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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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Founder  Joined: 18 Apr 2015
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Ray is 2 inches taller than Lin, and Ray is 3 inches taller [#permalink]
Expert's post 00:00

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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GRE Prep Club Members of the Month: Each member of the month will get three months free access of GRE Prep Club tests. GRE Instructor Joined: 10 Apr 2015
Posts: 3309
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Kudos [?]: 3721  , given: 62

Re: Ray is 2 inches taller than Lin, and Ray is 3 inches taller [#permalink]
1
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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 [?]: 7  , given: 8

Re: Ray is 2 inches taller than Lin, and Ray is 3 inches taller [#permalink]
1
KUDOS

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: 371
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Kudos [?]: 162 , 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.
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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

Intern Joined: 13 Jun 2018
Posts: 26
Followers: 0

Kudos [?]: 0 , given: 35

Re: Ray is 2 inches taller than Lin, and Ray is 3 inches taller [#permalink]
no testing s the best strategy
GRE Instructor Joined: 10 Apr 2015
Posts: 3309
Followers: 129

Kudos [?]: 3721 , given: 62

Re: Ray is 2 inches taller than Lin, and Ray is 3 inches taller [#permalink]
Expert's post
Quentin wrote:
no testing s the best strategy

How would you test numbers for this question?
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Brent Hanneson – Creator of greenlighttestprep.com Intern Joined: 20 Apr 2017
Posts: 1
Followers: 0

Kudos [?]: 0 , given: 2

Re: Ray is 2 inches taller than Lin, and Ray is 3 inches taller [#permalink]
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
Manager  Joined: 20 Jun 2019
Posts: 70
GRE 1: Q158 V162 Followers: 0

Kudos [?]: 26 , given: 20

Re: Ray is 2 inches taller than Lin, and Ray is 3 inches taller [#permalink]
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!
Founder  Joined: 18 Apr 2015
Posts: 11328
Followers: 241

Kudos [?]: 2838 , given: 10731

Re: Ray is 2 inches taller than Lin, and Ray is 3 inches taller [#permalink]
Expert's post
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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GRE Prep Club Members of the Month: Each member of the month will get three months free access of GRE Prep Club tests. Re: Ray is 2 inches taller than Lin, and Ray is 3 inches taller   [#permalink] 24 May 2020, 07:14
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