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
If 1/x - 1/(x+1) (OG16)
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Hi boomgoesthegmat,
I'm going to give you some hints so that you can try this question on your own:
[spoiler] 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
[/spoiler]
GMAT assassins aren't born, they're made,
Rich
I'm going to give you some hints so that you can try this question on your own:
[spoiler] 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
[/spoiler]
GMAT assassins aren't born, they're made,
Rich
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1/x - 1/(x+1) = 1/(x+4)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
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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Plugging in the answer choices is definitely faster, but here's an algebraic solution...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
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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We must first eliminate the fractions in the equation 1/x - 1/(x+1) = 1/(x+4).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
Thus, we will multiply the entire equation by the least common multiple of the denominators, which is:
x(x+1)(x+4)
We are now left with:
(x+1)(x+4) - x(x+4) = x(x+1)
x^2 + 5x + 4 - x^2 - 4x = x^2 + x
x + 4 = x^2 + x
4 = x^2
√4 = √x^2
x = 2 or x = -2
Alternate Solution:
Another option is to backsolve, substituting the answer choices into the given equation:
First, we can eliminate choices A, B and E because any one of them will make one of the denominators equal to 0 and we can't have denominator = 0. Choice A will make the denominator of the first fraction on the left hand side of the equation equal to 0; choice B will make the denominator of the second fraction on the left hand side of the equation equal to 0; and choice E will make the denominator of the fraction on the right hand side of the equation equal to 0.
So we only need to test choices C and D.
C. -2
1/(-2) - 1/(-2+1) = 1/(-2+4) ?
-1/2 - 1/(-1) = 1/2 ?
-1/2 + 1 = 1/2 ?
1/2 = 1/2 (Yes!)
We see that C is the correct choice, but let's show that D will not be the correct choice.
D. -3
1/(-3) - 1/(-3+1) = 1/(-3+4) ?
-1/3 - 1/(-2) = 1/1 ?
-1/3 + 1/2 = 1 ?
1/6 = 1 (No!)
Answer: C
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