Arun Sharma Test: Averages- 2 - CAT MCQ

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

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 x, y, 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.

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

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.

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

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

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

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

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.

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