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What is the average (arithmetic mean) of x and y?

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What is the average (arithmetic mean) of x and y?  [#permalink]

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New post 24 Dec 2013, 03:42
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The Official Guide For GMAT® Quantitative Review, 2ND Edition

What is the average (arithmetic mean) of x and y?

(1) The average of x and 2y is 10.
(2) The average of 2x and 7y is 32.

Data Sufficiency
Question: 1
Category: Algebra Statistics
Page: 153
Difficulty: 550


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Re: What is the average (arithmetic mean) of x and y?  [#permalink]

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New post 24 Dec 2013, 03:43
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SOLUTION

What is the average (arithmetic mean) of x and y?

The average (arithmetic mean) of x and y is \(\frac{x+y}{2}\). Thus we need to find the value of x+y.

(1) The average of x and 2y is 10 --> \(\frac{x+2y}{2}=10\). Not sufficient.

(2) The average of 2x and 7y is 32 --> \(\frac{2x+7y}{2}=32\). Not sufficient.

(1)+(2) We have two distinct linear equations with two unknowns, thus we can solve for both and get the value of x+y. Sufficient.

Answer: C.
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Re: What is the average (arithmetic mean) of x and y?  [#permalink]

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New post 24 Dec 2013, 16:52
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Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

What is the average (arithmetic mean) of x and y?

(1) The average of x and 2y is 10.
(2) The average of 2x and 7yis 32.

Data Sufficiency
Question: 1
Category: Algebra Statistics
Page: 153
Difficulty: 550


GMAT Club is introducing a new project: The Official Guide For GMAT® Quantitative Review, 2ND Edition - Quantitative Questions Project

Each week we'll be posting several questions from The Official Guide For GMAT® Quantitative Review, 2ND Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution.

We'll be glad if you participate in development of this project:
1. Please provide your solutions to the questions;
2. Please vote for the best solutions by pressing Kudos button;
3. Please vote for the questions themselves by pressing Kudos button;
4. Please share your views on difficulty level of the questions, so that we have most precise evaluation.

Thank you!


statement 1 : x+2y= 10

x =8, y = 1, avg = 4.5
x= 6, y = 2, avg = 4

since 2 answers or more hence insufficient.

Statement 2 : 2x+7y=32

x=9 , y =2, avg = 5.5
x=2 , y =4, avg = 3

Since 2 answers or more hence insufficient

1+2

2 equations and 2 unknowns we can solve
on solving we get y = 4 and x = 2 hence avg = 3

Sufficient.

Answer C.

( Difficulty level - 500 )
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Re: What is the average (arithmetic mean) of x and y?  [#permalink]

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New post 25 Dec 2013, 10:55
1
The question asks for average of x and y: (x+y)/2. So, it is sufficient if we know the values of x and y individually or (x+y) as a whole.

With either statements alone, it is not possible to arrive at (x+y) value.
When both statements are together, we can find out the (x+y) value since we have 2 equations and 2 unknowns.

Hence (C) is the answer.
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Re: What is the average (arithmetic mean) of x and y?  [#permalink]

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New post 30 Dec 2013, 04:34
What is the average (arithmetic mean) of x and y?

The average (arithmetic mean) of x and y is \(\frac{x+y}{2}\). Thus we need to find the value of x+y.

(1) The average of x and 2y is 10 --> \(\frac{x+2y}{2}=10\). Not sufficient.

(2) The average of 2x and 7y is 32 --> \(\frac{2x+7y}{2}=32\). Not sufficient.

(1)+(2) We have two distinct linear equations with two unknowns, thus we can solve for both and get the value of x+y. Sufficient.

Answer: C.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
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Re: What is the average (arithmetic mean) of x and y?  [#permalink]

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New post 16 Mar 2015, 17:19
Just a quick question somewhat related to this problem:

When you're asked for x+y, is it safe to assume that you need either x and y individually, or the value of x+y combined to achieve sufficiency? Will things like x+2y, 3x+4y, etc. always be insufficient? Whenever I'm faced with these problems, I find myself spending time trying to manipulate the x+2y into x+y, so it would be nice to know if I could just quickly say insufficient and move on.
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Re: What is the average (arithmetic mean) of x and y?  [#permalink]

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Re: What is the average (arithmetic mean) of x and y? &nbs [#permalink] 05 Aug 2018, 12:18
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