GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 30 Mar 2020, 12:36 ### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # The average (arithmetic mean) of a and b is 90; the average (arithmeti

Author Message
TAGS:

### Hide Tags

Math Expert V
Joined: 02 Sep 2009
Posts: 62353
The average (arithmetic mean) of a and b is 90; the average (arithmeti  [#permalink]

### Show Tags 00:00

Difficulty:   15% (low)

Question Stats: 83% (01:19) correct 17% (01:30) wrong based on 105 sessions

### HideShow timer Statistics

Competition Mode Question

The average (arithmetic mean) of a and b is 90; the average (arithmetic mean) of a and c is 150; what is the value of (b-c)/2?

A) 60
B) 120
C) 30
D) -60
E) -40

_________________
Director  D
Joined: 16 Jan 2019
Posts: 593
Location: India
Concentration: General Management
WE: Sales (Other)
Re: The average (arithmetic mean) of a and b is 90; the average (arithmeti  [#permalink]

### Show Tags

1
$$\frac{a+b}{2}=90$$ and so $$a+b=180$$
$$\frac{a+c}{2}=150$$ and so $$a+c=300$$

Subtracting the two,

$$a+b-a-c=180-300$$
$$b-c=-120$$
$$\frac{b-c}{2}=-60$$

Senior Manager  P
Joined: 01 Mar 2019
Posts: 482
Location: India
Concentration: Strategy, Social Entrepreneurship
Schools: Ross '22, ISB '20, NUS '20
GMAT 1: 580 Q48 V21
GPA: 4
Re: The average (arithmetic mean) of a and b is 90; the average (arithmeti  [#permalink]

### Show Tags

1
(a+b)/2 = 180
(a+c)/2=300

solving above we get (b-c)/2=-60

OA:D
GMAT Club Legend  V
Joined: 18 Aug 2017
Posts: 6059
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
Re: The average (arithmetic mean) of a and b is 90; the average (arithmeti  [#permalink]

### Show Tags

1
given
a+b= 180 and
a+c= 300
subtract
b-c= 120
so b-c/2= 60
IMO D

The average (arithmetic mean) of a and b is 90; the average (arithmetic mean) of a and c is 150; what is the value of (b-c)/2?

A) 60
B) 120
C) 30
D) -60
E) -40
VP  P
Joined: 24 Nov 2016
Posts: 1353
Location: United States
Re: The average (arithmetic mean) of a and b is 90; the average (arithmeti  [#permalink]

### Show Tags

1
Quote:
The average (arithmetic mean) of a and b is 90; the average (arithmetic mean) of a and c is 150; what is the value of (b-c)/2?

A) 60
B) 120
C) 30
D) -60
E) -40

a+b=90*2=180
a+c=150*2=300
b-c=-120
b-c/2=-120/2=-60

Ans (D)
Director  D
Joined: 07 Mar 2019
Posts: 905
Location: India
GMAT 1: 580 Q43 V27
WE: Sales (Energy and Utilities)
Re: The average (arithmetic mean) of a and b is 90; the average (arithmeti  [#permalink]

### Show Tags

1
The average (arithmetic mean) of a and b is 90; the average (arithmetic mean) of a and c is 150; what is the value of (b-c)/2?

A) 60
B) 120
C) 30
D) -60
E) -40

a + b = 180 - Eqn. 1
a + c + 300 - Eqn. 2
Eqn. 1 - Eqn. 2
a + b - a - c = 180 - 300
b - c = - 120
$$\frac{b-c}{2} = - 60$$

_________________
Ephemeral Epiphany..!

GMATPREP1 590(Q48,V23) March 6, 2019
GMATPREP2 610(Q44,V29) June 10, 2019
GMATPREPSoft1 680(Q48,V35) June 26, 2019
Manager  G
Joined: 20 Aug 2017
Posts: 110
Re: The average (arithmetic mean) of a and b is 90; the average (arithmeti  [#permalink]

### Show Tags

1
a+b = 180
a+c = 300
------------ (Subtracting both equations)
b - c = -120
$$\frac{(b-c)}{2}$$ = -60

IMO, D
CR Forum Moderator P
Joined: 18 May 2019
Posts: 807
Re: The average (arithmetic mean) of a and b is 90; the average (arithmeti  [#permalink]

### Show Tags

1
From the above,(a+b)/2=90, implies a+b=180.................(1)
(a+c)/2=150, implies a+c=300..................(2)
(1)-(2)=> b-c=-120
Hence (b-c)/2=-60.

Director  P
Joined: 25 Jul 2018
Posts: 647
Re: The average (arithmetic mean) of a and b is 90; the average (arithmeti  [#permalink]

### Show Tags

1
The average (arithmetic mean) of a and b is 90; the average (arithmetic mean) of a and c is 150; what is the value of $$\frac{(b-c)}{2}$$ ?

a+b =180
a+c =300
--> a+b-a -c= 180-300 --> b-c =-120
--> $$\frac{(b-c)}{2} = -\frac{120}{2}= -60$$

Manager  G
Joined: 17 Mar 2019
Posts: 162
Re: The average (arithmetic mean) of a and b is 90; the average (arithmeti  [#permalink]

### Show Tags

1
The average (arithmetic mean) of a and b is 90; the average (arithmetic mean) of a and c is 150; what is the value of (b-c)/2?

