On the graph above, when x = 1/2, y = 2; and when x = 1, y =

Question

https://gmatclub.com/forum/download/file.php?id=17933 On the graph above, when x = 1/2, y = 2; and when x = 1, y = 1. The graph is symmetric with respect to the vertical line at x = 2. According to the graph, when x = 3, y = (A) -1 (B) -1/2 (C) 0 (D) 1/2 (E) 1 Graph.png

BrentGMATPrepNow · Accepted Answer

We're told that the graph of the parabola is  symmetric  with respect to the vertical line at x = 2
So, for example, notice that the point  (0,3)  lies on the parabola. 
This point is 2 units to the LEFT of the line of symmetry. 
 https://i.imgur.com/CB1VNMS.png

This means that there's also a point that is 2 units to the RIGHT of the line of symmetry. 
So, the coordinates of that point are  (4,3) 
 https://i.imgur.com/uW4iASq.png

Likewise, we're told that the point  (1,1)  lies on the parabola. 
This point is 1 unit to the LEFT of the line of symmetry. 
 https://i.imgur.com/i8SPXfi.png

This means that there's also a point that is 1 unit to the RIGHT of the line of symmetry. 
So, the coordinates of that point are  (3,1) 
 https://i.imgur.com/iiUgQOZ.png

Answer: E

Cheers,
Brent

Bunuel · Answer

SOLUTION

https://gmatclub.com/forum/download/file.php?id=17933 
 On the graph above, when x = 1/2, y = 2; and when x = 1, y = 1. The graph is symmetric with respect to the vertical line at x = 2. According to the graph, when x = 3, y =

(A) -1
(B) -1/2
(C) 0
(D) 1/2
(E) 1

Since the graph is symmetric with respect to line  x = 2 , then the value of  y  when  x = 3  will be the same as the value of  y  when  x = 1 , so 1.

Answer: E.

navkaran · Answer

(E) 1

its symmetric with respect to x=2.
when x=1, 1 unit to the left of x(2), y is 1.
when x=3, 1 unit to the right of x(2), y should again be 1 as it is symmetric.

mbaiseasy · Answer

Half of the entire graph is a mirror image of the other side. The center coordinate is (2,0) according to the graph. Thus, y when x=1 and y when x-3 are equal.

Answer: E

luckyme17187 · Answer

graph is symmetric with respect to the vertical line

so if x = 1, y = 1 & x=2 , y=0 then x=3 , y=1 ...

JeffTargetTestPrep · Answer

We are given that the graph is SYMMETRIC along the vertical line x = 2. We are also given that when x = 1, y = 1. We are asked to determine the value of y when x is 3. Keep in mind that when x = 1, it is ONE UNIT away from the line x = 2, and when x = 3, it is also ONE UNIT away from the line x = 2.

Since the y-coordinate is 1, when x is 1, the y-coordinate is ALSO 1 when x is 3. Again, this is because the graph is symmetric with the line x = 2.

Another way to look at this problem is to see that the point (1,1) is actually being reflected over the line x = 2.

We see that the point (1,1) is exactly 1 unit from the line x = 2. In fact the point (2,1) is on the line x = 2 which is exactly 1 unit from (1,1). However, (1,1) is exactly 1 unit on the LEFT of (2,1), so by symmetry, the point that is exactly 1 unit on the RIGHT of (2,1) is (3,1). Thus the y-coordinate is 1.

Answer E.

TheUltimateWinner · Answer

Bunuel 
What if x=4? 
y would be 3?
Thanks__

AayushGargnitt · Answer

Y would be 1 as it is symmetrical around 2 so y at X=1 equal to y at x=3

Posted from my mobile device

Bunuel · Answer

_____________________________
Yes.

Vegita · Answer

BrentGMATPrepNow

I was just curious and tried to come up with the equation of the parabola but couldn't figure it out. Isn't (2, 0) the vertex of the parabola?

BrentGMATPrepNow · Answer

It LOOKS like (2, 0) is the vertex, but it isn't.

ArnauG · Answer

According to the given information, we know that the graph is symmetric with respect to the vertical line at x = 2. This means that if we reflect any point on the graph across the line x = 2, we will obtain another point on the graph.

Given that when x = 1/2, y = 2, we can observe that this point is located 1.5 units to the left of the line x = 2. Therefore, if we reflect this point across the line x = 2, the corresponding y-coordinate will be the same, but the x-coordinate will be 1.5 units to the right of the line x = 2.

So, the reflected point will have an x-coordinate of 2 + 1.5 = 3.5.

However, we are asked to find the value of y when x = 3, not x = 3.5. Since the graph is symmetric with respect to the line x = 2, the y-coordinate will also be symmetric. Thus, the value of y when x = 3 will be the same as the value of y when x = 3.5.

Given that when x = 1, y = 1, we can conclude that when x = 3, y will also be (E) 1.

bumpbot · Answer

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On the graph above, when x = 1/2, y = 2; and when x = 1, y =

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