The figure represents a boy who is 1.6 m tall standing in front of a l

Question

https://gmatclub.com/forum/download/file.php?mode=view&id=59950 The figure represents a boy who is 1.6 m tall standing in front of a lamppost that is 8 m tall. As shown, the boy casts a shadow that is 1.5 m long when he is 6 m from the lamppost. Note that \frac{8}{1.6} = \frac{6+1.5}{1.5} . As the boy walks in a straight line away from the lamppost, his distance from the lamppost increases and his shadow gets longer. When the boy is 7 m from the lamppost, he casts a shadow that is 1.75 m long. From each drop-down menu, select the option that creates the most accurate statement based on the information provided. 1. When the boy is 8 m from the lamppost, he casts a shadow that is GRAPH_1_PLACEHOLDER m long. 2. When the boy casts a shadow that is 3 m long, he is GRAPH_2_PLACEHOLDER m from the lamppost. 4.jpg

Sajjad1994 · Accepted Answer

Official Explanation

RO1

Notice that in the equation provided, the ratio of the height of the lamppost to the height of the boy     is equal to the ratio of the boy's distance from the lamppost plus the length of the shadow to the length of the shadow alone    . Thus, since the distance from the lamppost is 8, substituting x for the length of the shadow into the equation yields  \frac{8}{1.6}=\frac{8+x}{x} . Cross-multiplying,  8x = 1.6(8 + x) = 12.8 + 1.6x.  Subtracting 1.6x from each side of the equation gives  6.4x = 12.8.  Dividing both sides by 6.4 yields x = 2.
 
  The correct answer is 2.  
 
 RO2

Using the equation described in the analysis of RO1, substitute 3 for the length of the shadow and y for the distance from the lamppost. Thus,  \frac{8}{1.6}=\frac{y+3}{3} . Cross-multiplying,  24 = 1.6(y + 3) = 1.6y + 4.8.  Subtracting 4.8 from each side of the equation, 19.2 = 1.6y. Dividing each side by 1.6, 12 = y.
 
Alternatively, one could observe that in the diagram, the ratio of the distance from the lamppost to the length of the shadow is  \frac{6}{1.5} . Since we are told the length of the shadow is 3 m, which is twice the length in the diagram, one could simply double the distance from the lamppost in the diagram to get a distance of 12 m.
 
  The correct answer is 12.

TarunKumar1234 · Answer

Given, The figure represents a boy who is 1.6 m tall standing in front of a lamppost that is 8 m tall. As shown, the boy casts a shadow that is 1.5 m long when he is 6 m from the lamppost.

Note that 8/1.6=(6+1.5)/1.5. As the boy walks in a straight line away from the lamppost, his distance from the lamppost increases and  his shadow gets longer.    It is important to note down. 
When the boy is 7 m from the lamppost, he casts a shadow that is 1.75 m long.  (It is another example given)

If we look closely, height of lamp post / height of the boy 
= (Distance of boy from Lamp post + length of his shadow ) /length of his shadow;  it is from the property of similar triangles.

When the boy is 8 m from the lamppost, he casts a shadow that is__________m long.

So, we got, height of lamp post / height of the boy 
= (Distance of boy from Lamp post + length of his shadow)/length of his shadow
or, 8/1.6 = (8+x)/x; say x= length of his shadow
or, 5x= 8+x or x= 8/4 =  2 m. Ans. A.

When the boy casts a shadow that is 3 m long, he is__________m from the lamppost.

So, we got, height of lamp post / height of the boy 
= (Distance of boy from Lamp post + length of his shadow)/length of his shadow
or, 8/1.6 = (y+3)/3; say y= Distance of boy from Lamp post
or, 15= y+3 or y=  12 m. Ans. A.

Deepakjhamb · Answer

Q1 When the boy is 8 m from the lamppost, he casts a shadow that is__________m long.

answer is A)2 
A. 2
B. 2.25
C. 2.50
D. 2.75
E. 3

SOLUTION : FROM similar triangles we have , lets say shadow is x then x/(8+x) = 1.6/8

so 8x= 1.6*8 + 1.6x

6.4x= 1.6 *8

x= 2

answer is A) 2

Q2When the boy casts a shadow that is 3 m long, he is__________m from the lamppost.

ANSWER IS A)12 
A. 12
B. 9
C. 10
D. 11
E. 13

FROM similar triangles sides proportionality we have , lets say distance from lamppost = x than 3/(x+3 ) =1.6/8

so 24 = 1.6*3 +1.6x
1.6x= 24 -4.8
1.6x= 19.2

x= 12

so answer is A)12

Sumi1010 · Answer

Given
the height of the boy = 1.6 m (constant)
and 
1.6/8 = 1.5/(6+1.5)

when the boy is 7m from the lamppost
1.6/8 = 1.75/(7+1.75)

When the boy is 8 m from the lamppost , let the shadow be s meter.
1.6/8 = s/(8+s)
8/s =4
 s = 2

When the boy casts a shadow of 3 m , let he is d meter away from the post
1.6/8 = 3/(3+d)
d/3 = 4
 d = 12

Thus, 
 When the boy is 8 m from the lamppost, he casts a shadow that is__________m long. 
 A. 2

When the boy casts a shadow that is 3 m long, he is__________m from the lamppost. 
 A. 12

rocky620 · Answer

Case1:  When the boy is 6m away the shadow is 1.5
Also given -  \frac{8}{1.6}  =  \frac{(6+1.5)}{1.5}  = =>  \frac{8}{1.6} = \frac{7.5}{1.5} 
Where,
8=Post Height
1.6=Boy Height
6=Boy Distance form the post
1.5=Shadow height

Case2:  When the boy is 7m away the shadow is 1.75
Also given -  \frac{8}{1.6}  =  \frac{(7+1.75)}{1.75}  = =>  \frac{8}{1.6} = \frac{8.75}{1.75} 
Where,
8=Post Height
1.6=Boy Height
7=Boy Distance form the post
1.75=Shadow height

From Case1 & Case2, we can infer that the Ratio of the Sum of (distance of the boy From the post + length of the shadow) to the length of the shadow
will always be 5:1

When the boy is 8 m from the lamppost, he casts a shadow that is__________m long. 
Let the shadow length be x
So, as per above reasoning,
 \frac{(8+x)}{x}  = 5 => 8+x = 5x => 8 = 4x => x=2

IMO Option A

When the boy casts a shadow that is 3 m long, he is__________m from the lamppost. 
Let the distance from the post be y
So, as per above reasoning,
 \frac{(y+3)}{3}  = 5 => y+3 = 15 =>  y=12

IMO Option A

Option A for Both

Sajjad1994 · Answer

OA to this question is 2 for first blank and 12 for the second. It is an easy question overall, Excellent work by  rocky620

nikitathegreat · Answer

Instead of putting the solution in the equation, can we solve this using unitary method?
If 7m is 1.75, then i can calculate for 8m and also for the second ques using this method.

The answer that i am getting is same

riyamakwana_ · Answer

can i not simply say that if at 6m, the shadow is 1.5 and at 7m, its 1.75, then a difference pattern is seen and i can add 0.25 to find the dropdown answers?

riyamakwana_ · Answer

@bunuel can i not simply say that if at 6m, the shadow is 1.5 and at 7m, its 1.75, then a difference pattern is seen and i can add 0.25 to find the dropdown answers?

Adarsh_24 · Answer

The length of post by boys height is a constant 8/1.6=5

5 = (d from post + shadow length) / shadow length

This can be inferred from given equation.

bumpbot · Answer

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The figure represents a boy who is 1.6 m tall standing in front of a l

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