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Arun Sharma Test: Averages- 2 - CAT MCQ


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15 Questions MCQ Test Quantitative Aptitude (Quant) - Arun Sharma Test: Averages- 2

Arun Sharma Test: Averages- 2 for CAT 2024 is part of Quantitative Aptitude (Quant) preparation. The Arun Sharma Test: Averages- 2 questions and answers have been prepared according to the CAT exam syllabus.The Arun Sharma Test: Averages- 2 MCQs are made for CAT 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Arun Sharma Test: Averages- 2 below.
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Arun Sharma Test: Averages- 2 - Question 1

The average weight of the books carried by Kuku to school is 1.5 kg and 2.5 kg is the average weight of the exercise books. If Kuku is carrying only text books and exercise books in the ratio of 3:4, what is the total weight of his school bag? (Ignore any other weights such as that of school bag, stationary etc.)

Detailed Solution for Arun Sharma Test: Averages- 2 - Question 1

No data regarding the numbers of books is given, hence we cannot determine the weight of school bag. Hence, (d)

Arun Sharma Test: Averages- 2 - Question 2

The average of eight numbers is 25, that of the first two is 20 and of the next three is 26. The sixth number is less than the seventh by 4, and less than the eighth by 6. The last number is

Detailed Solution for Arun Sharma Test: Averages- 2 - Question 2

Given Data:

  • The average of 8 numbers is 25:
    • Sum of all 8 numbers = 8 × 25 = 200
  • The average of the first two numbers is 20:
    • Sum of the first two numbers = 2 × 20 = 40
  • The average of the next three numbers is 26:
    • Sum of the next three numbers = 3 × 26 = 78
  • The sixth number (x) is:
    • 4 less than the seventh (y): y = x + 4
    • 6 less than the eighth (z): z = x + 6

Step-by-Step Solution:

Step 1: Sum of the last three numbers

From the total sum:

Sum of the last three numbers = 200 - (Sum of the first five numbers)

Sum of the last three numbers = 200 - (40 + 78) = 200 - 118 = 82

Step 2: Equation for the last three numbers

The last three numbers are xy, and z. Using their relationships:

x + y + z = 82

Substitute y = x + 4 and z = x + 6 into the equation:

x + (x + 4) + (x + 6) = 82

3x + 10 = 82

3x = 72 ⇒ x = 24

Step 3: Find y and z

Using x = 24:

  • y = x + 4 = 24 + 4 = 28
  • z = x + 6 = 24 + 6 = 30

Verification:

The sum of the last three numbers is: 24 + 28 + 30 = 82

This matches the required sum, confirming our calculations.

Final Answer:

The last number is 30.

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Arun Sharma Test: Averages- 2 - Question 3

Three years ago , the average age of a family of 5 members was 17 years. Inspite of the birth of a child in the family, the present average age of the family remains the same. The present age of the child is

Detailed Solution for Arun Sharma Test: Averages- 2 - Question 3

Total age of family 3 years ago = 17x5 = 85 years

Total age of family now = 17x 6 = 102 years

Total age of family excluding the child now = (85 + 15) = 100 years

Age of child = 2 years

Arun Sharma Test: Averages- 2 - Question 4

The average marks of a class of 48 students is 35. Of them, two score zero, of the rest, the first 30 scored an average of 40, the next fourteen scored an average of 20. If the remaining two scored equal marks, what are their individual marks?

Detailed Solution for Arun Sharma Test: Averages- 2 - Question 4

Arun Sharma Test: Averages- 2 - Question 5

The average mark of a class of n students is 64. When eight new students with an average mark of 73 join the class, the new average of the entire class is a whole number. Find the number of students now in the class, given that n lies between 25 and 60.

Detailed Solution for Arun Sharma Test: Averages- 2 - Question 5

Let ‘x’ be the increase in the average 

For ‘x’ to be a whole number 72 (= 9 × 8) should be divisible by (n + 8) 
From the choices it can be said that 36 and 72 are two such factors. But 72 does not lie within the range. 
∴ number of students in class are 36.

Arun Sharma Test: Averages- 2 - Question 6

The average of 10 two-digit positive integers is Z. However, one number AB is taken as BA, then the average increases to Z + 2.7. What is the value of |B - A|?

Detailed Solution for Arun Sharma Test: Averages- 2 - Question 6

Arun Sharma Test: Averages- 2 - Question 7

The average rainfall for the first 3 days out of five days was recorded to be 0.45 inches. The rainfall on the last two days was in the ratio 2:3. The average of five days was 0.40 inches. What was the rainfall on the last day?

Detailed Solution for Arun Sharma Test: Averages- 2 - Question 7

Arun Sharma Test: Averages- 2 - Question 8

The average price of a share is the average of 5 readings taken at regular intervals in a day. The index price is taken by a weighted arithmetic average price of a class A and class B stock. The respective weights are 1.1 and 0.9 for the two kinds of stocks. If the five readings of a class A stock were 19, 26, 31, 35, 39 and for a class B stock the readings were 7, 8, 17, 20, 23 then what was the index price that day?

