Question: The average (arithmetic mean) score of x students on a certain exam is 81. If one additional student takes the exam and scores a 99, the average score will increase to 83. What is the value of x?
- 7
- 8
- 9
- 10
- 11
Correct Answer: B
Solution and Explanation:
Approach Solution 1:
Given:
- The arithmetic mean score of x students on a certain exam is 81.
Condition:
- If one additional student takes the exam and scores a 99, the average score will increase to 83.
Find Out:
- The value of x
The average (arithmetic mean) score of x students on a certain exam is 81
Therefore, there exists one possibility that each of the x students received a score of 81.
Hence, the total sum of all x scores = 81x
If one additional student takes the exam and scores a 99, we then have x + 1 scores
Also, the total sum of all x +1 scores = 81x + 99
Since the new average is 83, therefore, we can write: (81x + 99)/(x + 1) = 83
By multiplying both sides by (x+1), we get: 81x + 99 = 83(x + 1)
Expand: 81x + 99 = 83x + 83
Rearrange: 16 = 2x
Therefore, x = 8
Approach Solution 2:
Given:
- The arithmetic mean score of x students on a certain exam is 81.
Condition:
- If one additional student takes the exam and scores a 99, the average score will increase to 83.
Find Out:
- The value of x.
As per the problem statement, the initial average is 81
The final average is 83.
Hence, the increase in average =83-81
= 2 marks/student.
Now, one additional new student scored 99
We find the marks above average = 99 - 83 = 16.
Hence x or the number of initial students = 16/2 = 8.
Approach Solution 3:
The problem statement states that:
Given:
- The arithmetic mean score of x students on a certain exam is 81.
Condition:
- If one additional student takes the exam and scores a 99, the average score will increase to 83.
Find Out:
- The value of x.
As per the given condition in the question, we can say:
81x + 99 = (x + 1 ) 83
Or, 81x + 99 = 83x + 83
Or, 16 = 2x
Or, x = 8
Hence, the number of initial students = 8.
“The average (arithmetic mean) score of x students on a certain exam is”- is a topic of the GMAT Quantitative reasoning section of the GMAT exam. This topic has been taken from the book “501 GMAT Questions”. The GMAT Problem Solving questions test the capability of the candidate’s skills in calculating numerical problems accurately. GMAT Quant practice papers enable the candidates to practice varieties of questions that will boost their confidence to score better in the exam.
Suggested GMAT Problem Solving Questions
- What is the Largest Five-Digit Number which is Divisible by 17? GMAT Problem Solving
- If x is not equal to zero, and x + 1/x = 3, then what is the value of x^4 + 1/x_4? GMAT Problem Solving
- An Isosceles Right Triangle With a Leg of Length "a" And Perimeter "p" GMAT Problem Solving
- The Light In A Restroom Operates With a 15-Minute Timer GMAT Problem Solving
- Two Pipes Together Can Fill a Tank In 35 Minutes GMAT Problem Solving
- In a Shop, The Marked Price of an Article is Worked Out in Such a Way That it Generates a Profit of 33 1 by 3 GMAT Problem Solving
- If x = 3y = 4z, Which of The Following Must Equal 6x GMAT Problem Solving
- If 3x=2y=5, Then 24xy^2=? GMAT Problem Solving
- The Product Of Two Numbers is 2028 and Their HCF is 13 GMAT Problem Solving
- Two Friends Start Walking Towards Each Other With Speeds in the ratio 3 : 4 GMAT Problem Solving
- The Figure Shown Above Consists of a Shaded 9-Sided Polygon GMAT Problem Solving
- A and B Can Do a Piece Of Work in 10 Days, While B And C Can Do The Same Work in 15 Days And C and A in 25 Days GMAT Problem Solving
- How Many 3-digit Positive Integers With Distinct Digits Are There, Which are not Multiples of 10? GMAT Problem Solving
- If x^3 < 16x Which Of The Following Includes at Least Some of the Possible Solutions for x GMAT Problem Solving
- What Is The Smallest Five Digit Number That Is Divisible by 16, 24, 36 and 54? GMAT Problem Solving
- A list of measurements in increasing order is 4, 5, 6, 8, 10 and x GMAT Problem Solving
- If the population of a town is p in the beginning of any year then it becomes 3+2p GMAT Problem Solving
- The Revenues and Costs, in Thousands of Dollars, for a Small Company in the Year 2007 GMAT Problem Solving
- Which of the following is a perfect square? GMAT Problem Solving
- In the xy-plane, the Vertices of a Triangle have Coordinates (0,0),(3,3), and (7,0) GMAT Problem Solving
- Rahul Can Finish a Job in 30 Days GMAT Problem Solving
- How Many Two-Digit Numbers Are Divisible By Both 5 and 6? GMAT Problem Solving
- If O is the Center Of The Circle, What is The Perimeter Of The Sector GMAT Problem Solving
- The Sum of 5 Numbers in the Geometric Progression is 24 GMAT Problem Solving
- Two Students Appeared At An Examination. One of Them Secured 9 Marks GMAT Problem Solving
- x' is a Positive Integer and x^3 is Divisible by 27 GMAT Problem Solving
- Which of the Following Equation is NOT Equivalent to 25x^2 = y^2 - 4? GMAT Problem Solving
- The Variable x is Inversely Proportional to the Square of the Variable GMAT Problem Solving
- Which of the Following Fractions is Closest to 1/2? GMAT Problem Solving
- In a Certain Game, You Pick a Card From a Standard Deck GMAT Problem Solving
- The Average of 20 Numbers is Zero. Of them, at the Most, How Many May GMAT Problem Solving
- A Can Contains a Mixture of Two Liquids A and B in the Ratio 7:5 GMAT Problem Solving
- A Bag Contains 2 White and 3 Red Balls, And a Bag B Contains 4 White GMAT Problem Solving
- Which of the Following is Equal to x^18 For All Positive Values of x? GMAT Problem Solving
- 16 Ounces of Fresh Orange Juice Contains 216 Calories GMAT Problem Solving
- When 15 is Appended To a List of Integers, The Mean is Increased by 2 GMAT Problem Solving
- An Urn Contains 6 Red, 4 Blue, 2 Green and 3 Yellow marbles GMAT Problem Solving
- The price of raw materials has gone up by 15%, labour cost has also increased GMAT Problem Solving
- In a Class of 100 Students 70 Passed in Physics, 62 Passed in Mathematics GMAT Problem Solving
- If x and y Are Positive Odd Integers, And Both Numbers Have An Odd Number Of Positive Divisors GMAT Problem Solving
- Copper Pipe Costs x Cents Per Foot in 8-Foot Lengths GMAT Problem Solving
- Find The Smallest Positive 4-Digit Number Which, When Increased by 8, is Divisible by 12, 18, 30, and 45 GMAT Problem Solving
- How Much Pure Alcohol Should Be Added To 400 ml of a 15% Solution To Make The Strength Of The Solution 32%? GMAT Problem Solving
- If n = (33)^43 + (43)^33 What is the Unit Digit of n? GMAT Problem Solving
- Two Squares are Chosen at Random on a Chessboard. What is the GMAT Problem Solving
- What is the Remainder When 323232 is divided by 7? GMAT Problem Solving
- What is the Remainder When 43^86 is Divided by 5? GMAT Problem Solving
- 16 Ounces of Birdseed Mix Contains 10% Sesame Seed by Weight GMAT Problem Solving
- Two Trains are Moving in the Opposite Directions on Parallel Tracks at GMAT Problem Solving
- Two stations A and B are 110 km apart on a straight line. One train GMAT Problem Solving
Comments