Author 
Message 
TAGS:

Hide Tags

Senior Manager
Joined: 25 Dec 2018
Posts: 495
Location: India
Concentration: General Management, Finance
GMAT Date: 02182019
GPA: 3.4
WE: Engineering (Consulting)

Given a + 1 = b + 2 = c + 3 = d + 4 = a + b + c + d + 5, then what is
[#permalink]
Show Tags
06 Mar 2019, 01:29
Question Stats:
65% (02:39) correct 35% (02:48) wrong based on 129 sessions
HideShow timer Statistics
Given a + 1 = b + 2 = c + 3 = d + 4 = a + b + c + d + 5, then what is the value of a + b + c + d? A) 1 B) −(10/3) C) 12 D) 6 E) 2
Official Answer and Stats are available only to registered users. Register/ Login.




Intern
Joined: 07 Apr 2018
Posts: 4

Re: Given a + 1 = b + 2 = c + 3 = d + 4 = a + b + c + d + 5, then what is
[#permalink]
Show Tags
08 Mar 2019, 05:34
a+1=a+b+c+d+5 b+2=a+b+c+d+5 c+3=a+b+c+d+5 d+4=a+b+c+d+5
Adding all the equations we get: a+b+c+d+10=4(a+b+c+d)+20
Solving for (a+b+c+d) we get:
a+b+c+d=(10/3)
Posted from my mobile device




Intern
Joined: 13 Sep 2018
Posts: 20
Location: India
Mission : 750

Re: Given a + 1 = b + 2 = c + 3 = d + 4 = a + b + c + d + 5, then what is
[#permalink]
Show Tags
06 Mar 2019, 03:53
chetan2u, Bunuel, VeritasKarishma, Gladiator59, generis Please Help needed why its should be B not D Regards K.y.Shrenik Bimbsar



Senior PS Moderator
Status: It always seems impossible until it's done.
Joined: 16 Sep 2016
Posts: 732
GMAT 1: 740 Q50 V40 GMAT 2: 770 Q51 V42

Re: Given a + 1 = b + 2 = c + 3 = d + 4 = a + b + c + d + 5, then what is
[#permalink]
Show Tags
06 Mar 2019, 04:01
Hi ShrenikBimbsar, When so many variables are present the first order of business should be to convert everything into a single variable. This is easily possible in this case as multiple equations are given. It comes out that, b = a1 , c= a2 & d= a3 On substituting the above and converting the everything into a it comes out that a = 2/3 And a+b+c+d = 4a  6 Hence the answer is 10/3. Hope it helps. ShrenikBimbsar wrote:
Please Help needed why its should be B not D
Regards
K.y.Shrenik Bimbsar Posted from my mobile device
_________________
Regards, Gladi
“Do. Or do not. There is no try.”  Yoda (The Empire Strikes Back)



Intern
Joined: 13 Sep 2018
Posts: 20
Location: India
Mission : 750

Re: Given a + 1 = b + 2 = c + 3 = d + 4 = a + b + c + d + 5, then what is
[#permalink]
Show Tags
06 Mar 2019, 04:05
Thanks
Regards K.y.Shrenik Bimbsar



Intern
Joined: 13 Sep 2018
Posts: 20
Location: India
Mission : 750

Given a + 1 = b + 2 = c + 3 = d + 4 = a + b + c + d + 5, then what is
[#permalink]
Show Tags
06 Mar 2019, 04:06
Gladiator59 wrote: Hi ShrenikBimbsar, When so many variables are present the first order of business should be to convert everything into a single variable. This is easily possible in this case as multiple equations are given. It comes out that, b = a1 , c= a2 & d= a3 On substituting the above and converting the everything into a it comes out that a = 2/3 And a+b+c+d = 4a  6 Hence the answer is 10/3. Hope it helps. ShrenikBimbsar wrote:
Please Help needed why its should be B not D
Regards
K.y.Shrenik Bimbsar Posted from my mobile deviceThanks Regards K.y.Shrenik Bimbsar



Senior SC Moderator
Joined: 22 May 2016
Posts: 3653

Given a + 1 = b + 2 = c + 3 = d + 4 = a + b + c + d + 5, then what is
[#permalink]
Show Tags
06 Mar 2019, 10:06
mangamma wrote: Given a + 1 = b + 2 = c + 3 = d + 4 = a + b + c + d + 5, then what is the value of a + b + c + d?
A) 1 B) −(10/3) C) 12 D) 6 E) 2 You do not have to solve this problem all the way. (1) Express three of the variables in terms of one other. Use \(a\) or \(d\) for the sake of visual simplicity; both are on one end of the first string of equalitites. \(d+4=c+3\) \(c=(d+1)\) \(d+4=b+2\) \(b=(d+2)\) \(d+4=a+1\) \(a=(d+3)\) (2) Solve for \(d\) using the final equality. Substitute for \(a, b,\) and \(c\) \((d+4)=a+b+c+d+5\) \(d+4=d+3+d+2+d+1+d+5\) \(d+4=4d+11\) \(7=3d\) \(3d=7\) \(d=\frac{7}{3}\) Stop. The answer must be a fraction with a denominator of 3. If we add an integer to a fraction, the answer is a fraction with the same denominator. Only one option has a denominator of 3. The answer is (B).Why stop? \(a, b,\) and \(c\) all have values that equal \(d\)(a fraction) + an integer Test: If we add \(1\) to \(\frac{7}{3}\), then \(1\) must be changed to \(\frac{3}{3}\) \(c=(d+1)\) \(c=(\frac{7}{3})+(\frac{3}{3})\) \(c=\frac{4}{3}\) \(c\) = another fraction with a denominator of 3. \(a\) and \(b\) will also be fractions with a denominator of 3.  The sum of all four variables will be a fraction with a denominator of 3.  Only one option has a denominator of 3. The answer is (B).(3) if you are not sure, do all of the arithmetic Find each value \(a=(d+3)\) \(a=(\frac{7}{3})+(\frac{9}{3})\) \(a=\frac{2}{3}\) \(b=(d+2)\) \(b=(\frac{7}{3})+(\frac{6}{3})\) \(b=\frac{1}{3}\) From above, \(c=\frac{4}{3}\) \(a+b+c+d=\) \(\frac{2}{3}+((\frac{1}{3})+(\frac{4}{3})+(\frac{7}{3}))=\) \(\frac{2}{3}+(\frac{12}{3})=(\frac{2}{3}\frac{12}{3})=\frac{10}{3}\) Answer B
_________________
SC Butler has resumed! Get two SC questions to practice, whose links you can find by date, here.Never doubt that a small group of thoughtful, committed citizens can change the world; indeed, it's the only thing that ever has  Margaret Mead



