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

 It is currently 21 Feb 2019, 04:01

### 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

## Events & Promotions

###### Events & Promotions in February
PrevNext
SuMoTuWeThFrSa
272829303112
3456789
10111213141516
17181920212223
242526272812
Open Detailed Calendar

February 21, 2019

February 21, 2019

10:00 PM PST

11:00 PM PST

Kick off your 2019 GMAT prep with a free 7-day boot camp that includes free online lessons, webinars, and a full GMAT course access. Limited for the first 99 registrants! Feb. 21st until the 27th.
• ### Free GMAT RC Webinar

February 23, 2019

February 23, 2019

07:00 AM PST

09:00 AM PST

Learn reading strategies that can help even non-voracious reader to master GMAT RC. Saturday, February 23rd at 7 AM PT

# If 1/(1 + 1/(y - 1)) = 3/4 and y ≠ 1, then y =

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 53061
If 1/(1 + 1/(y - 1)) = 3/4 and y ≠ 1, then y =  [#permalink]

### Show Tags

12 Nov 2018, 00:22
00:00

Difficulty:

15% (low)

Question Stats:

85% (00:58) correct 15% (01:36) wrong based on 51 sessions

### HideShow timer Statistics

If $$\frac{1}{1 + \frac{1}{y - 1}} = \frac{3}{4}$$ and y ≠ 1, then y =

A. 4
B. 3
C. 2
D. 4/3
E. 1/3

_________________
Manager
Joined: 15 Feb 2018
Posts: 246
If 1/(1 + 1/(y - 1)) = 3/4 and y ≠ 1, then y =  [#permalink]

### Show Tags

13 Nov 2018, 12:51
1
First, want to clean up the denominator.

$$\frac{1}{{{(y-1)/(y-1)}+{1/(y-1)}}}$$

$$\frac{1}{{(y-1+1)/y-1}}$$

$$\frac{1}{{y/y-1}}$$

$$\frac{1}{1}÷\frac{y}{(y-1)}$$

$$\frac{1}{1}·\frac{(y-1)}{y}$$

$$\frac{y-1}{y}=\frac{3}{4}$$

Use cross multiplication
4(y-1)=3y
4y-4=3y
y-4=0
y=4

A

And for those that got distracted by y≠1, that is simply so the denominator y-1 doesn't become 1-1=0 as 0 cannot be the denominator.
Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 4947
Location: United States (CA)
Re: If 1/(1 + 1/(y - 1)) = 3/4 and y ≠ 1, then y =  [#permalink]

### Show Tags

27 Jan 2019, 19:29
Bunuel wrote:
If $$\frac{1}{1 + \frac{1}{y - 1}} = \frac{3}{4}$$ and y ≠ 1, then y =

A. 4
B. 3
C. 2
D. 4/3
E. 1/3

Multiplying the left side by (y-1)/(y-1), we have:

(y - 1)/[(y - 1) + 1] = 3/4

4y - 4 = 3y - 3 + 3

y = 4

Alternate solution:

We can cross multiply and obtain:

4 = 3 + 3/(y - 1)

1 = 3/(y - 1)

y - 1 = 3

y = 4

_________________

Scott Woodbury-Stewart
Founder and CEO

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Re: If 1/(1 + 1/(y - 1)) = 3/4 and y ≠ 1, then y =   [#permalink] 27 Jan 2019, 19:29
Display posts from previous: Sort by