CAT 2024 - Slot 1 Quant Question 18
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CAT 2024 Slot 1 - Quant
Let us assume the four numbers to be a, b, c and d in ascending order.
Average of first two numbers is 1 more than the first number
(a + b)/2 = a + 1
b – a = 2
b = a + 2
Average of first three numbers is 2 more than average of first two numbers
(a + b + c)/3 = (a + b)/2 + 2
2c = a + b + 12
Substituting the value for b
2c = a + a + 2 + 12
2c = 2a + 14
c = a + 7
Average of first four numbers is 3 more than average of first three numbers.
(a + b + c + d)/4 = (a + b + c)/3 + 3
3d = a + b + c + 36
Substituting the value of b and c
3d = a + a + 2 + a + 7 + 36
3d = 3a + 45
d = a + 15
d is the largest and a is the smallest and we know that d = a + 15
Hence the difference between the smallest and the largest values is 15.