Question: If 1/x − 1/x+1 = 1/x+4, then x could be

1. 0
2. -1
3. -2
4. -3
5. -4

Correct Answer: (C)
Solution and Explanation:
Approach Solution 1:

The problem statement indicates that 1/x − 1/x+1 = 1/x+4. The question asked here is to find out the value of x.
By simplifying the given equation, we get:
=> 1/x − 1/(x+1) = 1/(x+4)
=> {(x+1)−x} / {x(x+1)} = 1/(x+4)
=> 1/{x(x+1)} = 1/(x+4)

By cross multiplying, we get,
x + 4 = x(x+1)
=> x^2 - 4 = 0
=> (x-2)(x+2) = 0
Therefore, x = 2 or -2

Hence, as per the given answer choices, the value of x would be -2.

Approach Solution 2:

The problem statement implies that

Given:

• 1/x − 1/x+1 = 1/x+4.

Asked:

• To find out the value of x

This question can be solved in the quickest and easiest approach as follows:
For this, we need to verify each of the options.
It is evident that the value of x cannot be 0, -1 or -4, since one of the terms will have then 0 in the denominator.
A fraction cannot hold 0 in the denominator, therefore, x could be either -2 or -3.
By putting x = -2, we get:
1/(−2) − 1/(−2+1) = 1/(−2+4)
1 - (1/2) = 1/2
1/2 = 1/2

Therefore, x = -2 satisfies.

Approach Solution 3:

The problem statement implies that

Given:

• 1/x − 1/x+1 = 1/x+4.

Find out:

• The value of x

As we know, multiplying both sides by the least common multiple (LCM) of all the denominators will help to eliminate the fractions.
The LCM of x, x+1 and x+4 is (x)(x+1)(x+4)

The equation given in the question is: 1/x − 1/x+1 = 1/x+4

By multiplying both sides by (x)(x+1)(x+4) we get:
=> (x)(x+1)(x+4)[1/x − 1/x+1] = (x)(x+1)(x+4)[1/x+4]

By simplifying, we get:
=>(x+1)(x+4)−(x)(x+4) = (x)(x+1)

By expanding we get:
=>[x^2 + 5x + 4]−[x^2+4x] = x^2 +x

By simplifying we get:
=>x+4= x^2+x

By subtracting x from both sides, we get:
=>4=x^2
Therefore, x=2 or x=−2.

Hence, as per the given answer choices, the value of x would be -2.

“If 1/x − 1/x+1 = 1/x+4, then x could be”- is a topic of the GMAT Quantitative reasoning section of the GMAT exam. This question has been taken from GMAT Official Guide 2022. GMAT Problem Solving questions examine candidates’ numerical knowledge to calculate different quantitative problems. GMAT Quant practice papers help the candidates to analyse various kinds of questions to boost their mathematical understanding.

