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

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Dan and Alex measure themselves against a tree in their backyard. The  [#permalink]

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13 Jun 2017, 06:01
00:00

Difficulty:

45% (medium)

Question Stats:

70% (01:51) correct 30% (01:56) wrong based on 82 sessions

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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.

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Re: Dan and Alex measure themselves against a tree in their backyard. The  [#permalink]

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13 Jun 2017, 06:32
Bunuel wrote:
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.

Alex = A
Dan = D

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

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Re: Dan and Alex measure themselves against a tree in their backyard. The  [#permalink]

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13 Jun 2017, 06:39
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.
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Re: Dan and Alex measure themselves against a tree in their backyard. The  [#permalink]

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15 Jun 2017, 16:00
1
Bunuel wrote:
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.

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%

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Re: Dan and Alex measure themselves against a tree in their backyard. The  [#permalink]

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28 Sep 2018, 06:14
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Re: Dan and Alex measure themselves against a tree in their backyard. The   [#permalink] 28 Sep 2018, 06:14
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