Dan and Alex measure themselves against a tree in their

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BTGmoderatorLU: Moderator; Posts: 2505; Joined: Sun Oct 15, 2017 1:50 pm; Followed by:6 members

Dan and Alex measure themselves against a tree in their

by BTGmoderatorLU » Tue Feb 26, 2019 2:53 pm

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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

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Source: Beat The GMAT — Problem Solving | Tue Feb 26, 2019 2:53 pm

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Jay@ManhattanReview: GMAT Instructor; Posts: 3008; Joined: Mon Aug 22, 2016 6:19 am; Location: Grand Central / New York; Thanked: 470 times; Followed by:34 members

by Jay@ManhattanReview » Tue Feb 26, 2019 10:16 pm

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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swerve: Legendary Member; Posts: 2499; Joined: Sun Oct 29, 2017 2:04 pm; Followed by:6 members

by swerve » Wed Feb 27, 2019 7:02 am

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 inches, making the tree's height 180 inches
Since its given the tree is 20% more than Alex.
Alex's height = 180/1.2 = 150 inches.

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

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Fri Mar 01, 2019 9:41 am

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

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