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

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Ray is 2 inches taller than Lin, and Ray is 3 inches taller [#permalink] New post 06 Nov 2018, 14:16
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Question Stats:

88% (01:59) correct 11% (02:06) wrong based on 9 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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Re: Ray is 2 inches taller than Lin, and Ray is 3 inches taller [#permalink] New post 08 Nov 2018, 08:39
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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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Re: Ray is 2 inches taller than Lin, and Ray is 3 inches taller [#permalink] New post 09 Nov 2018, 14:30
The answer is Quant A:

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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Re: Ray is 2 inches taller than Lin, and Ray is 3 inches taller [#permalink] New post 09 Nov 2018, 19:20
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.
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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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Ray is 2 inches taller than Lin, and Ray is 3 inches taller

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