|
|
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
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
06 Feb 2020, 05:33
Kudos
Bookmarks
C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
15%
(low)
Question Stats:
81% (01:31) correct
19%
(01:47)
wrong
based on 227
sessions
History
Date
Time
Result
Not Attempted Yet
If \(\frac{1}{(x – 2)} = \frac{1}{(x + 2)} + \frac{1}{(x – 1)}\), which of the following is a possible value of x?
(A) –2
(B) –1
(C) 0
(D) 1
(E) 2
(A) –2
(B) –1
(C) 0
(D) 1
(E) 2
shameekv1989
GMAT 3: 720 Q50 V38
Posts: 816
06 Feb 2020, 05:53
Kudos
Bookmarks
If 1/(x–2)=1/(x+2)+1/(x–1), which of the following is a possible value of x?
(A) –2
(B) –1
(C) 0
(D) 1
(E) 2
Since we have (x-2), (x-1) and (x+2) in denominator we can not have values of x as 2, 1 and -2 since it will result in no defined values - Hence eliminate E, D and A.
Now we can substitute B and C to find which is the correct answer
With B) -> \(\frac{1}{(-1-2)}\) = \(\frac{1}{(-1+2)}\) + \(\frac{1}{(-1-1)}\) -> \(\frac{-1}{3}\) = 1 - \(\frac{1}{2}\) -> \(\frac{1}{2}\) = \(\frac{-1}{3}\) which is not true - Hence Eliminated
With C) -> \(\frac{1}{(0-2)}\) = \(\frac{1}{(0+2)}\) + \(\frac{1}{(0-1)}\) -> \(\frac{-1}{2}\) = \(\frac{1}{2}\) - 1 -> \(\frac{-1}{2}\) = \(\frac{-1}{2}\) which is true - Hence Answer
Answer - C
(A) –2
(B) –1
(C) 0
(D) 1
(E) 2
Since we have (x-2), (x-1) and (x+2) in denominator we can not have values of x as 2, 1 and -2 since it will result in no defined values - Hence eliminate E, D and A.
Now we can substitute B and C to find which is the correct answer
With B) -> \(\frac{1}{(-1-2)}\) = \(\frac{1}{(-1+2)}\) + \(\frac{1}{(-1-1)}\) -> \(\frac{-1}{3}\) = 1 - \(\frac{1}{2}\) -> \(\frac{1}{2}\) = \(\frac{-1}{3}\) which is not true - Hence Eliminated
With C) -> \(\frac{1}{(0-2)}\) = \(\frac{1}{(0+2)}\) + \(\frac{1}{(0-1)}\) -> \(\frac{-1}{2}\) = \(\frac{1}{2}\) - 1 -> \(\frac{-1}{2}\) = \(\frac{-1}{2}\) which is true - Hence Answer
Answer - C
18 Jun 2020, 10:18
Kudos
Bookmarks
Bunuel
A super-fast approach is to test the answer choices
IMPORTANT: Our work will be made even faster if we recognize that none of denominators (in the given equation) can equal zero. Otherwise, that fraction will be undefined.
So, we can automatically eliminate answer choices A, D and E, since they will all yield denominators that are equal to 0.
We're left with only answer choices B and C (and we haven't even done any work yet!!!)
Let's test answer choice B
Replace \(x\) with\( -1\) to get: \(\frac{1}{(-1) – 2} = \frac{1}{(-1) + 2} + \frac{1}{(-1) – 1}\)
Simplify to get: \(-\frac{1}{3} = \frac{1}{1} + -\frac{1}{2}\)
Doesn't work!!
Eliminate house for choice B.
By the process of elimination, the correct answer is C
Aside: If we're confident in the work we've done so far, we did not actually test answer choice C. But, if you're not convinced let's check..
Replace \(x\) with \(0\) to get: \(\frac{1}{0 – 2} = \frac{1}{0 + 2} + \frac{1}{0 – 1}\)
Simplify to get: \(-\frac{1}{2} = \frac{1}{2} - 1\)
It WORKS!
Answer: C
Cheers,
Brent
