Question

7. In a set of four integers, the average of the two smallest integers is 102, the average of the
three smallest integers is 103, the average of all four is 104. Which is the greatest of these
integers?
Sol.​

Answer 1

Answer:Let the integers be a,b,c,d

such that a<b<c<d

2

a+b

​  

=102⇒a+b=204

3

a+b+c

​  

=103⇒a+b+c=309

4

a+b+c+d

​  

=104⇒a+b+c+d=416

                                     ⇒d=416−309=107

Step-by-step explanation:

Answer 2

S O L U T I O N :

• Let , All four given set of integers be a , b , c , d.

• Here, a < b < c < d respectively.

• Avg of given observations = ( sum of observations ) / given no. of observations.

According to question :

• The average of the two smallest integers is 102.

$\implies \: \dfrac{a + b}{2} = 102$

$\implies \: a + b \: = 102 \times 2$

$\implies \: a + b = 204$

So , a + b = 204 , let this be eq (1)

• The average of the three smallest integers is 103.

$\implies \: \dfrac{a + b + c}{3} = 103$

$\implies \: a + b + c = 309$

So, a + b + c = 309 , let this be eq(2)

• The average of all four is 104.

$\implies \: \dfrac{a + b + c + d}{4} = 104$

$\implies \: a + b + c + d \: = 416$

so , a + b + c + d = 416 , let it be eq(3)

• put eq(2) in eq(3)

$\implies \: (309) + d = 416$

$\implies \: d \: = 416 - 309$

$\implies \: d \: = 107$

• We're asked to find the greatest integer of 4 , we know that d is the greatest of all four , so d = 107.