Detailed Solution for Arun Sharma Test: Averages- 2 - Question 8

Arun Sharma Test: Averages- 2 - Question 9

The average age of 24 students and the class teacher is 16 years. If the age of the class teacher is excluded the average reduces by 1 year. What is the age of the class teacher?

Detailed Solution for Arun Sharma Test: Averages- 2 - Question 9

Arun Sharma Test: Averages- 2 - Question 10

There are 20 students in Mr Rahul Ghosh’s class. He conducts an examination out of 100 and then arranged the marks in an ascending order. He found Chandan, the topper of the class, had slipped to the tenth position. When he was adding the scores of the last 11 students the average was 64 and that of the top 10 was 67. If the average marks obtained by all the students of his class was 65, how many marks did Chandan score?

Detailed Solution for Arun Sharma Test: Averages- 2 - Question 10

Score of Chandan = 64 x 11 + 10 x 67 - 20 x 65 = 704 + 670 - 1300 
= 1374 -1300 = 74

Arun Sharma Test: Averages- 2 - Question 11

The average marks of a student in 10 papers are 80. If the highest and the lowest scores are not considered, the average is 81. If his highest score is 92, find the lowest

Detailed Solution for Arun Sharma Test: Averages- 2 - Question 11

Total marks = 80 x 10 = 800
Total marks except highest and lowest marks = 81 x 8 = 648
So Summation of highest marks and lowest marks will be = 800 - 648 = 152
When highest marks is 92, lowest marks will be = 152-92 = 60

Arun Sharma Test: Averages- 2 - Question 12

Prof. Suman takes a number of quizzes for a course. All the quizzes are out of 100. A studentcan get an A grade in the course if the average of her scores is more than or equal to 90.Grade B isawarded to a student if the average of her scores is between 87 and 89 (both included). If the average isbelow 87, the student gets a C grade. Ramesh is preparing for the last quiz and he realizes that he willscore a minimum of 97 to get an A grade. After the quiz, he realizes that he will score 70, and he will justmanage a B. How many quizzes did Prof. Suman take?

Detailed Solution for Arun Sharma Test: Averages- 2 - Question 12

Grade A greater than equal to 90 and Grade B = 87 to 89

If Ramesh scores 70 instead of 97, => Change of marks = 97 - 70 = 27

It creates a change from grade A to B, this means an overall change in average by

= Minimum marks for grade A - Minimum marks for Grade B = 90 - 87 = 3
Number of subjects 27/3 = 9

Arun Sharma Test: Averages- 2 - Question 13

The average of 7 consecutive numbers is P. If the next three numbers are also added, the average shall

Detailed Solution for Arun Sharma Test: Averages- 2 - Question 13

Let the 7 consecutive numbers be a-3, a-2, a-1, a, a+1, a+2 and a+3.
The sum of the numbers = 7a and the average of these numbers = a
If next 3 numbers a+4, 4+5 and a+6 are also added then the average of these 10  numbers =
7a+a+ 4 + a+ 5 + a+ 6 / 10 = a+ 1.5
Thus, the average increases by 1.5

Arun Sharma Test: Averages- 2 - Question 14

In an apartment complex, the number of people aged 51 years and above is 30 and there are at most 39 people whose ages are below 51 years. The average age of all the people in the apartment complex is 38 years. What is the largest possible average age, in years, of the people whose ages are below 51 years?

Detailed Solution for Arun Sharma Test: Averages- 2 - Question 14

The possible average age of people whose ages are below 51 years will be maximum if the average age of the number of people aged 51 years and above is minimum. Hence, we can say that that there are 30 people having same age 51 years.
Let 'x' be the maximum average age of people whose ages are below 51.
Then we can say that,

Hence, we can say that option D is the correct answer.

Arun Sharma Test: Averages- 2 - Question 15

Ramesh and Gautam are among 22 students who write an examination. Ramesh scores 82.5. The average score of the 21 students other than Gautam is 62. The average score of all the 22 students is one more than the average score of the 21 students other than Ramesh. The score of Gautam is

Detailed Solution for Arun Sharma Test: Averages- 2 - Question 15

Assume the average of 21 students other than Ramesh = a
Sum of the scores of 21 students other than Ramesh = 21 a
Hence the average of 22 students = a+1
Sum of the scores of all 22 students = 22(a+1)
The score of Ramesh = Sum of scores of all 22 students - Sum of the scores of 21 students other than Ramesh = 22(a+1)-21a=a+22 = 82.5 (Given)
=> a = 60.5
Hence, sum of the scores of all 22 students = 22(a+1) = 22*61.5 = 1353
Now the sum of the scores of students other than Gautam = 21 *62 = 1302
Hence the score of Gautam = 1353-1302=51

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