If 2x + y = 7 and x + 2y = 5, then (x + y)/3 = : Problem Solving (PS)

Mun20

Intern

Joined: 24 Jul 2015

Posts: 12

Own Kudos [?]: 5 [2]

Given Kudos: 24

Send PM

Re: If 2x + y = 7 and x + 2y = 5, then (x + y)/3 = [#permalink]

15 Oct 2015, 20:51

1

Kudos

1

Bookmarks

Bunuel wrote:

If 2x + y = 7 and x + 2y = 5, then (x + y)/3 =

(A) 1
(B) 4/3
(C) 17/5
(D) 18/5
(E) 4

Kudos for a correct solution.

Adding the 2 equations
3x + 3y= 12
Dividing both sides by 3
X+y=12/3
Again dividing both sides by 3
(X+y)/3=4/3

L

MathRevolution

Math Revolution GMAT Instructor

Joined: 16 Aug 2015

Posts: 10161

Own Kudos [?]: 16598 [2]

Given Kudos: 4

GMAT 1: 760 Q51 V42

GPA: 3.82

Send PM

Re: If 2x + y = 7 and x + 2y = 5, then (x + y)/3 = [#permalink]

07 Oct 2020, 02:20

2

Kudos

Expert Reply

Since there are two variables and two distinct equations, we can often solve it by elimination or substitution. But before applying those approach, look at the question what does it need and try adding both the equations or subtracting one from the other and it likely happens 90% times that we get the same kind equation which is in question.

2x + y = 7 and x + 2y = 5

Adding both the equations: 2x + y + x + 2y = 7 + 5

=> 3x + 3y = 12

=> x + y = $\frac{12}{3}$ = 4

=> $\frac{(x + y)}{3}$ = $\frac{4}{3}$

Answer B

L

ScottTargetTestPrep

Target Test Prep Representative

Joined: 14 Oct 2015

Status:Founder & CEO

Affiliations: Target Test Prep

Posts: 18761

Own Kudos [?]: 22052 [2]

Given Kudos: 283

Location: United States (CA)

Send PM

Re: If 2x + y = 7 and x + 2y = 5, then (x + y)/3 = [#permalink]

01 May 2021, 07:13

2

Kudos

Expert Reply

Bunuel wrote:

If 2x + y = 7 and x + 2y = 5, then (x + y)/3 =

(A) 1
(B) 4/3
(C) 17/5
(D) 18/5
(E) 4

Solution:

If we add the two given equations, we have:

3x + 3y = 12

Dividing the above equation by 3, we have:

x + y = 4

Dividing again by 3, we have:

(x + y)/3 = 4/3

Answer: B

asethi

Manager

Joined: 08 Sep 2015

Status:tough ... ? Naaahhh !!!!

Posts: 58

Own Kudos [?]: 37 [1]

Given Kudos: 6

Location: India

Concentration: Marketing, Strategy

WE:Marketing (Computer Hardware)

Send PM

Re: If 2x + y = 7 and x + 2y = 5, then (x + y)/3 = [#permalink]

14 Oct 2015, 21:34

1

Kudos

x=3, y=1, so x+y/3=4/3

Ans:B

L

Skywalker18

Verbal Forum Moderator

Joined: 08 Dec 2013

Status:Greatness begins beyond your comfort zone

Posts: 2101

Own Kudos [?]: 8810 [1]

Given Kudos: 171

Location: India

Concentration: General Management, Strategy

GPA: 3.2

WE:Information Technology (Consulting)

Send PM

Re: If 2x + y = 7 and x + 2y = 5, then (x + y)/3 = [#permalink]

14 Oct 2015, 22:09

1

Bookmarks

2x+y = 7 --1
x +2y= 5 --2
Adding equations 1 and 2 , we get
3x+3y=12
=>x+y=4

(x+y)/3 = 4/3
Answer B

camlan1990

Manager

Joined: 11 Sep 2013

Posts: 96

Own Kudos [?]: 259 [1]

Given Kudos: 26

Schools: Kenan-Flagler '17 SMU '17 McCombs '19

Send PM

Re: If 2x + y = 7 and x + 2y = 5, then (x + y)/3 = [#permalink]

15 Oct 2015, 11:11

1

Kudos

3x + 3y = 12
Divide both sides by 9 to get: 4/3

Ans B

BASSLJ

Intern

Joined: 11 Jul 2015

Posts: 16

Own Kudos [?]: 21 [1]

Given Kudos: 8

Location: United States

Schools: Kenan-Flagler '19 (A$) Goizueta '19 (WL) Duke '19 (WL) Owen '19 (A$) Georgia Tech '19 (A)

GMAT 1: 650 Q47 V32

GMAT 2: 710 Q46 V41

GPA: 3.4

WE:Supply Chain Management (Aerospace and Defense)

Send PM

Re: If 2x + y = 7 and x + 2y = 5, then (x + y)/3 = [#permalink]

15 Oct 2015, 14:07

1

Kudos

2*(x+2y = 5) equals 2x+4y=10
2x+4y=10
- 2x + y= 7
= 3y=3
Therefore Y = 1

Plug and solve...

2x + 1 = 7
2x=6
x=3

(3+1)/3= 4/3

L

AkshdeepS

VP

Joined: 13 Apr 2013

Status:It's near - I can see.

Posts: 1479

Own Kudos [?]: 1603 [1]

Given Kudos: 1002

Location: India

Concentration: International Business, Operations

GPA: 3.01

WE:Engineering (Real Estate)

Send PM

Re: If 2x + y = 7 and x + 2y = 5, then (x + y)/3 = [#permalink]

16 Oct 2015, 03:07

1

Kudos

Bunuel wrote:

If 2x + y = 7 and x + 2y = 5, then (x + y)/3 =

(A) 1
(B) 4/3
(C) 17/5
(D) 18/5
(E) 4

Kudos for a correct solution.

My Solution:

2x+y=7 ----- (1) and x+2y=5 ------>(2)

Solving eqn. (1) & (2) we get x = 3 and y = 1,

Therefore, x+y/3 will be (3+1)/ 3

Answer = 4/3 Option B

L

AkshdeepS

VP

Joined: 13 Apr 2013

Status:It's near - I can see.

Posts: 1479

Own Kudos [?]: 1603 [1]

Given Kudos: 1002

Location: India

Concentration: International Business, Operations

GPA: 3.01

WE:Engineering (Real Estate)

Send PM

Re: If 2x + y = 7 and x + 2y = 5, then (x + y)/3 = [#permalink]

18 Mar 2018, 07:09

1

Kudos

Bunuel wrote:

If 2x + y = 7 and x + 2y = 5, then (x + y)/3 =

(A) 1
(B) 4/3
(C) 17/5
(D) 18/5
(E) 4

Kudos for a correct solution.

Add both equations:

3x + 3y = 12

3 (x + y) = 12

x + y = 4

(x + y)/3

4/3

(B)

S

kanusha

Manager

Joined: 25 Mar 2013

Posts: 166

Own Kudos [?]: 130 [0]

Given Kudos: 101

Location: United States

Concentration: Entrepreneurship, Marketing

Schools: Yale '17 HBS '17 Stanford '17

GPA: 3.5

Send PM

Re: If 2x + y = 7 and x + 2y = 5, then (x + y)/3 = [#permalink]

28 Dec 2016, 10:07

Multiply 2nd equation with 2, on solving
-3y = -3
y =1
Substitute, x = 3
$\frac{4}{3}$
B

L

Mo2men

RSM Erasmus Moderator

Joined: 26 Mar 2013

Posts: 2461

Own Kudos [?]: 1360 [0]

Given Kudos: 641

Concentration: Operations, Strategy

Schools: Erasmus (II)

Send PM

Re: If 2x + y = 7 and x + 2y = 5, then (x + y)/3 = [#permalink]

18 Mar 2018, 08:10

Bunuel wrote:

If 2x + y = 7 and x + 2y = 5, then (x + y)/3 =

(A) 1
(B) 4/3
(C) 17/5
(D) 18/5
(E) 4

Kudos for a correct solution.

2x + y = 7.............1

x + 2y = 5.............2
-----------------------------Sum the 2 eqautions

3x +3 y = 12 .................Divide by 3

x + y =4........................ divide by 3

(x + y)/3 =4/3

Answer: B

B

adkor95

Intern

Joined: 06 Mar 2020

Posts: 34

Own Kudos [?]: 13 [0]

Given Kudos: 80

Send PM

Re: If 2x + y = 7 and x + 2y = 5, then (x + y)/3 = [#permalink]

07 Oct 2020, 01:02

BrentGMATPrepNow wrote:

Bunuel wrote:

If 2x + y = 7 and x + 2y = 5, then (x + y)/3 =

(A) 1
(B) 4/3
(C) 17/5
(D) 18/5
(E) 4

Kudos for a correct solution.

