Dan and Alex measure themselves against a tree in their backyard. The

Question

Dan and Alex measure themselves against a tree in their backyard. The tree is 80% taller than Dan and 20% taller than Alex. Which of the following statements is true?

A. Dan is 60% taller than Alex.
B. Dan is 40% taller than Alex.
C. Alex is 33.3% taller than Dan.
D. Alex is 40% taller than Dan.
E. Alex is 50% taller than Dan.

GMATinsight · Answer

Alex = A
Dan = D

Tree = 1.8*D = 1.2 A
i.e. A = 1.5 D

ANswer: option E

pushpitkc · Answer

Since we need to establish a relationship between the height of Dan and Alex, 
we need to bring both of their heights in similar terms.
Assume Dan's height to be 100 inch, making the tree's height 180 inch
Since its given the tree is 20% more than Alex. 
Alex's height = 180/1.2 = 150 inch

Alex's height is 50% more than Dan which is Option E is the correct answer.

ScottTargetTestPrep · Answer

We can let t = the tree’s height, d = Dan’s height, and a = Alex’s height.
 
Since the tree is 80% taller than Dan:
 
t = 1.8d
 
t/1.8 = d
 
10t/18 = d
 
5t/9 = d
 
Since the tree is 20% taller than Alex:
 
t = 1.2a
 
t/1.2 = a
 
10t/12 = a
 
5t/6 = a
 
Since the tree is 80% taller than Dan and only 20% taller than Alex, we see that Alex is taller than Dan. Let’s determine by how much, using the percent difference formula:
 
  x 100
 
  x 100
 
  x 100
 
(5t/18)/(10t/18) x 100
 
1/2 x 100 = 50%
 
Answer: E

fireagablast · Answer

Why do we look at the percent change in this case?
Why is the answer not simply 33% taller?

d/a = 12/18 = 2/3
d = 66.6%
a = 99.9%

99.9%-66.6% = 33.3%

Edit: On further reflection, it becomes clear that 99% is 50% MORE than 66% i.e 66+ 0.5(66) = 99

SS.56 · Answer

Let Dan's height be 100,

Tree height=180

Alex height=A(6/5)=180=150

Clearly, Alex is 50% taller than Dan.

Answer D

OR

Let Dan's height be D and Alex's height be A

Tree= (18/10)D= (12/10)A

3D=2A
A=1.5D

Answer D

Paras96 · Answer

The tree is 80% taller than Dan and 20% taller than Alex

Let Dan's height be d, Alex's height be a, and Tree's height be H

According to the given problem,

=>H=1.8d=1.2a

=> 1.8d=1.2a
=>a/d=1.5

hence Alex is 50% more taller than Dan

Hence E

Dan and Alex measure themselves against a tree in their backyard. The

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