GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 17 Oct 2019, 06:08

Close

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
Your Progress

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.

Close

Request Expert Reply

Confirm Cancel

If A + B = C, A + D = B, 2C = 3D and A, B, C, and D are positive integ

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Find Similar Topics 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 58417
If A + B = C, A + D = B, 2C = 3D and A, B, C, and D are positive integ  [#permalink]

Show Tags

New post 26 Jul 2019, 07:59
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

70% (01:52) correct 30% (02:23) wrong based on 297 sessions

HideShow timer Statistics

Director
Director
avatar
D
Joined: 20 Jul 2017
Posts: 913
Location: India
Concentration: Entrepreneurship, Marketing
WE: Education (Education)
Re: If A + B = C, A + D = B, 2C = 3D and A, B, C, and D are positive integ  [#permalink]

Show Tags

New post 26 Jul 2019, 08:12
3
A+B=C
—> A = C - B ....... (1)
A+D=B
—> B = C - B + D
—> 2B = C + D ....... (2)

2C=3D
—> C = 3D/2

From (2),
2B = 3D/2 + D = 5D/2
—> B = 5D/4

So, B should be a multiple of 5
—> Least value = 5

IMO Option C

Pls Hit kudos if you like the solution

Posted from my mobile device
RC Moderator
User avatar
V
Joined: 24 Aug 2016
Posts: 790
GMAT 1: 540 Q49 V16
GMAT 2: 680 Q49 V33
GMAT ToolKit User Premium Member Reviews Badge CAT Tests
Re: If A + B = C, A + D = B, 2C = 3D and A, B, C, and D are positive integ  [#permalink]

Show Tags

New post 26 Jul 2019, 08:13
2
Given 2C=3D
Now, substituting with the other equations: 2A+2B=-3A+3B => 5A=B
As, 'A, B, C, and D are positive integers' , the least value of A could be 1.
Thus least value of B is 5. .... Hence Ans C.
_________________
Please let me know if I am going in wrong direction.
Thanks in appreciation.
Senior Manager
Senior Manager
User avatar
G
Joined: 10 Aug 2018
Posts: 336
Location: India
Concentration: Strategy, Operations
WE: Operations (Energy and Utilities)
Reviews Badge
Re: If A + B = C, A + D = B, 2C = 3D and A, B, C, and D are positive integ  [#permalink]

Show Tags

New post 26 Jul 2019, 08:15
1
A+B=C----1
A+D=B----2
2C=3D----3

Subtracting eq 2 from 1 we get B-D=C-B ===> 2B=C+D===> 4B=2C+2D====> 4B=5D====> B has to be 5.

C is the correct answer.
_________________
On the way to get into the B-school and I will not leave it until I win. WHATEVER IT TAKES.

" I CAN AND I WILL"

GMAT:[640 Q44, V34, IR4, AWA5]


Need advice: https://gmatclub.com/forum/profile-evaluation-indian-29-male-energy-sector-need-advice-308286.html
SVP
SVP
User avatar
P
Joined: 03 Jun 2019
Posts: 1698
Location: India
Premium Member Reviews Badge CAT Tests
Re: If A + B = C, A + D = B, 2C = 3D and A, B, C, and D are positive integ  [#permalink]

Show Tags

New post 26 Jul 2019, 08:16
1
If A+B=C, A+D=B, 2C=3D and A, B, C, and D are positive integers, what is the least possible value of B?

A. 1
B. 4
C. 5
D. 6
E. 10

Given: A+B=C, A+D=B, 2C=3D and A, B, C, and D are positive integers

Asked: what is the least possible value of B?

A=C-B=B-D => 2B=C+D => B=(C+D)/2

2C = 3D = k
C= k/2 is a positive integer
D=k/3 is a positive integer
B= (k/2+k/3)/2 = 5k/12 is a positive integer
For B to be an integer k=12m
B=5m
Least possible value of B = 5

IMO C
_________________
"Success is not final; failure is not fatal: It is the courage to continue that counts."

Please provide kudos if you like my post. Kudos encourage active discussions.

