OG2015 PS If 1 + 1/x

This topic has expert replies
User avatar
Senior | Next Rank: 100 Posts
Posts: 62
Joined: Wed Aug 09, 2017 3:54 pm

OG2015 PS If 1 + 1/x

by lionsshare » Wed Sep 13, 2017 9:44 pm
If 1 + 1/x = 2 - 2/x, then x =

(A) -1
(B) 1/3
(C) 2/3
(D) 2
(E) 3

OA: E

Please explain the solution to this problem. Thank you.

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 3008
Joined: Mon Aug 22, 2016 6:19 am
Location: Grand Central / New York
Thanked: 470 times
Followed by:34 members

by Jay@ManhattanReview » Wed Sep 13, 2017 9:54 pm
lionsshare wrote:If 1 + 1/x = 2 - 2/x, then x =

(A) -1
(B) 1/3
(C) 2/3
(D) 2
(E) 3

OA: E

Please explain the solution to this problem. Thank you.
1 + 1/x = 2 - 2/x

Transposing 2/x to left-hand side and 1 to the right-hand side, we get

1/x + 2/x = 2 - 1

3/x = 1

Cross-multiplying, we get 3 = 1*x => x = 3.

The correct answer: E

Hope this helps!

Download free ebook: Manhattan Review GMAT Quantitative Question Bank Guide

-Jay
_________________
Manhattan Review GMAT Prep

Locations: New York | Jakarta | Nanjing | Berlin | and many more...

Schedule your free consultation with an experienced GMAT Prep Advisor! Click here.

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 16207
Joined: Mon Dec 08, 2008 6:26 pm
Location: Vancouver, BC
Thanked: 5254 times
Followed by:1268 members
GMAT Score:770

by Brent@GMATPrepNow » Thu Sep 14, 2017 6:28 am
lionsshare wrote:If 1 + 1/x = 2 - 2/x, then x =

(A) -1
(B) 1/3
(C) 2/3
(D) 2
(E) 3

OA: E
Another approach is to eliminate the fractions at step 1.
Given: 1 + 1/x = 2 - 2/x
Multiply both sides by x to get: x + 1 = 2x - 2
Add 2 to both sides: x + 3 = 2x
Subtract x from both sides: 3 = x

Answer: E
Brent Hanneson - Creator of GMATPrepNow.com
Image

GMAT/MBA Expert

User avatar
Elite Legendary Member
Posts: 10392
Joined: Sun Jun 23, 2013 6:38 pm
Location: Palo Alto, CA
Thanked: 2867 times
Followed by:511 members
GMAT Score:800

by [email protected] » Fri Sep 15, 2017 9:28 am
Hi lionsshare,

Based on the 'design' of this question and the answer choices, you can use the answers 'against' the prompt and TEST THE ANSWERS.

We're told that 1 + 1/X = 2 - 2/X

In simple terms, we're adding something to "1" and subtracting something else from "2" and ending with the same result. This means that each 'side' of the equation is the same value - and that value is something BETWEEN 1 and 2. Thus, whatever we're adding to 1 and subtracting from 2 must be POSITIVE FRACTIONS. Only two of the answer choices, when placed as the value of X, will create positive fractions: Answers D and E.

IF... X = 2, then the two sides of the equation are...
1 + 1/2 = 1.5
2 - 2/2 = 1
These results are NOT equal, so D is NOT the answer.

IF... X = 3, then the two sides of the equation are...
1 + 1/3 = 4/3
2 - 2/3 = 6/3 - 2/3 = 4/3
These results ARE equal, so E is the answer.

Final Answer: E

GMAT assassins aren't born, they're made,
Rich
Contact Rich at [email protected]
Image

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 1462
Joined: Thu Apr 09, 2015 9:34 am
Location: New York, NY
Thanked: 39 times
Followed by:22 members

by Jeff@TargetTestPrep » Tue Sep 19, 2017 2:57 pm
lionsshare wrote:If 1 + 1/x = 2 - 2/x, then x =

(A) -1
(B) 1/3
(C) 2/3
(D) 2
(E) 3

OA: E
We can simplify the given equation:

1 + 1/x = 2 - 2/x

Add 2/x to both sides of the equation and subtract 1 from each side to obtain:

3/x = 1

3 = x

Alternate solution:

We can multiply both sides of the equation by x and obtain:

x + 1 = 2x - 2

3 = x

Answer: E

Jeffrey Miller
Head of GMAT Instruction
[email protected]

Image

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews