12 Days of Christmas GMAT Competition - Day 3: In the image above, the

Question

12 Days of Christmas GMAT Competition with Lots of Fun

In the image above, the green bar has a height of 1 and casts a shadow of 2 on the floor and the red bar has a height of 6 and casts a shadow of 4 on the floor which continues to a height of x on a parallel to the bars wall. What is the value of x? (Assume that the light source is distant, the floors and walls are perfectly flat, and the floor is perpendicular to the bars and walls)

A. 1.5
B. 2
C. 2.5
D. 3
E. 4

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M37-102

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2.png

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Official Answer

E

Bunuel · Accepted Answer

Official Solution:

https://gmatclub.com/tests-beta/resources/import/img/M37-102.png 
 
In the image above, the green bar has a height of 1 and casts a shadow of 2 on the floor and the red bar has a height of 6 and casts a shadow of 4 on the floor which continues to a height of  x  on a parallel to the bars wall. What is the value of  x ? (Assume that the light source is distant, the floors and walls are perfectly flat, and the floor is perpendicular to the bars and walls)

A.  1.5 
B.  2 
C.  2.5 
D.  3 
E.  4

Consider the side view of the figure:
 
  https://gmatclub.com/tests-beta/resources/import/img/M37-102-2.png 
 
Notice that the rays of light should make the same angle  α  at the ground. So, all three angles in two triangles shown are equal to each other, which makes these triangles similar. The ratio of the base to the height of the bottom triangle is  2:1 , hence ratio of the base to the height of the top triangle must also be  2:1 . So, the base of the top triangle is  6*2=12  (this means that if there were no wall, the red bar would cast a shadow of 12). In this case the base of the little blue triangle at the top is  12-4=8 .
 
Now, consider the top triangle. The entire top triangle is similar to its part on the right (little blue triangle) so again since the ratio of the base to the height of entire top triangle is  2:1 , hence ratio of the base to the height ( x ) of the little blue triangle must also be  2:1 . So, the height ( x ) of the little blue triangle  8:2=4

Answer: E

Gmatfox · Answer

https://gmatclub.com/forum/download/file.php?id=59430 
In the image above, the green bar has a height of 1 and casts a shadow of 2 on the floor and the red bar has a height of 6 and casts a shadow of 4 on the floor which continues to a height of x on a parallel to the bars wall. What is the value of x? (Assume that the light source is distant, the floors and walls are perfectly flat, and the floor is perpendicular to the bars and walls)

A. 1.5
B. 2
C. 2.5
D. 3
E. 4

In general, Length of shadow : Height of the bar = 2 : 1, according to the example of the green bar.
If there is no wall, then the red bar will cast a shadow of 12. But there is a wall, then let see the picture as attached8 : 2 = 
--> x : 8 = 1 : 2 --> x = 8 : 2 = 4
-->  Correct answer: E

imeanup · Answer

My approach would be as follows;
First I will find the opposite  \angle  between the height and base of the green pole.  tan x = \frac{1}{2} 
This could be used in the red pole;

\frac{6}{x} = \frac{1}{2} = tan x

x=12

Now consider another triangle with x and (12-4) as a side with the same angle extended.

\frac{x}{8 }= \frac{1}{2}

x= 4

Ans E

Sumi1010 · Answer

The light source is placed in such a way that the shadow of the vertical bars get elongated to double.

If there were no wall, the shadow of the red bar would have been 6x2 = 12 units on the floor.
Of the 12 units, 4 units are on the floor, but remaining units fall on the wall. The equivalent of 8 units length (that would have been on floor) is 4 units length (length on wall = half of the length on floor .

E

shyam30 · Answer

Going for option E.

https://i.ibb.co/8YwYkTp/Solution.png

Kinshook · Answer

Given: In the image above, the green bar has a height of 1 and casts a shadow of 2 on the floor and the red bar has a height of 6 and casts a shadow of 4 on the floor which continues to a height of x on a parallel to the bars wall. 
Asked: What is the value of x? (Assume that the light source is distant, the floors and walls are perfectly flat, and the floor is perpendicular to the bars and walls)

Shadow of height 1 is 2 on the floor and 1 on the wall.
Since shadow of 4 is on the floor, height of 2 is consumed and balance 4 (6-2) will be shown on the wall.

IMO E

vv65 · Answer

My answer is E (4)

If the wall were not there, the shadow of the 6 foot pillar would be 12 foot long
Because the shadow of the 1 foot pillar is 2 foot

The wall is 4 feet away from the pillar

By using the laws of similar triangles, we can see that x is 4

bumpbot · Answer

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