+y.

D. x+y =8, then xy=8 (4*2), 14-8=6 NOT equal to x+y.

if x+y = 8, why xy =8?

E. x+y =9, then xy =20, 14-20 =-6 NOT eqaul to x+y.

1+x+y+xy=(1+x)(1+y)=15, 所以可以试着推算1+x, 1+y,等于3，5，那么x,y则分别等于2,4, x+y=2+4=6

1 + x + y + xy = 15

=> XY=15-1-X-Y

=> XY<12

=> XY=11 ? 10? 9 ? IMPOSSIBLE

=> 8  POSSIBLE

=> X,Y COULD BE 2,4