Question: The sequence \(a_1,a_2,...,a_n,...\)is such that \(a_n=2a_{n-1}-x\)for all positive integers \(n\geq2\)and for certain number x. If \(a_5=99,a_3=27\), what is the value of x?

1. 3
2. 9
3. 18
4. 36
5. 45

Answer:
Solution with Explanation:
Approach Solution (1):

We know that:

\(a_5=2*a_4-x=99\)
\(a_4=2*a_3-x=2*27-x\)

Therefore,

\(a_5=2*(54-x)-x=99\)
\(108-3*x=99\)

Therefore, x = 3

Correct Option: A

Approach Solution (2):

Given:

\(a_n=2a_{n-1}-x\)
\(a_5=99\)
\(a_3=27\)
\(a_5=2a_4-x=2(a_3-x)-x=4a_3-3x=99\)
\(4(27)-3x=993x=108-99=9\)
\(x=3\)

Correct Option: A

Approach Solution (3):

Plug the known values \(a_5=99,a_3=27\)into the formula:

\(a_5=2(a_4)-x\)
\(99=2(a_4)-x\)
\(a_4=2(a_3)-x\)
\(a_4=2(27)-x=54-x\)
Substitute 54 – x for \(a_4\) in the top equation:
99 = 2(54 – x) – x
99 = 108 – 3x
3x = 9
x = 3
Correct Option: A

“The sequence \(a_1,a_2,...,a_n,...\)is such that \(a_n=2a_{n-1}-x\) for all positive integers \(n\geq2\) and for certain number x. If \(a_5=99,a_3=27\), what is the value of x?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Official Guide Quantitative Review”. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. The GMAT Quant topic in the problem-solving part requires calculative mathematical problems that should be solved with proper mathematical knowledge.

Suggested GMAT Problem Solving Samples

• Find The Altitude Of An Equilateral Triangle Whose Side is 20 GMAT Problem Solving
• Which of the following is the value of √3√0.000064? GMAT Problem Solving
• Two Dice are Thrown Simultaneously. What is the Probability of Getting Two Numbers Whose Product is Even? GMAT Problem Solving
• The Smallest 3-Digit Positive Integer Obtained By Adding Two Positive Two-Digit Numbers GMAT Problem Solving
• Train A Leaves New York at 9am Eastern Time on Monday, Headed for Los Angeles at a Constant Rate GMAT Problem Solving
• An Express Train Traveled At An Average Speed of 100 Kilometers Per Hour GMAT Problem Solving
• If m Lies Between The Integers p and s On the Number Line Shown GMAT Problem Solving
• A Cube Of Side 7 cm Is Coloured On Pair of Opposite Faces By Red, Green and Yellow Shades GMAT Problem Solving
• If x^2 − 5x − 6 = 0, which of the following could be x ? GMAT Problem Solving
• How Many Numbers Between 1 and 1000, Inclusive Have an Odd Number of Factors? GMAT Problem Solving
• GMAT Problem Solving- Given f(x) = x/(x + 1), For What Value k Does f(f(k)) = 2/3 ?
• Which Among the Following is the Smallest 7-digit Number that is Exactly Divisible by 43? GMAT Problem Solving
• During a Trip, Francine Traveled x Percent of the Total Distance at an Average Speed of 40 Miles GMAT Problem Solving
• Which of the Following Expressions CANNOT have a Negative Value? GMAT Problem Solving
• Which of the following is greatest? GMAT Problem Solving
• The Cost Price of 20 Articles is The Same as The Selling Price of x Articles GMAT Problem Solving
• In The Figure Shown, If The Area of The Shaded Region is 3 Times The Area of The Smaller Circular Region GMAT Problem Solving
• A Regular Hexagon has a Perimeter of 30 units GMAT Problem Solving
• All the Numbers 2, 3, 4, 5, 6, 7 are Assigned to the Six Faces of a Cube, One Number to Each Face GMAT Problem Solving
• If it is true that x > -2 and x < 7, which of the following must be true? GMAT Problem Solving
• In a Drawer, There are 4 White Socks, 3 Blue Socks, and 5 Grey Socks GMAT Problem Solving
• There are 100 Apples in a Bag of which 98% are Green and Rest are Red GMAT Problem Solving
• A palindrome is a number that reads the same forward and backward GMAT Problem Solving
• Three Cars Leave From A To B In Equal Time Intervals GMAT Problem Solving
• An Inlet Pipe can Fill in an Empty Cistern in 30 minutes GMAT Problem Solving
• A Zookeeper Counted the Heads of the Animals in a Zoo and Found it to be 80 GMAT Problem Solving
• A Shop Stores x kg of Rice. The First Customer Buys half this Amount Plus half a kg of Rice GMAT Problem Solving
• In a Class of 120 Students Numbered 1 to 120, All Even Numbered Students Opt for Physics GMAT Problem Solving
• Machine A Produces bolts at a Uniform Rate of 120 Every 40 seconds GMAT Problem Solving
• Out of 7 Consonants and 4 Vowels, How Many Words of 3 Consonants and 2 Vowels Can be Formed? GMAT Problem Solving
• 4 Bells Toll Together at 9:00 A.M. They Toll After 7, 8, 11 and 12 Seconds GMAT Problem Solving
• 12 Marbles are Selected at Random from a Large Collection of White, Red, Green and Yellow Marbles GMAT Problem Solving
• Find the greatest number that will divide 43, 91 and 183 GMAT Problem Solving
• Of the 150 Houses in a Certain Development GMAT Problem Solving
• A man can hit a target once in 4 shots. If he fires 4 shots in succession GMAT Problem Solving
• If 75 Percent of a Class Answered the First Question on a Certain Test Correctly GMAT Problem Solving
• A Clock Strikes 4 taking 9 seconds. GMAT Problem Solving
• What is the Largest Power of 3 Contained in 200! GMAT Problem Solving
• Find The Value Of x GMAT Problem Solving
• GMAT Problem Solving - Which of the following expressions has the greatest values?
• GMAT Problem Solving – If @ x=x^2/2x^2-2 , What is the Units Digit of @ (@4)?
• GMAT Problem Solving – What is the product of all possible solutions of the equation |x+2|- 5|x+2| = -6?
• GMAT Problem Solving – Metropolis Corporation has 4 Shareholders
• GMAT Problem Solving – What is the number of integers from 1 to 1000, inclusive that are not divisible by 11 or by 35?
• GMAT Problem Solving – If m is Three Times n, and if 2n + 3 is 20% of 25, What is the value of m?
• GMAT Problem Solving – If Ben Were to Lose the Championship, Mike would be the Winner
• GMAT Problem Solving – A Train Travelling at a Certain Constant Speed takes 30 seconds
• GMAT Problem Solving – A conference room is equipped with a total of 45 metal or wooden chairs.
• GMAT Problem Solving – A welder received an order to make a 1 million litre cube-shaped tank.
• GMAT Problem Solving – After 6 games, Team B had an average of 61.5 points per game