Which of the following is NOT a possible value of $$\frac{1}{4-x}?$$
A -4
B 4/17
C 0
D 4
E 17/4
[spoiler]OA=C[/spoiler].
Why is C the correct answer? How can I obtain 4/17? Or 17/4? I need some help here. Thanks in advance.
Which of the following is NOT a possible value of
This topic has expert replies
-
- Legendary Member
- Posts: 1622
- Joined: Thu Mar 01, 2018 7:22 am
- Followed by:2 members
Timer
00:00
Your Answer
A
B
C
D
E
Global Stats
-
- Legendary Member
- Posts: 2898
- Joined: Thu Sep 07, 2017 2:49 pm
- Thanked: 6 times
- Followed by:5 members
Hello Gmat_mission.
Let's take a look at your question.
We have the fraction $$\frac{1}{4-x}.$$ We know that a fraction is equal to 0 if, and only if, the numerator is equal to 0. Since 1 is different from 0, we have that the given fraction can't be equal to 0.
This is why the correct answer is the option C.
Now, you asked how can we obtain 4/17 and 17/4, this can be known by solving the equations $$\frac{1}{4-x}=\frac{4}{17}\ \ \ \Rightarrow\ \ 4-x=\frac{17}{4}\ \Rightarrow\ \ x=4-\frac{17}{4}=-\frac{1}{4}.$$ And $$\frac{1}{4-x}=\frac{17}{4}\ \ \ \Rightarrow\ \ 4-x=\frac{4}{17}\ \Rightarrow\ \ x=4-\frac{4}{17}=\frac{64}{17}.$$ I hope it can help you.
Let's take a look at your question.
We have the fraction $$\frac{1}{4-x}.$$ We know that a fraction is equal to 0 if, and only if, the numerator is equal to 0. Since 1 is different from 0, we have that the given fraction can't be equal to 0.
This is why the correct answer is the option C.
Now, you asked how can we obtain 4/17 and 17/4, this can be known by solving the equations $$\frac{1}{4-x}=\frac{4}{17}\ \ \ \Rightarrow\ \ 4-x=\frac{17}{4}\ \Rightarrow\ \ x=4-\frac{17}{4}=-\frac{1}{4}.$$ And $$\frac{1}{4-x}=\frac{17}{4}\ \ \ \Rightarrow\ \ 4-x=\frac{4}{17}\ \Rightarrow\ \ x=4-\frac{4}{17}=\frac{64}{17}.$$ I hope it can help you.
GMAT/MBA Expert
- Brent@GMATPrepNow
- 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
When we scan the answer choices, we can see that 1/(4-x) can never equal 0.Gmat_mission wrote:Which of the following is NOT a possible value of $$\frac{1}{4-x}?$$
A -4
B 4/17
C 0
D 4
E 17/4
[spoiler]OA=C[/spoiler].
Why is C the correct answer? How can I obtain 4/17? Or 17/4? I need some help here. Thanks in advance.
To see why, take 1/(4-x) = 0 and multiply each side by (4-x) to get: 1 = 0, doesn't work.
Answer: C
B) 4/17Why is C the correct answer? How can I obtain 4/17? Or 17/4? I need some help here. Thanks in advance.
Let 1/(4-x) = 4/17
Cross multiply to get: (1)(17) = (4)(4 - x)
Expand: 17 = 16 - 4x
Subtract 16 from both sides: 1 = 4x
Solve, x = 1/4
WORKS!
E) 17/4
Let 1/(4-x) = 17/4
Cross multiply to get: (1)(4) = (17)(4 - x)
Expand: 4 = 68 - 17x
Subtract 68 from both sides: -64 = -17x
Solve, x = 64/17
WORKS!
Cheers,
Brent
GMAT/MBA Expert
- Scott@TargetTestPrep
- GMAT Instructor
- Posts: 7251
- Joined: Sat Apr 25, 2015 10:56 am
- Location: Los Angeles, CA
- Thanked: 43 times
- Followed by:29 members
Since the numerator is not 0, there is no way for 1/(4 - x) to become zero.Gmat_mission wrote:Which of the following is NOT a possible value of $$\frac{1}{4-x}?$$
A -4
B 4/17
C 0
D 4
E 17/4
Answer: C
Scott Woodbury-Stewart
Founder and CEO
[email protected]
See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews