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## OG2015 PS If 1 + 1/x

tagged by: Brent@GMATPrepNow

This topic has 4 expert replies and 0 member replies
lionsshare Senior | Next Rank: 100 Posts
Joined
09 Aug 2017
Posted:
62 messages

#### OG2015 PS If 1 + 1/x

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.

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Jay@ManhattanReview GMAT Instructor
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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.

Hope this helps!

-Jay
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Brent@GMATPrepNow GMAT Instructor
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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

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Rich.C@EMPOWERgmat.com Elite Legendary Member
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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.

GMAT assassins aren't born, they're made,
Rich

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Jeff@TargetTestPrep GMAT Instructor
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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

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