CAT 2024 Slot 3 QA Question 19: The average of three distinct real numbers is $28$. If the smallest number is increased by $7$ and the largest number is reduced by $10$, the order of the numbers remains unchanged, and the new arithm

Question

The average of three distinct real numbers is $28$. If the smallest number is increased by $7$ and the largest number is reduced by $10$, the order of the numbers remains unchanged, and the new arithm

Accepted Answer

Let the three distinct real numbers be $a

$a + b + c = 3	imes28 = 84$

After the changes, the new numbers are $a + 7$, $b$, and $c - 10$. Their sum is:

$(a + 7) + b + (c - 10) = a + b + c - 3 = 81$
$	ext{New mean} = \dfrac{81}{3} = 27$

The new mean is $2$ more than the middle number.

$27 = b +