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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:

61% (01:30) correct 38% (00:45) wrong based on 101 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
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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

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Re: Ray is 2 inches taller than Lin, and Ray is 3 inches taller [#permalink] New post 22 Jan 2020, 06:59
no testing s the best strategy
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Re: Ray is 2 inches taller than Lin, and Ray is 3 inches taller [#permalink] New post 22 Jan 2020, 07:03
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Quentin wrote:
no testing s the best strategy


How would you test numbers for this question?
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Re: Ray is 2 inches taller than Lin, and Ray is 3 inches taller [#permalink] New post 05 Mar 2020, 12:40
Can we solve it by picking numbers?

Let's say L=50 cm, R= 52 cm, S = 49 cm

Option A: Av of R, L, S = (50+52+49)/3 = 50.3
Option B: Median (49, 50,52) = 50

So A>B
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Re: Ray is 2 inches taller than Lin, and Ray is 3 inches taller [#permalink] New post 24 May 2020, 01:12
GreenlightTestPrep wrote:
Quentin wrote:
no testing s the best strategy


How would you test numbers for this question?


I solved through your way but here goes nothing.

Assume R=13. Then we get L=11 and S=10.

A= 13+11+10/3 whereas B= 11. This simplifies to 34 > 33.

As long as the parameters are followed this can work with any number. Do let me know if if I have made a mistake!
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Re: Ray is 2 inches taller than Lin, and Ray is 3 inches taller [#permalink] New post 24 May 2020, 07:14
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No

This question is better to solve conceptually.

You do know only that R=L+2 and R =S+3 but you do not know R. It could be any value, fraction included.
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Re: Ray is 2 inches taller than Lin, and Ray is 3 inches taller   [#permalink] 24 May 2020, 07:14
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