My GMAT Resources: -

Efficient Learning
All you need to know about GMAT quant

Tele: +91-11-40396815
Mobile : +91-9910661622
E-mail : kinshook.chaturvedi@gmail.com
Manager
Manager
User avatar
G
Joined: 08 Jan 2018
Posts: 129
CAT Tests
If A + B = C, A + D = B, 2C = 3D and A, B, C, and D are positive integ  [#permalink]

Show Tags

New post Updated on: 26 Jul 2019, 22:16
1
A, B, C and D are positive integers.

A + B = C -> 2A + 2B = 2C -> (a)
A + D = B -> 3A + 3D = 3B -> 3B – 3A = 3D -> (b)
2C = 3D -> (c)
Putting (a) and (b) in (c)

2A + 2B = 3B – 3A => 5A = B => A = B/5 -> (d)

From (d), B has to be a multiple of 5. So eliminate options A, B, and D.

When B = 5
A=1, C= 6, D = 4. This certainly satisfies all the equations

Therefore, least possible value of B is 5. Answer C

Originally posted by Sayon on 26 Jul 2019, 08:17.
Last edited by Sayon on 26 Jul 2019, 22:16, edited 1 time in total.
Manager
Manager
avatar
S
Joined: 24 Jun 2017
Posts: 71
CAT Tests
Re: If A + B = C, A + D = B, 2C = 3D and A, B, C, and D are positive integ  [#permalink]

Show Tags

New post 26 Jul 2019, 08:18
1
A. 1
B. 4
C. 5
D. 6
E. 10

By substituting variables we get
D = 4A
C = 6A
B = 5A

writing all variables in terms of B --> A = B/5
C= 6B/5
D = 4B/5

So when B=1,4 etc A,C,D will not be integers - so the minimum possible value for B is 5
Manager
Manager
avatar
S
Joined: 30 May 2018
Posts: 156
Location: Canada
GMAT 1: 710 Q49 V36
GPA: 3.8
Premium Member Reviews Badge CAT Tests
Re: If A + B = C, A + D = B, 2C = 3D and A, B, C, and D are positive integ  [#permalink]

Show Tags

New post 26 Jul 2019, 08:20
1
C

If we solve the three equations, we basically get B=5A, D=4A, and C=6A.

Now, since all parameters are positive integers, minimum possible value of A is 1, so least possible value of B is 5.
Intern
Intern
avatar
B
Joined: 13 Mar 2019
Posts: 28
Location: India
GMAT ToolKit User
Re: If A + B = C, A + D = B, 2C = 3D and A, B, C, and D are positive integ  [#permalink]

Show Tags

New post 26 Jul 2019, 08:20
1
Given all are positive integers, A, B, C, and D are positive integers, what is the least possible value of B?
A+B=C
A+D=B,
2C=3D

we can solve it using the options.
1 can never be a option because A+D=B(remember A&D are positive integers so min value B can have is 2)

Lets take B as 5 and A=1
C=6.D=4 and it accepts 2C=3D. We have a answer in C. A,D&E options goes away(min value of B)

when you take B=4, cases that can happen are A=1,D=3 or A=2,D=2 or A=3,D=1
case B=4,A=1,D=3=>C=5, 2C!=3D
case B=4,A=2,D=2=>C=6,2C!=3D
case B=4,A=3,D=1=>C=7,2C!=3D

So option B goes wrong.
therefore option C is the answer.
Manager
Manager
User avatar
G
Joined: 28 Jan 2019
Posts: 125
Location: Peru
Premium Member
Re: If A + B = C, A + D = B, 2C = 3D and A, B, C, and D are positive integ  [#permalink]

Show Tags

New post 26 Jul 2019, 08:20
1
Here we have A+B=C (1), A+D=B (2) and 2C=3D (3)

From (1) and (3) we have that A+B=1.5D (4).

Then, from (2) and (4) we have that A + A+D = 1.5D, so 2A = 1/2D, finally A=0.25D (5)

From (4) and (5) we have that B = 5/4D, so the least value of B (since they are + integers) must be 5.

(C) is our answer.
GMAT Club Legend
GMAT Club Legend
User avatar
D
Joined: 18 Aug 2017
Posts: 5003
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
GMAT ToolKit User Premium Member
Re: If A + B = C, A + D = B, 2C = 3D and A, B, C, and D are positive integ  [#permalink]

Show Tags

New post 26 Jul 2019, 08:22
1
If A+B=CA+B=C, A+D=BA+D=B, 2C=3D2C=3D and A, B, C, and D are positive integers, what is the least possible value of B?

A. 1
B. 4
C. 5
D. 6
E. 10

solving
we get
A+B=C
A+D=B
2C=3D
we get
5A=B
and C=6A and D= 4A
so least value of B=5
IMO C
Manager
Manager
User avatar
S
Joined: 10 Mar 2019
Posts: 75
Location: Russian Federation
Schools: Haas '21
GPA: 3.95
CAT Tests
Re: If A + B = C, A + D = B, 2C = 3D and A, B, C, and D are positive integ  [#permalink]

Show Tags

New post 26 Jul 2019, 08:25
1
If A+B=C, A+D=B, 2C=3D and A, B, C, and D are positive integers, what is the least possible value of B?

Let's solve an equation
2A+2B=2C
3A+3D=3B
3D=3B-3A
since 3D=2C
2A+2B=3B-3A
B=5A
Since A and B are positive integers we can assume the least value for A=1 and thus the least value of B=5

The answer is C
Manager
Manager
User avatar
B
Joined: 30 Oct 2018
Posts: 71
Location: India
Schools: IE '22
CAT Tests
Re: If A + B = C, A + D = B, 2C = 3D and A, B, C, and D are positive integ  [#permalink]

Show Tags

New post 26 Jul 2019, 08:30
1
A+B=3/2 D
A+B= 3/2(B-A)
2A+2B=3B-3A
2A+3A=B
5A=B
Taking A as min
B should be 5 (C)
_________________

----------------------------------
Plz Kudos! if my post helps....
Manager
Manager
avatar
G
Joined: 26 Jan 2016
Posts: 178
CAT Tests
Re: If A + B = C, A + D = B, 2C = 3D and A, B, C, and D are positive integ  [#permalink]

Show Tags

New post 26 Jul 2019, 08:40
1
Quote:
If A+B=C, A+D=B, 2C=3D and A, B, C, and D are positive integers, what is the least possible value of B?

A. 1
B. 4
C. 5
D. 6
E. 10


A+B=C -> A-C=B-----------------1
A+D=B................2
2C=3D...................3

Multiplying 1 by 2 and 2 by 3 and solving both as we have

we get, 5A=B
And minimum possible value of A=1
hence C
_________________
Your Kudos can boost my morale..!!

I am on a journey. Gradually I'll there..!!
Manager
Manager
avatar
G
Joined: 29 Nov 2018
Posts: 147
Location: India
Concentration: Entrepreneurship, General Management
GPA: 3.99
WE: Engineering (Computer Hardware)
If A + B = C, A + D = B, 2C = 3D and A, B, C, and D are positive integ  [#permalink]

Show Tags

New post Updated on: 26 Jul 2019, 08:42
1
If A+B=C, A+D=B, 2C=3D and A, B, C, and D are positive integers, what is the least possible value of B?

A. 1
B. 4
C. 5
D. 6
E. 10

A+B = C
A + D = B
Therefore, A + D = C - A, 2A + D = C
Now 2C = 3D, Substituting in above equation we get 2A = 1/2*D, D = 4A.
Therefore A + 4A = B, B = 5A.
Least value of A can be 1 as it is a positive number so least value of B = 5.
Answer = C

Originally posted by ruchik on 26 Jul 2019, 08:41.
Last edited by ruchik on 26 Jul 2019, 08:42, edited 1 time in total.
Intern
Intern
avatar
B
Joined: 29 May 2018
Posts: 23
Location: India
GMAT 1: 680 Q49 V33
GMAT ToolKit User CAT Tests
If A + B = C, A + D = B, 2C = 3D and A, B, C, and D are positive integ  [#permalink]

Show Tags

New post Updated on: 26 Jul 2019, 11:58
1
Given:

A+B=C -- 1

A+D=B -- 2

2C=3D -- 3

From the third equation we get:

\(D=\frac{2}{3}C\) and we know from equation 1 that C =A+B, which means:

D= \(\frac{2}{3}(A+B)\)

Substituting value of D in equation 2 ==>

A+\(\frac{2}{3}(A+B)\)=B

\(\frac{5}{3}A + \frac{2}{3}B = B\)

\(\frac{5}{3}A=\frac{B}{3}\)

5A=B

Least possible value for A is 1 as it is a positive integer.

Thus least value of B=5

Originally posted by Ajiteshmathur on 26 Jul 2019, 08:41.
Last edited by Ajiteshmathur on 26 Jul 2019, 11:58, edited 1 time in total.
Intern
Intern
avatar
B
Joined: 30 Aug 2018
Posts: 15
Re: If A + B = C, A + D = B, 2C = 3D and A, B, C, and D are positive integ  [#permalink]

Show Tags

New post 26 Jul 2019, 08:44
1
Here,
2C=3D
So, C=(3D/2)

A+B=C
A+D=B
So, A+D=C-A
2A=C-D

2A=3D/2 -D
2A=D/2
4A=D

So, if A+D=B
then, A+4A=B
5A=B
We know that all A , B, C, D are positve intergers so A can be least as 1.
Putting A=1 we get B=5*1=5
SO our answer becomes C
Senior Manager
Senior Manager
User avatar
P
Joined: 20 Mar 2018
Posts: 372
Location: Ghana
Concentration: Finance, Real Estate
Re: If A + B = C, A + D = B, 2C = 3D and A, B, C, and D are positive integ  [#permalink]

Show Tags

New post 26 Jul 2019, 08:45
1
A+B=C , A+D=B , 2C=3D
and A, B, C, and D are positive integers, what is the least possible value of B?

So C= A+B , D= B-A
Let’s substitute them into the constraint 2C = 3D
2(A+B) = 3(B-A)
2A+2B = 3B-3A —> 5A =3B-2B
A= B/5
Now least +ve value =5 ,since A has to be an integer
.: A =5/5 =Integer
.: B =5
Smash that C

Posted from my mobile device
Senior Manager
Senior Manager
User avatar
G
Joined: 05 Mar 2017
Posts: 261
Location: India
Concentration: General Management, Marketing
GPA: 3.6
WE: Marketing (Hospitality and Tourism)
Reviews Badge CAT Tests
Re: If A + B = C, A + D = B, 2C = 3D and A, B, C, and D are positive integ  [#permalink]

Show Tags

New post 26 Jul 2019, 08:46
If A+B=C, A+D=B, 2C=3D and A, B, C, and D are positive integers, what is the least possible value of B?

A= B-D
b-D+B =C
2B+D =C
2B+2/3C =C
B=2/3C


A. 1
B. 4
C. 5
D. 6
E. 10

IMO D.
Senior Manager
Senior Manager
avatar
P
Joined: 27 Aug 2014
Posts: 338
Location: Netherlands
Concentration: Finance, Strategy
Schools: LBS '22, ISB '21
GPA: 3.9
WE: Analyst (Energy and Utilities)
Re: If A + B = C, A + D = B, 2C = 3D and A, B, C, and D are positive integ  [#permalink]

Show Tags

New post 26 Jul 2019, 08:46
1
IMO answer is C

for B =5, we ned up with integer values for A,C and D which are A=1, B=5, C=6 and D = 4
only B=5, answer choice C is min possible value for B
GMAT Club Bot
Re: If A + B = C, A + D = B, 2C = 3D and A, B, C, and D are positive integ   [#permalink] 26 Jul 2019, 08:46

Go to page    1   2   3   4   5    Next  [ 85 posts ] 

Display posts from previous: Sort by

If A + B = C, A + D = B, 2C = 3D and A, B, C, and D are positive integ

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne