CAT 2024 Slot 1 QA Question 12: There are four numbers such that average of first two numbers is 1 more than the first number, average of first three numbers is 2 more than average of first two numbers, and average of first four num

Question

There are four numbers such that average of first two numbers is 1 more than the first number, average of first three numbers is 2 more than average of first two numbers, and average of first four num

Accepted Answer

Let the four numbers be $a$, $b$, $c$ and $d$.
$\dfrac{a+b}{2} = a + 1$
$\Rightarrow b = a + 2$
$\dfrac{a+b+c}{3} = (a+1) + 2 = a + 3$
$\Rightarrow a + (a+2) + c = 3a + 9$
$\Rightarrow c = a + 7$
$\dfrac{a+b+c+d}{4} = (a+3) + 3 = a + 6$
$\Rightarrow a + (a+2) + (a+7) + d = 4a + 24$
$\Rightarrow d =