Question

http://sat.collegeboard.org/SAT/public/image/FPT_Math_Q85_122109.png

In the figure above, point B lies on line AC. If x and y are integers, which of the following is a possible value of x?

Answer 1

A)30
B)35
C)40
D)50
E)55

Answer 2

Okay, there's 3 y angles, and x and y must be integers.

Now, what's the degree for a horizontal line?

Answer 3

It should add up to 180 degrees, right?

Answer 4

Yes, what equation would put x, y and 180 in relationship?

Answer 5

3y+x=180

Answer 6

That's all i have so far

Answer 7

Nice! Now
A)30
B)35
C)40
D)50
E)55

Try to plug them in your equation, to see if y would be an integer

Answer 8

Let me give you an example
E)55
3y+x=180
3y+55 = 180
125 = 3x
x = 125/3
x = 41.6666666

So E) doesn't work.

Answer 9

Well is it not possible for all of those to be true? Since the diagram is not drawn to scale.

Answer 10

How does E not work?

Answer 11

because x and y must be integers

Answer 12

and for some value of x, y cannot be an integer

Answer 13

Oh I see.

Answer 14

Whole numbers.

Answer 15

right :)

Answer 16

It's been a while since I've done this, taking the SAT tomorrow, forgetting those key words. Most of this stuff is more reading than actual math.

So at this point it is just process of elimination, which is easy. I can take it from here, thanks for the help, you're awesome.

Answer 17

You are welcome ;)

Answer 18

zepp's way isn't the only method to do it, and IMO is the least productive. Good you know how to do it though :)

Answer 19

@Retract, I know there another method, like looking for a whole number that's divisible by 3, and that could represent 3y as a whole, then to find x, simply substract this number from 180.
but imo, there's quite a lot of possibilities it would be better to go with the trial and error method in this case. :)

Answer 20

lot of possibilities talking about x could be 171 and y is 3, you know.

Answer 21

since the figure isn't drawn to scale.

Answer 22

@zepp I always disagree with trial and error methods. There's a better method to do them almost all of the time.

Answer 23

but in this case, the trial and error method is the best way to go.
Alright, want all the possibilites? let me list them

And if it's not convincing enough, please tell me :)

x = 177 y = 1
x = 174 y = 2
x = 171 y = 3
x = 168 y = 4
x = 165 y =5
x = 162 y = 6
x = 159 y = 7
x = 156 y = 8
x = 153 y = 9
x = 150 y = 10
x = 147 y = 11
x = 144 y = 12
x = 141 y = 13
x = 138 y = 14
x = 135 y = 15
x = 132 y = 16
x = 129 y = 17
x = 126 y = 18
x = 123 y = 19
x = 120 y = 20
x = 117 y = 21
x = 114 y = 22
x = 111 y = 23
x = 108 y = 24
x = 105 y = 25
x = 102 y = 26
x = 99 y = 27
x = 96 y = 28
x = 93 y = 29
x = 90 y = 30
x = 87 y = 31
x = 84 y = 32
x = 81 y = 33
x = 78 y = 34
x = 75 y = 35
x = 72 y = 36
x = 69 y = 37
x = 66 y = 38
x = 63 y = 39
x = 60 y = 40
x = 57 y = 41
x = 54 y = 42
x = 51 y = 43
x = 48 y = 44
x = 45 y = 45

Answer 24

@zepp You pick the most inefficient way to do it to show me that trial and error works best? Okay. This discussion is over.

Answer 25

Fine then, if you say so.

Answer 26

I'm just shocked that you said that my way for this question is the least productive, that's all.

Answer 27

@zepp, you're in 10th grade, I'm studying calculus at a university level. I don't think there's any need for this.

Answer 28

So now you are judging me by the grade I am at?