Last visit was: 21 Jun 2024, 01:14 It is currently 21 Jun 2024, 01:14
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
SORT BY:
Date
Tags:
Show Tags
Hide Tags
Math Expert
Joined: 02 Sep 2009
Posts: 93895
Own Kudos [?]: 633521 [6]
Given Kudos: 82410
Send PM
Most Helpful Reply
GMAT Club Legend
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 6806
Own Kudos [?]: 30600 [1]
Given Kudos: 799
Location: Canada
Send PM
General Discussion
GMAT Club Legend
GMAT Club Legend
Joined: 08 Jul 2010
Status:GMAT/GRE Tutor l Admission Consultant l On-Demand Course creator
Posts: 6016
Own Kudos [?]: 13649 [2]
Given Kudos: 125
Location: India
GMAT: QUANT+DI EXPERT
Schools: IIM (A) ISB '24
GMAT 1: 750 Q51 V41
WE:Education (Education)
Send PM
Intern
Intern
Joined: 19 Jun 2016
Posts: 32
Own Kudos [?]: 5 [0]
Given Kudos: 23
Location: India
GMAT 1: 710 Q50 V35
GPA: 3.85
Send PM
Re: If 1/y − 1/(y+1) = 1/(y+4), what is the sum of all solutions for y? [#permalink]
Bunuel wrote:
If \(\frac{1}{y} − \frac{1}{(y+1)} = \frac{1}{(y+4)}\), what is the sum of all solutions for y?

A. -2
B. -1
C. 0
D. 1
E. 2



1/y−1/(y+1) = 1/(y+4)
=>1/y(y+1) = 1/(y+4)
=> y(y+1) = (y+4)
=> y^2 +y = y +4
=> y^2-4=0
=>y = +2 or -2
Ans C
Manager
Manager
Joined: 06 Nov 2016
Posts: 94
Own Kudos [?]: 53 [0]
Given Kudos: 15
Location: India
GMAT 1: 710 Q50 V36
GPA: 2.8
Send PM
Re: If 1/y − 1/(y+1) = 1/(y+4), what is the sum of all solutions for y? [#permalink]
solving:

(y + 1 - y)/y(y+1) = 1/y+4

y + 4 = y^2 + y

(y-2)(y+2) = 0

y = 2 or - 2

sum of roots is 0
Target Test Prep Representative
Joined: 14 Oct 2015
Status:Founder & CEO
Affiliations: Target Test Prep
Posts: 19030
Own Kudos [?]: 22447 [0]
Given Kudos: 286
Location: United States (CA)
Send PM
Re: If 1/y − 1/(y+1) = 1/(y+4), what is the sum of all solutions for y? [#permalink]
Expert Reply
Bunuel wrote:
If \(\frac{1}{y} − \frac{1}{(y+1)} = \frac{1}{(y+4)}\), what is the sum of all solutions for y?

A. -2
B. -1
C. 0
D. 1
E. 2



We start by combining the two fractions on the left hand side, obtaining:

(y + 1 - y)/[y(y + 1)] = 1/(y + 4)

1/[y^2 + y)] = 1/(y + 4)

We now cross-multiply to obtain:

y^2 + y = y + 4

y^2 = 4

So y = 2 or y = -2, and therefore, the sum of the solutions is 0.

Answer: C
GMAT Club Bot
Re: If 1/y − 1/(y+1) = 1/(y+4), what is the sum of all solutions for y? [#permalink]
Moderator:
Math Expert
93896 posts