GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 19 Oct 2019, 23:23 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

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  If 1/x - 1/(x+1) = 1/(x+4), then x could be

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

Hide Tags

Intern  Joined: 09 Mar 2011
Posts: 6
If 1/x - 1/(x+1) = 1/(x+4), then x could be  [#permalink]

Show Tags

5
25 00:00

Difficulty:   5% (low)

Question Stats: 85% (01:17) correct 15% (01:38) wrong based on 1879 sessions

HideShow timer Statistics

If $$\frac{1}{x} - \frac{1}{x+1} = \frac{1}{x+4}$$, then x could be

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

Originally posted by ArmorPierce on 09 Mar 2011, 19:23.
Last edited by Bunuel on 17 Jul 2014, 06:56, edited 2 times in total.
Edited the question.
Veritas Prep GMAT Instructor V
Joined: 16 Oct 2010
Posts: 9706
Location: Pune, India
Re: If 1/x - 1/(x+1) = 1/(x+4), then x could be  [#permalink]

Show Tags

20
10
ArmorPierce wrote:
Hey guys, I'm having trouble with the below problem. Can anyone explain it to me? please explain it like you would a child step by step. Thanks.

If (1/x) - (1/(x+1)) = (1/(x+4)), then x could be
a 0
b -1
c -2
d -3
e -4

There are multiple ways of solving this.
You can directly solve for x:
$$\frac{1}{x} - \frac{1}{(x+1)} = \frac{1}{(x+4)}$$

$$\frac{(x+1) - x}{x(x+1)} = \frac{1}{(x+4)}$$

$$\frac{1}{x(x+1)} = \frac{1}{(x+4)}$$

Cross multiply to get,
x + 4 = x(x+1)
x^2 - 4 = 0
(x-2)(x+2) = 0
x = 2 or -2

Though a much faster approach would be to use the options.
You can see that x cannot be 0/-1/-4 because then one of the terms will have 0 in the denominator. A fraction cannot have 0 in the denominator hence x must be either -2 or -3.
Put x = -2 and check:
$$\frac{1}{(-2)} - \frac{1}{(-2+1)} = \frac{1}{(-2+4)}$$
1 - (1/2) = 1/2
1/2 = 1/2

So x = -2 satisfies and hence, is the answer.
_________________
Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >
General Discussion
Manager  Joined: 07 Mar 2011
Posts: 52
Concentration: Entrepreneurship, Finance
Schools: Chicago (Booth) - Class of 2014
GMAT 1: 710 Q50 V36 GPA: 3.3
WE: Other (Other)
Re: If 1/x - 1/(x+1) = 1/(x+4), then x could be  [#permalink]

Show Tags

1
Hi,

I think the first step is to get the variables up to the numerator. To do this we should find the common factor on the left side:

1/x - 1/(x+1) => becomes (x+1)/(x)(x+1) - (x)/(x)(x+1)
=> combines to (x+1) - (x) / (x)(x+1)
=> notice that the top two Xs cancel out 1 / (x)(x+1)

We now have the full equation: 1 / (x)(x+1) = 1 / (x+4)

We can simply swap the denominators around to have: (x+4) = x(x+1)

After we expand the equation we get (x+4) = x^2+x
Notice that the two Xs cancel out leaving us with: 4 = x^2
Thus we have the solution x = 2 or -2
_________________
Sent from my Slapchop
Director  Joined: 01 Feb 2011
Posts: 545
Re: If 1/x - 1/(x+1) = 1/(x+4), then x could be  [#permalink]

Show Tags

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

=> 1/(x(x+1)) = 1/(x+4)

=> x^2 +x= x+ 4 => x^2 =4 => x = 2 or -2

we dont have 2 in the answer , so x = -2 .

Retired Moderator Joined: 20 Dec 2010
Posts: 1577
Re: If 1/x - 1/(x+1) = 1/(x+4), then x could be  [#permalink]

Show Tags

1
$$\frac{1}{x} - \frac{1}{x+1} = \frac{1}{x+4}$$

$$\frac{x+1-x}{x(x+1)} = \frac{1}{x+4}$$

$$\frac{1}{x(x+1)} = \frac{1}{x+4}$$

Don't need to factorize any further.

Just by looking at the denominator; we can say x can't be 0,-4 or -1; a,b,e are ruled out as the answer.

Let's substitute x=-2 in the equation;

$$\frac{1}{2} = \frac{1}{2}$$

No need to look for "d".