Suggested GMAT Problem Solving Questions

• A Dealer Offers a Cash Discount of 20%. Further, a Customer Bargains GMAT Problem Solving
• There are Two Vessels A and B. Vessel A is Containing 40 Litres of GMAT Problem Solving
• At A Certain Fruit Stand, The Price Of Each Apple Is 40 Cents GMAT Problem Solving
• The Coordinates Of Vertices P And Q Of An Equilateral Triangle PQR Are GMAT Problem Solving
• A Certain Roller Coaster has 3 Cars, and A Passenger is Equally Likely GMAT Problem Solving
• A Manufacturer Produces a Certain Men's Athletic Shoe in GMAT Problem Solving
• In The Figure Shown Below, The Area of Square Region ACEG is 729 GMAT Problem Solving
• How Many Dimes are There in 4x - 1 Cents? (1 dime = 10 cents) GMAT Problem Solving
• In How Many Ways The Letter Of The Word "Family" Can Be When GMAT Problem Solving
• A Fair Coin Is Tossed 4 Times. What Is The Probability Of Getting At GMAT Problem Solving
• In A Sequence 1, 2, 4, 8, 16, 32, ... Each Term After The First Is Twice GMAT Problem Solving
• What Is The Sum Of Odd Integers From 35 To 85, Inclusive? GMAT Problem Solving
• If x = -3, What Is The Value Of -3x^2? GMAT Problem Solving
• If 2p + 1/p = 4, Then what is the Value of p^3 + 1/8p^3 ? GMAT Problem Solving
• There are 12 Pipes that are Connected to a Tank. Some of them are fill GMAT Problem Solving
• A wire is cut into three equal parts. The resulting segments are then cut GMAT Problem Solving
• There Were R Red Balls And Y Yellow Balls In A Bag. Three Red Balls GMAT Problem Solving
• With An Average Speed Of 40 Km/H, A Train Reaches Its Destination On GMAT Problem Solving
• A Photographer Will Arrange 6 People Of 6 Different Heights GMAT Problem Solving
• What Is The Radius Of The Incircle Of The Triangle Whose Sides Measure GMAT Problem Solving
• The Value Of (2^(-14) + 2^(-15) + 2^(-16) + 2^(-17))/5 Is GMAT Problem Solving
• Points A And B Are 120 Km Apart. A Motorcyclist Starts From GMAT Problem Solving
• A student took five papers in an examination, where the full marks GMAT Problem Solving
• In how many ways can letters the word ATTITUDE be rearranged such that GMAT Problem Solving
• A merchant mixes three varieties of rice costing $20/kg, $24/kg GMAT Problem Solving
• ABC is an equilateral triangle, and point D is the midpoint of side BC GMAT Problem Solving
• A Batsman Makes a Score of 87 Runs in the 17th Match and Thus Increases GMAT Problem Solving
• If M= √4+3√4+4√4, Then the Value of M is GMAT Problem Solving
• An Octagon Is Inscribed In A Circle As Shown Above. What Of The Area GMAT Problem Solving
• In a Company of Only 20 Employees, 10 Employees make $80,000/yr GMAT Problem Solving
• A bag contains blue and red balls only GMAT Problem Solving
• (4.8*10^9)^(1/2) is closest in value to GMAT Problem Solving
• What Is The Units Digit Of 2222^333 ∗ 3333^222? GMAT Problem Solving
• What Is The Tens Digit Of 6^17? GMAT Problem Solving
• If m=−2, What Is −m^(−m)? GMAT Problem Solving
• An Automated Manufacturing Plant Uses Robots To Manufacture Products GMAT Problem Solving
• The Surface Distance Between 2 Points on the Surface of a Cube is the GMAT Problem Solving
• The Average Monthly Expenditure of a Family for the First Four Months GMAT Problem Solving
• When a Certain Perfect Square is Increased by 148, the Result is GMAT Problem Solving
• If p#q Denotes the Least Common Multiple of p and q, Then ((12#16) GMAT Problem Solving
• In How Many Ways Can One Divide 12 Different Chocolate Bars Into Four GMAT Problem Solving
• Employee X's Annual Salary Is $12,000 More Than Half Of Employee Y's GMAT Problem Solving
• What is the Area of Quadrilateral ABCD Shown? GMAT Problem Solving
• Eleven Chairs are Numbered 1 Through 11. Four Girls and Seven Boys GMAT Problem Solving
• Two Friends, Tanaya and Stephen were Standing Together GMAT Problem Solving
• If x is a number such that x^2 - 3x + 2 = 0 and x^2 - x - 2 = 0 GMAT Problem Solving
• Barney is forming two large cubes, A and B, with small identical cubes GMAT Problem Solving
• It Takes Printer A 4 Minute More than Printer B to Print 40 GMAT Problem Solving
• A synchronized diving competition will feature 25 synchronized GMAT Problem Solving
• The Earth Travels Around The Sun At A Speed Of Approximately 18.5 miles GMAT Problem Solving