A) 60
B) 120
C) 30
D) -60
E) -40

Solution : a+b/2= 90 there fore a+b= 180
a+c/2=150 Therefore a+c=300

a+b=180
- a+c=300
=b-c=-120

Therefor b-c/2= -60

IMO D
Intern  Joined: 16 Dec 2019
Posts: 3
Re: The average (arithmetic mean) of a and b is 90; the average (arithmeti  [#permalink]

### Show Tags

1
(a+b)/2 = 90.....(i)
(a+c)/2 = 150.....(ii)

(i) - (ii) gives us:
(a+b-a-c)/2 = 90-150
=> (b-c)/2 = -60

Posted from my mobile device
Board of Directors D
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 4880
Location: India
GPA: 3.5
Re: The average (arithmetic mean) of a and b is 90; the average (arithmeti  [#permalink]

### Show Tags

Quote:
The average (arithmetic mean) of a and b is 90; the average (arithmetic mean) of a and c is 150; what is the value of (b-c)/2?

So, $$a + b = 180$$ ; $$a + c = 300$$

Now, $$(a + b ) - ( a + c ) = a - c$$

Or, $$\frac{a - c }{2}= \frac{180 - 300}{2}$$

Or, $$\frac{a - c }{2} = -60$$, Hence, Answer must be (D) -60
_________________
Thanks and Regards

Abhishek....

PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS

How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only )
Math Expert V
Joined: 02 Sep 2009
Posts: 62353
Re: The average (arithmetic mean) of a and b is 90; the average (arithmeti  [#permalink]

### Show Tags

Bunuel wrote:

Competition Mode Question

The average (arithmetic mean) of a and b is 90; the average (arithmetic mean) of a and c is 150; what is the value of (b-c)/2?

A) 60
B) 120
C) 30
D) -60
E) -40

OFFICIAL EXPLANATION

Translate the question into algebra, using the formula that the average equals the sum of the terms divided by the number of terms.
90 = (a + b)/2
Multiply by 2: 180 = a + b

150 = (a + c)/2
Multiply by 2: 300 = a + c

At this point, there are two ways to manipulate the algebra.

Method 1
Line up the two equations so that you can subtract them.
Equation 1: a+b = 180
Equation 2: a+c = 300
Notice that the equations are lined up such that if you subtract them, you end up with b-c on the left and a number on the right. Since you are trying to find (b-c)/2, this setup will get you most of the way to the answer.
Subtract the two equations:
Equation 1: a+b = 180
Equation 2: a+c = 300
Equation 1 - 2: a - a + b - c = 180 - 300 = -120
Equation 1 - 2 (cont.): b-c = -120
With b-c = -120, if you divide by two, you arrive at the equation that you are being asked for:
(b-c)/2 = -120/2 = -60

Method 2
Since the question asks for the value of (b-c)/2, solve the two equations for the variable a so that they can be combined.
a = 180 – b
a = 300 – c
Combine the two equations by setting them equal to each other (since a = a) and manipulate them such that (b-c)/2 is on one side of the equation and a number is on the other.
180 – b = 300 – c
180 – 300 = b – c
-120 = b-c
-60 = (b – c)/2
_________________
Target Test Prep Representative V
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 9901
Location: United States (CA)
Re: The average (arithmetic mean) of a and b is 90; the average (arithmeti  [#permalink]

### Show Tags

Bunuel wrote:

Competition Mode Question

The average (arithmetic mean) of a and b is 90; the average (arithmetic mean) of a and c is 150; what is the value of (b-c)/2?

A) 60
B) 120
C) 30
D) -60
E) -40

We can create the equations:

a + b = 180

and

a + c = 300

Subtracting the second equation from the first, we have:

(b - c) = -120

Therefore, (b - c)/2 = -120/2 = -60.

_________________

# Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Intern  Joined: 09 Dec 2019
Posts: 4
Re: The average (arithmetic mean) of a and b is 90; the average (arithmeti  [#permalink]

### Show Tags

The average (arithmetic mean) of a and b is 90, this should translate to:

(a + b)/2 = 90

=> a + b = 180 ------ (1)

Similarly,

a + c = 300 ------ (2)

Now the question requires us to find (b - c), thus, subtract (2) from (1) & we will get:

b - c = -120

divide both the sides by 2 to get the requisite value;

(b - c)/2 = -60

Thus, the correct answer is D.
_________________
Quant Faculty

CrackVerbal
Intern  B
Joined: 02 Nov 2019
Posts: 11
Re: The average (arithmetic mean) of a and b is 90; the average (arithmeti  [#permalink]

### Show Tags

$$\frac{(a+b)}{2}=90$$ and $$\frac{(a+c)}{2}=150$$

(a+b)=180 and (a+c)=300

$$a=180-b$$ and $$a=300-c$$

$$180-b=300-c$$

$$b=180$$
$$c=300$$

$$\frac{(180-300)}{2}=-60$$

_________________
Feel free to give feedback on my explanations, I'm still learning  Re: The average (arithmetic mean) of a and b is 90; the average (arithmeti   [#permalink] 02 Jan 2020, 15:07
Display posts from previous: Sort by

# The average (arithmetic mean) of a and b is 90; the average (arithmeti  