Ans: "c"
_________________
Intern  Joined: 09 Mar 2011
Posts: 6
Re: If 1/x - 1/(x+1) = 1/(x+4), then x could be  [#permalink]

Show Tags

okay thanks a lot guys I now understand this method to solving it. The method that I'm still stuck on in the book is how they get it from factoring

Denominators are eliminated leading to this:
(x+1)(x+4)-x(x+4)=x(x+1)

I don't understand how it gets from that to the following:
(x+4)(x+1-x)=x(x+1)
(x+4)(1)=x(x+1)
Retired Moderator Joined: 20 Dec 2010
Posts: 1577
Re: If 1/x - 1/(x+1) = 1/(x+4), then x could be  [#permalink]

Show Tags

1
ArmorPierce wrote:
okay thanks a lot guys I now understand this method to solving it. The method that I'm still stuck on in the book is how they get it from factoring

Denominators are eliminated leading to this:
(x+1)(x+4)-x(x+4)=x(x+1)

I don't understand how it gets from that to the following:
(x+4)(x+1-x)=x(x+1)
(x+4)(1)=x(x+1)

########
a*b-a*z=k
a(b-z)=k;;;;;;;;;; Taking "a" as common from a*b and a*z
########

(x+1)(x+4)-x(x+4)=x(x+1)
(x+1)*(x+4)-x*(x+4)=x*(x+1)
Taking (x+4) common
(x+4){x+1-x} = x*(x+1)
(x+4)*1=x*(x+1)
_________________
Director  Status: Impossible is not a fact. It's an opinion. It's a dare. Impossible is nothing.
Affiliations: University of Chicago Booth School of Business
Joined: 03 Feb 2011
Posts: 654
Re: If 1/x - 1/(x+1) = 1/(x+4), then x could be  [#permalink]

Show Tags

Start from option C.
LHS = a. RHS = b. a should be b
If the answer is too low, go down the options. If the answer is too high, go up the options. You will hit the answer pretty soon !
Veritas Prep GMAT Instructor V
Joined: 16 Oct 2010
Posts: 9706
Location: Pune, India
Re: If 1/x - 1/(x+1) = 1/(x+4), then x could be  [#permalink]

Show Tags

3
gmat1220 wrote:
Start from option C.
LHS = a. RHS = b. a should be b
If the answer is too low, go down the options. If the answer is too high, go up the options. You will hit the answer pretty soon !

0, -1 and -4 cannot be the answers since denominator cannot be 0 and each of these values makes one of the denominator 0.
Just check for -2 and -3.
_________________
Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >
Intern  Joined: 09 Mar 2011
Posts: 6
Re: If 1/x - 1/(x+1) = 1/(x+4), then x could be  [#permalink]

Show Tags

fluke wrote:
########
a*b-a*z=k
a(b-z)=k;;;;;;;;;; Taking "a" as common from a*b and a*z
########

(x+1)(x+4)-x(x+4)=x(x+1)
(x+1)*(x+4)-x*(x+4)=x*(x+1)
Taking (x+4) common
(x+4){x+1-x} = x*(x+1)
(x+4)*1=x*(x+1)

Thanks, thats actually very simple, or a lot more simple than I made it out to be.
Current Student D
Joined: 12 Aug 2015
Posts: 2567
Schools: Boston U '20 (M)
GRE 1: Q169 V154 Re: If 1/x - 1/(x+1) = 1/(x+4), then x could be  [#permalink]

Show Tags

VeritasPrepKarishma wrote:
ArmorPierce wrote:
Hey guys, I'm having trouble with the below problem. Can anyone explain it to me? please explain it like you would a child step by step. Thanks.

If (1/x) - (1/(x+1)) = (1/(x+4)), then x could be
a 0
b -1
c -2
d -3
e -4

There are multiple ways of solving this.
You can directly solve for x:
$$\frac{1}{x} - \frac{1}{(x+1)} = \frac{1}{(x+4)}$$

$$\frac{(x+1) - x}{x(x+1)} = \frac{1}{(x+4)}$$

$$\frac{1}{x(x+1)} = \frac{1}{(x+4)}$$

Cross multiply to get,
x + 4 = x(x+1)
x^2 - 4 = 0
(x-2)(x+2) = 0
x = 2 or -2

Though a much faster approach would be to use the options.
You can see that x cannot be 0/-1/-4 because then one of the terms will have 0 in the denominator. A fraction cannot have 0 in the denominator hence x must be either -2 or -3.
Put x = -2 and check:
$$\frac{1}{(-2)} - \frac{1}{(-2+1)} = \frac{1}{(-2+4)}$$
1 - (1/2) = 1/2
1/2 = 1/2

So x = -2 satisfies and hence, is the answer.

Here too..!!
the easier and faster(depends on how much one is compatible with algebra) is to use the LCM process..

Again Personal Opinion regards
_________________
Target Test Prep Representative D
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 8109
Location: United States (CA)
Re: If 1/x - 1/(x+1) = 1/(x+4), then x could be  [#permalink]

Show Tags

1
ArmorPierce wrote:
If $$\frac{1}{x} - \frac{1}{x+1} = \frac{1}{x+4}$$, then x could be

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

We must first eliminate the fractions in the equation 1/x - 1/(x+1) = 1/(x+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

The answer is C.

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!)

The answer is C.
_________________

Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Intern  B
Joined: 16 May 2017
Posts: 17
Re: If 1/x - 1/(x+1) = 1/(x+4), then x could be  [#permalink]

Show Tags

Using the arithmetic approach we can see that x can be "+" or "-" 2.

The only answer choice matches our results is C.
Manager  G
Joined: 12 Jun 2016
Posts: 212
Location: India
WE: Sales (Telecommunications)
Re: If 1/x - 1/(x+1) = 1/(x+4), then x could be  [#permalink]

Show Tags

My 50 Cents here.