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9775
Location: Pune, India

Re: Given a + 1 = b + 2 = c + 3 = d + 4 = a + b + c + d + 5, then what is
[#permalink]
Show Tags
06 Mar 2019, 23:59
mangamma wrote: Given a + 1 = b + 2 = c + 3 = d + 4 = a + b + c + d + 5, then what is the value of a + b + c + d?
A) 1 B) −(10/3) C) 12 D) 6 E) 2 So this is what I observed: a + 1 = b + 2 = c + 3 = d + 4 This means the values of the variables are reducing by 1 as we move to the right. So b is 1 less than a. c is 1 less than b and so on. So a, b, c and d could be something like 4, 3, 2, 1 respectively. d + 4 = a + b + c + d + 5 a + b + c + d = d  1 So (a + b + c + d) is further 1 less than d so taking the above example, it will go down one step further and be 0. Hence, a, b, c, d, a+b+c+d are consecutive numbers in decreasing order. Now this is not possible if a, b, c and d are all positive numbers since their sum will be greater than individual numbers. So a+b+c+d cannot be 6 or 12. If a+b+c+d = 1, then d = 0, c = 1, b = 2 and a = 3 Does not satisfy. If a+b+c+d = 2, then d = 1, c = 0, b = 1 and a = 2 Does not satisfy. If a+b+c+d = (10/3), then d = 7/3, c = 4/3, b = 1/3 and a = 2/3 Satisfies. Answer (B)
_________________
Karishma Veritas Prep GMAT Instructor
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >



Intern
Joined: 08 Jan 2019
Posts: 1

Re: Given a + 1 = b + 2 = c + 3 = d + 4 = a + b + c + d + 5, then what is
[#permalink]
Show Tags
12 Mar 2019, 07:37
a+1 = b+2 => b = a1 ——— (1) a+1 = c+3 => c = a2 ——— (2) a+1 = d+4 => d = a3 ——— (3)
a+1 = a+b+c+d+5 => b+c+d = 4 ——— (4)
(1)+(2)+(3) => b+c+d = 3a6 ——— (5)
From (4) and (5) 3a6 = 4 => a = 2/3 ——— (6)
From (4) and (6) a+b+c+d = 2/3  4 => 10/3
Answer (B)



Senior Manager
Joined: 25 Feb 2019
Posts: 336

Re: Given a + 1 = b + 2 = c + 3 = d + 4 = a + b + c + d + 5, then what is
[#permalink]
Show Tags
12 Mar 2019, 09:33
mangamma wrote: Given a + 1 = b + 2 = c + 3 = d + 4 = a + b + c + d + 5, then what is the value of a + b + c + d?
A) 1 B) −(10/3) C) 12 D) 6 E) 2 I have attached the solution. All are equal, let us assume that all are equal to K (any constant) we can find the value of K by solving equation in the picture amd then find the value of required expression Posted from my mobile device
Attachments
File comment: Solution
IMG_20190312_220112.jpg [ 1.23 MiB  Viewed 1050 times ]



Intern
Joined: 10 Jul 2017
Posts: 17

Re: Given a + 1 = b + 2 = c + 3 = d + 4 = a + b + c + d + 5, then what is
[#permalink]
Show Tags
22 Mar 2019, 09:14
VeritasKarishma wrote: mangamma wrote: Given a + 1 = b + 2 = c + 3 = d + 4 = a + b + c + d + 5, then what is the value of a + b + c + d?
A) 1 B) −(10/3) C) 12 D) 6 E) 2 So this is what I observed: a + 1 = b + 2 = c + 3 = d + 4 This means the values of the variables are reducing by 1 as we move to the right. So b is 1 less than a. c is 1 less than b and so on. So a, b, c and d could be something like 4, 3, 2, 1 respectively. d + 4 = a + b + c + d + 5 a + b + c + d = d  1 So (a + b + c + d) is further 1 less than d so taking the above example, it will go down one step further and be 0. Hence, a, b, c, d, a+b+c+d are consecutive numbers in decreasing order. Now this is not possible if a, b, c and d are all positive numbers since their sum will be greater than individual numbers. So a+b+c+d cannot be 6 or 12. If a+b+c+d = 1, then d = 0, c = 1, b = 2 and a = 3 Does not satisfy. If a+b+c+d = 2, then d = 1, c = 0, b = 1 and a = 2 Does not satisfy. If a+b+c+d = (10/3), then d = 7/3, c = 4/3, b = 1/3 and a = 2/3 Satisfies. Answer (B) Hi "VeritasKarishma" I have taken another approach, what will be your suggestion? Thanks in advance.
Attachments
20190322_170735.jpg [ 2.11 MiB  Viewed 763 times ]




Re: Given a + 1 = b + 2 = c + 3 = d + 4 = a + b + c + d + 5, then what is
[#permalink]
22 Mar 2019, 09:14






