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#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here. # Ray is 2 inches taller than Lin, and Ray is 3 inches taller  Question banks Downloads My Bookmarks Reviews Important topics
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Kudos [?]: 2044 , given: 8095

Ray is 2 inches taller than Lin, and Ray is 3 inches taller [#permalink]
Expert's post 00:00

Question Stats: 65% (01:25) correct 34% (00:47) wrong based on 46 sessions

Ray is 2 inches taller than Lin, and Ray is 3 inches taller than Sam.

 Quantity A Quantity B The average (arithmetic mean) height of Ray, Lin, and Sam The median height of Ray, Lin, and Sam

A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
[Reveal] Spoiler: OA

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Kudos [?]: 2731  , given: 40

Re: Ray is 2 inches taller than Lin, and Ray is 3 inches taller [#permalink]
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Expert's post
Carcass wrote:
Ray is 2 inches taller than Lin, and Ray is 3 inches taller than Sam.

 Quantity A Quantity B The average (arithmetic mean) height of Ray, Lin, and Sam The median height of Ray, Lin, and Sam

A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.

Let's write all heights in terms of Ray's height.

Let R = Ray's height (in inches)
So, R - 2 = Lin's height
And R - 3 = Sam's height

Average height = [R + (R-2) + (R-3)]/3
= [3R - 5]/3
= 3R/3 - 5/3
= R - 5/3

To find the median height, arrange heights in ASCENDING ORDER: R-3, R-2, R
So, the median height = R-2

So, we get:
QUANTITY A: R - 5/3
QUANTITY B: R - 2

Subtract R from both quantities to get:
QUANTITY A: -5/3
QUANTITY B: -2

Since -5/3 is greater than -2, the correct answer is A

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Brent Hanneson – Creator of greenlighttestprep.com

Intern Joined: 04 Nov 2018
Posts: 44
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Kudos [?]: 6 , given: 8

Re: Ray is 2 inches taller than Lin, and Ray is 3 inches taller [#permalink]

Ray= 2+Lin's age
Ray= 3+Sam's age
If Lin is aged 6 then Ray is 8 which means Sam (8-3) is 5
Quant A=5+6+8=(20/3)= 6+
Quant B=6 is the median
So Quant A is greater

Please share if there is an easier way to solve this.
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Joined: 01 Nov 2017
Posts: 370
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Kudos [?]: 137 , given: 4

Re: Ray is 2 inches taller than Lin, and Ray is 3 inches taller [#permalink]
Expert's post
Carcass wrote:
Ray is 2 inches taller than Lin, and Ray is 3 inches taller than Sam.

 Quantity A Quantity B The average (arithmetic mean) height of Ray, Lin, and Sam The median height of Ray, Lin, and Sam

A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.

2 inches and 3 inches more means the lower two heights are consecutive integers.But the third height is not consecutive but slightly more..
Had the third height too been consecutive, both median and mean would be EQUAL.
Because the third number is not consecutive but slightly more, the mean will be greater .

You can check with values..
x,x+1,X+3...
Median is x+1
Mean is x+$$\frac{4}{3}$$
So A is more.
_________________

Some useful Theory.
1. Arithmetic and Geometric progressions : https://greprepclub.com/forum/progressions-arithmetic-geometric-and-harmonic-11574.html#p27048
2. Effect of Arithmetic Operations on fraction : https://greprepclub.com/forum/effects-of-arithmetic-operations-on-fractions-11573.html?sid=d570445335a783891cd4d48a17db9825
3. Remainders : https://greprepclub.com/forum/remainders-what-you-should-know-11524.html
4. Number properties : https://greprepclub.com/forum/number-property-all-you-require-11518.html
5. Absolute Modulus and Inequalities : https://greprepclub.com/forum/absolute-modulus-a-better-understanding-11281.html Re: Ray is 2 inches taller than Lin, and Ray is 3 inches taller   [#permalink] 09 Nov 2018, 19:20
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