We have two equations:
2x + y = 7
x + 2y = 5

Notice that something nice happens when we ADD them. We get:
3x + 3y = 12
Divide both sides by 3 to get: x + y = 4

So, (x + y)/3 = 4/3

Answer: B

Cheers,
Brent

Thanks BrentGMATPrepNow very quick and efficient. But I'm curious how you spotted it so quickly? I tried subst./elimination first before I realised adding was quicker.

Was there a clue you picked up on?

Cheers

L

BrentGMATPrepNow

GMAT Club Legend

Joined: 12 Sep 2015

Posts: 6820

Own Kudos [?]: 29930 [0]

Given Kudos: 799

Location: Canada

Send PM

Re: If 2x + y = 7 and x + 2y = 5, then (x + y)/3 = [#permalink]

07 Oct 2020, 06:27

Expert Reply

Top Contributor

adkor95 wrote:

BrentGMATPrepNow wrote:

Bunuel wrote:

If 2x + y = 7 and x + 2y = 5, then (x + y)/3 =

(A) 1
(B) 4/3
(C) 17/5
(D) 18/5
(E) 4

Kudos for a correct solution.

We have two equations:
2x + y = 7
x + 2y = 5

Notice that something nice happens when we ADD them. We get:
3x + 3y = 12
Divide both sides by 3 to get: x + y = 4

So, (x + y)/3 = 4/3

Answer: B

Cheers,
Brent

Thanks BrentGMATPrepNow very quick and efficient. But I'm curious how you spotted it so quickly? I tried subst./elimination first before I realised adding was quicker.

Was there a clue you picked up on?

Cheers

If a question involves a system of two equations, and we're asked to find the value of ONE specific variable, then we're pretty much forced to solve the system.
HOWEVER, if the question asks us to find the SUM (or DIFFERENCE) of the variables, then I look for some kind of shortcut in which we combine the two equations.

arileib

Intern

Joined: 12 Jan 2021

Posts: 2

Own Kudos [?]: 5 [0]

Given Kudos: 0

Concentration: Finance, General Management

GPA: 3.71

WE:Accounting (Accounting)

Send PM

Re: If 2x + y = 7 and x + 2y = 5, then (x + y)/3 = [#permalink]

06 Apr 2021, 10:49

I solved using substitution:

2x + y = 7...
y = 7 - 2x (plug this into the other equation now)...
x + 2(7 - 2x) = 5 ...
x + 14 - 4x = 5 ...
14 - 3x = 5 ...
-3x = -9
x = 3 (plug this into either original equation given in question to find y)...

2(3) + y = 7 ...
6 + y = 7 ...
y = 1 (now we have both our x and y, which is 3 and 1 respectively)...

3 + 1/ 3 = 4/3
Ans: B

L

GMATinsight

GMAT Club Legend

Joined: 08 Jul 2010

Status:GMAT/GRE Tutor l Admission Consultant l On-Demand Course creator

Posts: 5960

Own Kudos [?]: 13387 [0]

Given Kudos: 124

Location: India

GMAT: QUANT+DI EXPERT

Schools: IIM (A) ISB '24

GMAT 1: 750 Q51 V41

WE:Education (Education)

Send PM

Re: If 2x + y = 7 and x + 2y = 5, then (x + y)/3 = [#permalink]

06 May 2021, 23:57

Expert Reply

Bunuel wrote:

If 2x + y = 7 and x + 2y = 5, then (x + y)/3 =

(A) 1
(B) 4/3
(C) 17/5
(D) 18/5
(E) 4

Wanna make solving the Official Questions interesting???

Click here and solve 1000+ Official Questions with Video solutions as Timed Sectional Tests
and Dedicated Data Sufficiency (DS) Course

Answer: Option B

Video solution by GMATinsight

Get TOPICWISE: Concept Videos | Practice Qns 100+ | Official Qns 50+ | 100% Video solution CLICK HERE.
Two MUST join YouTube channels : GMATinsight (1000+ FREE Videos) and GMATclub

bumpbot

Non-Human User

Joined: 09 Sep 2013

Posts: 32679

Own Kudos [?]: 822 [0]

Given Kudos: 0

Send PM

Re: If 2x + y = 7 and x + 2y = 5, then (x + y)/3 = [#permalink]

13 Aug 2023, 11:54

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.

gmatclubot

Re: If 2x + y = 7 and x + 2y = 5, then (x + y)/3 = [#permalink]

13 Aug 2023, 11:54

GMAT Problem Solving (PS) Questions

If 2x + y = 7 and x + 2y = 5, then (x + y)/3 =