Dan and Alex measure themselves against a tree in their

BTGmoderatorLU wrote:Source: Veritas Prep

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.

The OA is E

Say the height of Dan is 100 ft, thus, the height of the tree = 180 feet

=> Height of Alex = Height of the tree / (120%) = 180 / 120% = 150 feet

Thus, Alex is taller than Dan by 150 – 100 = 50%.

The correct answer: E

Hope this helps!

-Jay
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BTGmoderatorLU wrote:Source: Veritas Prep

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.

The OA is E

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:

[(Alex’s height - Dan’s height)/Dan’s height] x 100

[(5t/6 - 5t/9)/(5t/9)] x 100

[(15t/18 - 10t/18)/(10t/18)] x 100

(5t/18)/(10t/18) x 100

1/2 x 100 = 50%

Answer: E