Which of the following is NOT a possible value of

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Gmat_mission: Legendary Member; Posts: 1622; Joined: Thu Mar 01, 2018 7:22 amFollowed by: 2 members

by Gmat_mission » Mon Jun 18, 2018 2:07 am

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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.

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Vincen: Legendary Member; Posts: 2898; Joined: Thu Sep 07, 2017 2:49 pmFollowed by: 5 members; Thanked: 6 times

by Vincen » Mon Jun 18, 2018 2:53 am

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.

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Mon Jun 18, 2018 4:44 am

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.

When we scan the answer choices, we can see that 1/(4-x) can never equal 0.
To see why, take 1/(4-x) = 0 and multiply each side by (4-x) to get: 1 = 0, doesn't work.

Answer: C

Why is C the correct answer? How can I obtain 4/17? Or 17/4? I need some help here. Thanks in advance.

B) 4/17
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

Brent Hanneson - Creator of GMATPrepNow.com

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8136; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

by Scott@TargetTestPrep » Wed Jun 20, 2018 4:03 pm

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

Since the numerator is not 0, there is no way for 1/(4 - x) to become zero.

Answer: C

Scott Woodbury-Stewart
Founder and CEO
[email protected]

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