I think its much faster here to Substitute the answer choices

A. Will make $$\frac{1}{x}$$ as Infinity. Not Possible.

B. Will make $$\frac{1}{x+1}$$ as infinity. Not Possible.

C. $$\frac{-1}{2}$$ - (-$$\frac{1}{1}$$) = $$\frac{1}{2}$$. Turns out $$\frac{1}{2}$$ = $$\frac{1}{2}$$. Possible.

D. $$\frac{-1}{3}$$- (-$$\frac{1}{2}$$) = 1. Not Possible

E. -$$\frac{1}{4}$$ - (-$$\frac{1}{3}$$) = $$\frac{1}{8}$$. Not possible.

Final Answer = C.
_________________
My Best is yet to come!
GMAT Club Legend  V
Joined: 12 Sep 2015
Posts: 4009
Re: If 1/x - 1/(x+1) = 1/(x+4), then x could be  [#permalink]

Show Tags

1
Top Contributor
ArmorPierce wrote:
If $$\frac{1}{x} - \frac{1}{x+1} = \frac{1}{x+4}$$, then x could be

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

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

RELATED VIDEO

_________________
Manager  D
Joined: 12 Mar 2013
Posts: 233
If 1/x - 1/(x+1) = 1/(x+4), then x could be  [#permalink]

Show Tags

We can try each of the options. Only (-2) will satisfy the requirment, So answer is C
_________________
We Shall Overcome... One day...
EMPOWERgmat Instructor V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 15287
Location: United States (CA)
GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: If 1/x - 1/(x+1) = 1/(x+4), then x could be  [#permalink]

Show Tags

Hi All,

I'm a big fan of Brent's approach to this question (TESTing the ANSWERS); on certain Quant questions on the GMAT, strategically plugging in the answers to find the one that matches will get the correct answer faster than the traditional "math approach."

There is one additional Number Property in this question that meshes with what Brent already showed you: one involving Common Denominators….

Here, we're subtracting one fraction from another to get a third fraction.

Notice that the first two fractions are over "X" and over "X+1"…

If X = odd, then X+1 = even
If X = even, then X+1 = odd

With one even and one odd, we'll end up with a common denominator that is EVEN…

So, X+4 = EVEN

Thus, X MUST be EVEN

Combining this deduction with Brent's eliminations, the correct answer would have to be

GMAT assassins aren't born, they're made,
Rich
_________________
SVP  V
Status: It's near - I can see.
Joined: 13 Apr 2013
Posts: 1687
Location: India
Concentration: International Business, Operations
Schools: INSEAD Jan '19
GPA: 3.01
WE: Engineering (Real Estate)
Re: If 1/x - 1/(x+1) = 1/(x+4), then x could be  [#permalink]

Show Tags

ArmorPierce wrote:
If $$\frac{1}{x} - \frac{1}{x+1} = \frac{1}{x+4}$$, then x could be

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

It can be done with Algebra approach, but that will be time consuming.

As we know denominator can never be "0", then any answer choice that makes any of the three denominators "0". We can eliminate A, B, & E. Now we can test C & D.

C gives the right answer.
_________________
"Do not watch clock; Do what it does. KEEP GOING."
Intern  Joined: 13 Nov 2018
Posts: 1
If 1/x - 1/(x+1) = 1/(x+4), then x could be  [#permalink]

Show Tags

Hi, I am really bad in math (specially with fractions ), so I tried to solve this question but I don't know what was my mistake.

I did Like this

1/x - 1/X+1 = 1/x+4

1/x = 1/x+4 + 1/X+1

I didn't know what to do after this... so I tried to calculate it as it was.

MMC (I don't know if I can do this)
X+4,X+1 | X+4
1,X+1 | X+1
1,1 | (X+4)*(X+1) = X²+5x +4

1/x = (X²+5x +4) + (X²+5x +4) / X²+5x +4 >>> 2X²+10x+8/X²+5x +4 = 2 (I tought this equation would be just like 4/2, so = 2)

Now I have 1/x = 2 >>> 2x = 1 >>> X = 0,5...
SVP  P
Joined: 03 Jun 2019
Posts: 1732
Location: India
Re: If 1/x - 1/(x+1) = 1/(x+4), then x could be  [#permalink]

Show Tags

ArmorPierce wrote:
If $$\frac{1}{x} - \frac{1}{x+1} = \frac{1}{x+4}$$, then x could be

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

$$x \neq 0, -1, -4$$
If x=-2
-1/2 -(-1)=1/2=1/(4-2)=1/2

IMO C

Posted from my mobile device
_________________
"Success is not final; failure is not fatal: It is the courage to continue that counts."

Please provide kudos if you like my post. Kudos encourage active discussions.

My GMAT Resources: -

Efficient Learning
All you need to know about GMAT quant

Tele: +91-11-40396815
Mobile : +91-9910661622
E-mail : kinshook.chaturvedi@gmail.com Re: If 1/x - 1/(x+1) = 1/(x+4), then x could be   [#permalink] 15 Sep 2019, 05:50
Display posts from previous: Sort by

If 1/x - 1/(x+1) = 1/(x+4), then x could be

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne  