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Moe is 20% taller than Jane. If Moe is x inches tall,

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Moe is 20% taller than Jane. If Moe is x inches tall,  [#permalink]

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New post 22 Jul 2018, 08:35
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Question Stats:

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Moe is 20% taller than Jane. If Moe is x inches tall, which of the following represents Jane's height in inches?

A) 4x/5
B) 5x/6
C) 2x/3
D) 5x/4
E) 6x/5

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Re: Moe is 20% taller than Jane. If Moe is x inches tall,  [#permalink]

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New post 22 Jul 2018, 09:05
GMATPrepNow wrote:
Moe is 20% taller than Jane. If Moe is x inches tall, which of the following represents Jane's height in inches?

A) 4x/5
B) 5x/6
C) 2x/3
D) 5x/4
E) 6x/5


OA: B
Moe's Height =\(\frac{120}{100}\) Jane's Height
Jane's Height =\(\frac{100}{120}\)Moe's Height
Moe's Height =x
Jane's Height = \(\frac{5}{6}\)x
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Re: Moe is 20% taller than Jane. If Moe is x inches tall,  [#permalink]

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New post 22 Jul 2018, 09:13
GMATPrepNow wrote:
Moe is 20% taller than Jane. If Moe is x inches tall, which of the following represents Jane's height in inches?

A) 4x/5
B) 5x/6
C) 2x/3
D) 5x/4
E) 6x/5



The most important thing here is to be sure what the DENOMINATOR will be
So \(\frac{M}{J} = \frac{x}{J}=1.2=\frac{12}{10}=\frac{6}{5}......\frac{x}{J}=\frac{6}{5}...J=\frac{5x}{6}\)...
B
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Re: Moe is 20% taller than Jane. If Moe is x inches tall,  [#permalink]

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New post 24 Jul 2018, 10:37
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GMATPrepNow wrote:
Moe is 20% taller than Jane. If Moe is x inches tall, which of the following represents Jane's height in inches?

A) 4x/5
B) 5x/6
C) 2x/3
D) 5x/4
E) 6x/5


I created this question to highlight a common misconception that goes something like this:
If Moe is 20% taller then Jane, then Jane must be 20% shorter than Moe. If you have this misconception, then you will incorrectly choose A as your answer.
For more on this common misconception, read https://www.gmatprepnow.com/articles/co ... 93-part-ii

Moe is 20% taller than Jane.
Let J = Jane's height (in inches)
So, 1.2J = Moe's height

Moe is x inches tall.
We just learned that 1.2J = Moe's height
So, we can write: 1.2J = x
Since 1.2 = 6/5, we can rewrite the equation as follows: (6/5)J = x

Which of the following represents Jane's height in inches?
Solve the equation (6/5)J = x for J
Multiply both sides of the above equation by 5/6 to get: J = (5/6)(x)
Simplify: J = 5x/6

Answer: B

Cheers,
Brent
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Re: Moe is 20% taller than Jane. If Moe is x inches tall,  [#permalink]

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New post 24 Jul 2018, 10:57
GMATPrepNow wrote:
Moe is 20% taller than Jane. If Moe is x inches tall, which of the following represents Jane's height in inches?

A) 4x/5
B) 5x/6
C) 2x/3
D) 5x/4
E) 6x/5

120% of J = x

So, J = 100x/120

Or, J = 5x/6 , Answer must be (B)
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Re: Moe is 20% taller than Jane. If Moe is x inches tall,  [#permalink]

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New post 25 Jul 2018, 17:39
GMATPrepNow wrote:
Moe is 20% taller than Jane. If Moe is x inches tall, which of the following represents Jane's height in inches?

A) 4x/5
B) 5x/6
C) 2x/3
D) 5x/4
E) 6x/5


Letting j = Jane’s height, we can create the equation:

x = 1.2j

x/1.2 = j

10x/12 = j

5x/6 = j

Answer: B
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Re: Moe is 20% taller than Jane. If Moe is x inches tall, &nbs [#permalink] 25 Jul 2018, 17:39
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