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If 1/x - 1/(x+1) (OG16)

This topic has 2 expert replies and 1 member reply
boomgoesthegmat Senior | Next Rank: 100 Posts Default Avatar
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If 1/x - 1/(x+1) (OG16)

Post Thu May 19, 2016 3:49 pm
If 1/x - 1/(x+1) = 1/(x+4), then x could be

A) 0
B) -1
C) -2
D) -3
E) -4

OA: C

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GMAT/MBA Expert

Post Wed Aug 23, 2017 5:05 pm
boomgoesthegmat wrote:
If 1/x - 1/(x+1) = 1/(x+4), then x could be

A) 0
B) -1
C) -2
D) -3
E) -4

OA: C
Plugging in the answer choices is definitely faster, but here's an algebraic solution...

One way to eliminate fractions is to multiply both sides by the least common multiple (LCM) of all the denominators.
The LCM of x, x+1 and x+4 is (x)(x+1)(x+4)

Given: 1/x - 1/(x+1) = 1/(x+4)
Multiply both sides by (x)(x+1)(x+4) to get: (x)(x+1)(x+4)[1/x - 1/(x+1)] = (x)(x+1)(x+4)[1/(x+4)]
Simplify: (x+1)(x+4) - (x)(x+4) = (x)(x+1)
Expand: [x² + 5x + 4] - [x² + 4x] = x² + x
Simplify: x + 4 = x² + x
Rearrange: x² = 4
Solve: x = 2 OR x = -2

Answer: C

Cheers,
Brent

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OptimusPrep Master | Next Rank: 500 Posts
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GMAT Score:
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Post Thu May 19, 2016 8:02 pm
boomgoesthegmat wrote:
If 1/x - 1/(x+1) = 1/(x+4), then x could be

A) 0
B) -1
C) -2
D) -3
E) -4

OA: C
1/x - 1/(x+1) = 1/(x+4)
You can do this question both by testing values and algebraically.
I will solve it algebraically

x + 1 - x / (x)(x + 1) = 1/(x + 4)
1/x*(x + 1) = 1/(x + 4)

x + 4 = x^2 + x
x^2 = 4

x = 2 or -2

Correct Option: C

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Post Thu May 19, 2016 5:05 pm
Hi boomgoesthegmat,

I'm going to give you some hints so that you can try this question on your own:

The GMAT does NOT test you on the concept of 'undefined' numbers, so you won't have to deal with a calculation that is divided by 0. In this prompt, you'll notice that there are 3 fractions, but since none of them can be "over 0", we can eliminate the answers that would cause that to happen: 0, -1 and -4.

That means there are only two possibilities: -2 or -3. By plugging those values into the equation, you should quickly be able to determine which one 'balances' out the equation. THAT answer will be your solution....

Final Answer: C


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

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